metadata: authors: 0: author: Heyns,Andries Michiel
1: author: Banick,Robert Steven
2: author: Regmi,Suraj
count: Nepal
docna: 0: docna: Roads Development Optimization for
            All-Season Service Accessibility Improvement in Rural Nepal
            Using a Novel Cost-Time Model and Evolutionary Algorithm
docty: Policy Research Working Paper
subtopic: Transport Services,Rural Roads & Transport,Health Care Services Industry,Inequality,ICT Policy and Strategies
teratopic: Transport,Rural Development,Industry,Poverty Reduction,Information and Communication Technologies
abstracts: cdata!: Existing methods of prioritizing rural
            roads for construction in hilly and mountainous settings
            require expensive data collection or major simplifications
            of ground conditions. Traditional social surplus
            based-methods favor economic and political decision criteria
            over social criteria, despite evidence of the latter's
            importance, and struggle to scale beyond major roads to
            feeder roads, forcing local governments with limited
            capacity to adopt ad-hoc alternative criteria. Using roads
            proposed for construction in Nepal's remote Karnali
            province, this paper develops a scalable method to
            prioritize these roads for inclusion in construction plans
            with the aim of optimizing potential accessibility
            improvements to specified services in dry and monsoon
            seasons -- within Karnali's infrastructure budget
            constraints. Road-specific improvements in accessibility to
            services are measured by estimating accessibility changes
            resulting from each proposed road within a multimodal
            accessibility model. In this paper, walking across
            Karnali's mountainous, high-elevation terrain is
            incorporated as a primary modality -- a rarity in related
            accessibility literature. These improvements are implemented
            within heuristic and integer-linear programming optimization
            models. Optimization-determined solutions were calculated
            within a day, and substantially outperformed the actual
            roads selected by Karnali's provincial government in
            terms of accessibility, efficiency, and political economy.
geo_reg_key: 517198,517191,517212
repnme: repnme: Roads Development Optimization for
            All-Season Service Accessibility Improvement in Rural Nepal
            Using a Novel Cost-Time Model and Evolutionary Algorithm
display_title: Roads Development Optimization for
            All-Season Service Accessibility Improvement in Rural Nepal
            Using a Novel Cost-Time Model and Evolutionary Algorithm
listing_relative_url: /research/2021/01/32778515/roads-development-optimization-all-season-service-accessibility-improvement-rural-nepal-using-novel-cost-time-model-evolutionary-algorithm
topicv3: Transport m1326661 135,Poverty m1326687 695,Rural Roads(RR) m1327606 786,Monsoon m1503657 3193,Health m1504661 3480
publishtoextweb_dt: 2021-01-26T00:00:00Z
historic_topic: Transport,Rural Development,Industry,Poverty Reduction,Information and Communication Technologies
origu: EFI-SAR-POV-Poverty and Equity (ESAPV)
no_of_pages: 52
author_keys: 0: author_key: 1744223
1: author_key: 1411341
2: author_key: 1666745
model_extractions: Policy Research Working Paper 9526 Roads Development Optimization for All-Season Service Accessibility Improvement in Rural Nepal Using a Novel Cost-Time Model and Evolutionary Algorithm _Andries Heyns Robert Banick Suraj Regmi_ Poverty and Equity Global Practice January 2021
Policy Research Working Paper 9526

# **Abstract**

Existing methods of prioritizing rural roads for construction in hilly and mountainous settings require expensive data collection or major simplifications of ground conditions. Traditional social surplus based-methods favor economic and political decision criteria over social criteria, despite evidence of the latter’s importance, and struggle to scale beyond major roads to feeder roads, forcing local governments with limited capacity to adopt ad-hoc alternative criteria. Using roads proposed for construction in Nepal’s remote Karnali province, this paper develops a scalable method to prioritize these roads for inclusion in construction plans with the aim of optimizing potential accessibility improvements to specified services in dry and monsoon seasons—within Karnali’s infrastructure budget constraints. Road-specific improvements in accessibility to services are measured by estimating accessibility changes resulting from each proposed road within a multimodal accessibility model. In this paper, walking across Karnali’s mountainous, high-elevation terrain is incorporated as a primary modality—a rarity in related accessibility literature. These improvements are implemented within heuristic and integer-linear programming optimization models. Optimization-determined solutions were calculated within a day, and substantially outperformed the actual roads selected by Karnali’s provincial government in terms of accessibility, efficiency, and political economy.

This paper is a product of the Poverty and Equity Global Practice. It is part of a larger effort by the World Bank to provide open access to its research and make a contribution to development policy discussions around the world. Policy Research Working Papers are also posted on the Web at http://www.worldbank.org/prwp. The authors may be contacted at rbanick@worldbank.org, sregmi@worldbank.org, and andriesheyns@gmail.com.

_The Policy Research Working Paper Series disseminates the findings of work in progress to encourage the exchange of ideas about development issues. An objective of the series is to get the findings out quickly, even if the presentations are less than fully polished. The papers carry the names of the authors and should be cited accordingly. The findings, interpretations, and conclusions expressed in this paper are entirely those of the authors. They do not necessarily represent the views of the International Bank for Reconstruction and Development/World Bank and its affiliated organizations, or those of the Executive Directors of the World Bank or the governments they represent._ Produced by the Research Support Team
# Roads Development Optimization for All-Season Service Accessibility Improvement in Rural Nepal Using a Novel Cost-Time Model and Evolutionary Algorithm

Andries Heyns<sup>a,b,∗</sup> , Robert Banick<sup>c</sup> , Suraj Regmi<sup>c</sup>

> aHumanitarian Logistics and Supply Chain Research Institute, Hanken School of Economics, Helsinki, Finland

> bLaboratory for Location Science, University of Alabama, Tuscaloosa, AL, USA

> cWorld Bank, Poverty and Equity Global Practice

## 1. Background

Due to Nepal’s lack of infrastructure and accessibility challenges brought upon by severe terrain and isolated rural populations, roadworks construction is an important element of development plans made by the Nepali government. Improved transportation links are seen as key to reducing food insecurity and unlocking the economic potential of rural areas (Thapa and Shively, 2017). As a result, Nepal’s total road length has proliferated from a base of 2,700 km in the 1970s to over 80,000km in 2015; over 7,500km of new roads were built in 2017 and 2018 alone (World Bank, 2017; Ministry of Finance, 2015). Further propelling this spree are local political economies wherein every incentive aligns towards more road building: constituents routinely cite roads as the highest priority in meetings or surveys (Sapkota, 2018; World Bank, 2016).

A significant portion of recent road construction, particularly at the local level, is characterized by a lack of policy coordination, little to no study of anticipated benefits, haphazard construction standards, and disregard for environmental safeguards (World Bank, 2018). Accessibility improvements are unstructured and fragmented since roads are often built based on political expediency, without reference to studies or master plans (Coburn, 2020; World Bank, 2018). Furthermore, the government’s capacity is so constrained that it usually only spends 70%-80% of its capital budget and the average lifespan of roadworks projects is 12 years (World Bank, 2017). Besides perpetuating an infrastructure gap, these delays degrade the accuracy and resulting informational value of standard measures of project worth – e.g. Net Present Value (NPV) (Belli et al., 2001) or Adjusted Present Value (APV) (Myers, 1974) – and hinder the synchronization of infrastructure investments with other development activities. This is unfortunate, given that Nepal’s scarce resources and harsh terrain merit meticulous, targeted approaches to maximize gains. Mechanisms for integrated planning at the provincial and municipal levels are under development but their adoption is inconsistent and the methods are relatively basic (Rural Access Programme (RAP3), 2019) when compared to established ones previously implemented by the national government in collaboration with donors (World Bank, 2019).

Nepal’s northwestern Karnali province (also known as Province 6) exhibits extreme levels of inaccessibility even by Nepal’s standards. With a predominantly rural population, access to critical services is often measured in hours, walking is a primary transport modality, and it contains the only two districts (of 77) whose headquarters are not connected by vehicular roads of any sort, Humla and Dolpa (Devkota et al., 2012). An illustration of the magnitude of Karnali’s accessibility challenges is provided in Figure 1, in which the provincial population share with long average travel times to financial institutions is markedly higher in Karnali than all other provinces (Banick and Kawasoe, 2019).

Like much of Nepal, damages from rains and landslides further constrain access to services during Nepal’s June-September monsoon season, when heavy rains intensely damage almost all of Karnali’s poorly maintained roads (Huber, 2015). In Figure 2, examples of typical monsoon road conditions in Karnali are provided, showing their vulnerability to bad weather. Significant reductions in travel speeds (40%-80%) for affected road segments are common during this season, particularly for poorly engineered roads with inadequate drainage, and/or poor surfaces (Pantha et al., 2010). Since terrain and available budget effectively prohibit redundancy in roads, damage to a single road can severely impact entire regional populations.

> ∗Corresponding author, contactable at andries.heyns@hanken.fi
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Because Karnali’s severe terrain impedes accessibility, many remote areas are poorly covered by existing roads and services (see Figure 3(a)), while branch roads usually only reach small populations and are costlier to construct in remote, mountainous areas in its sparsely populated north and northwest (such as the Dolpo region of Karnali in Figure 3(b)). Quantifying this remoteness has always challenged analysts; linear distances and routes are inaccurate and misleading in a mountainous environment with substantial ups, downs, and detours around impassable features.

Karnali’s Multidimensional Poverty Index (MPI) headcount ratio is the worst of any province in Nepal and development is a policy imperative (National Planning Commission and Central Bureau of Statistics, 2020).<sup>1</sup> To deliver rapid economic growth and alleviate poverty government officials have expressed interest in adopting more data driven approaches to planning development projects – especially road building projects, given the aforementioned infrastructure gap and high citizen demand. To support their efforts we investigated a more data driven approach for prioritizing rural roads construction and strategically aligning it with other key components of development. This paper describes that approach, which accommodates the basic realities of budget, data availability, and institutional capacity in Nepal. The novel contributions resulting from the work produced in this paper are primarily a) a workflow to generate and compare multi-modal accessibility models for planned infrastructure in rural, mountainous contexts, and b) an optimization approach that takes the resulting accessibility data as inputs and returns numerous possible roads construction alternatives with optimal characteristics across a budget range, as opposed to traditional optimization methods which typically return a single solution with minimal comparative insight. We present the work as a complement or easily scalable alternative to traditional roads investment decision tools in rural, mountainous settings where data collection may be prohibitively costly.

By applying our methods, we are able to determine numerous candidate roads development plans within a large budget range, selected from 92 candidate roads for inclusion in Karnali’s 5-year Provincial Transport Master Plan, a final draft of which was shared by Nepal’s Rural Access Programme 3 (RAP3). When compared to the actual roads selected by Karnali’s government, our solutions outperformed their plan by 1.5 to 3 times when evaluated with respect to accessibility improvements to health care, financial services, and government/market centers at equivalent cost levels, or yielded 1 to 2 times the improvements at half the cost.

The rest of this paper is structured as follows. In Section 2 we present an overview of relevant literature from several disciplines considered in the development of our approach, including development and roads in rural areas, geospatial accessibility models, optimization approaches investigated for roads planning, and rural roads planning specifically in Nepal. In Section 3 we reveal the input data that were used, describe our geospatial analysis methodology, and elucidate our optimization methodology. In Section 4 we present our optimization results and compare the quality of the solutions to the roads development plan recently selected for Karnali’s Provincial Master Transport Plan. In Section 5 we elaborate further on the significance of the results, discuss the applicability of our methods within Nepal, identify limitations, and suggest future improvements and research directions. We close with a brief conclusion in Section 6.

# 2. Literature

# 2.1. Development, roads and accessibility in rural areas

Close links between rural development and access to markets, services, and employment centers are a common theme of development literature (Edmonds, 1998; Booth et al., 2000; Porter, 1997, 2002a,b; Bird et al., 2002; Christiaensen et al., 2003; Stifel et al., 2003). As physical access is primarily dependent on transportation infrastructure, traditionally focus has fallen on quantifying the economic impacts of rural roads investment (Jalan and Ravallion, 2002). Decades of academic research indicate that the realized benefits of rural roads – like improvements in household consumption, school attendance, food and nonfood item market prices, and non-farm employment – vary considerably based on contextual characteristics. These include agronomic potential (Binswanger et al., 1993), initial level of development (Khandker et al.,

> 1Multidimensional poverty is a composite measure of poverty based on multiple potential deprivations, including noneconomic measures like access to health care, education, or overall standard of living. More information can be found at http://hdr.undp.org/en/content/what-multidimensional-poverty-index.

3
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2009; Bryceson et al., 2008), local market characteristics (Casaburi et al., 2013), and lack of agglomeration economies and/or human capital (Asher et al., 2018).

Given this contextual uncertainty, evidence exists that the most consistent living standards improvements from rural roads are not economic in nature but instead linked to improved access to services such as health (Van de Walle and Cratty, 2002), finance (Binswanger et al., 1993), education (Adukia et al., 2020; Kristjanson et al., 2005), or administration. Comparing Asian Development Bank projects in the Philippines, Indonesia, and Sri Lanka, Hettige (2006) finds that rural roads most consistently benefit the poor through improved access to services, whereas poverty reduction is conditional on the contextual factors listed above or complementary investments.

The relationship between rural accessibility and human development is pronounced in South Asia compared to global norms. Whereas 29% and 11% of rural and urban populations respectively live in multidimensional poverty globally, in South Asia 64% and 25% do because of the excessive concentration of economic opportunity in urban areas (Asher et al., 2018; United Nations Development Programme, 2017). In India, increasing distance from towns and their services correlates with reduced household earnings (Asher et al., 2018) and improving rural road connectivity increases rural household consumption and reduces rural poverty (Rao and Jayasree, 2003; Khandker and Koolwal, 2011). In Nepal, Jacoby (2000) and Fafchamps and Shilpi (2003) demonstrated that income, cropping intensity, access to non-farm employment, and education levels in rural areas progressively fall as travel times to markets increase. In a small-scale study of 3 Nepali village development committees, Sapkota (2018) found that households with longer travel times to services have higher poverty levels and lower levels of health, education, and reported happiness. Shrestha (2012) found that a 1% increase in travel times to paved roads decreased rural farmland values and implied profits by 0.25%.

# 2.2. Measures of accessibility

Measuring accessibility baselines and improvements is critical to establishing rural roads’ benefits. Simple metrics like linear distance, densities of roads and services, or reported travel times in household surveys are easy to compute or parse from existing data sources but are often difficult to scale, only tangentially related to access, influenced by idiosyncratic survey responses (Ahlstr ̈om et al., 2011), or inaccurate in mountainous areas (Huber, 2015). Nevertheless, these are commonly used in economists’ evaluations of rural roads: for instance, Banerjee et al. (2012) and Thapa and Shively (2017) measure accessibility in terms of road length density per administrative area in China and Nepal, respectively.

Planners and researchers looking for greater accuracy and scalability will typically employ geospatial models of accessibility. The foundational models employed are network and cost-time models, which may be further elaborated in gravity models or measures of geographic and potential accessibility (Rodrigue, 2016). Network analysis calculates the anticipated travel time between one or many origins and destinations over an integrated transportation network. Transportation networks can take the form of roads, paths, railways, waterways, flights, or combinations thereof. Speeds are assigned to segments of this network which are used to calculate travel times between origin-destination pairs, with adjustments for impedances like traffic or border crossings. Implementations of network analysis range from the study of P ́aez (2004) on network accessibility’s relationship to economic activity in East Asia, the study of intra-city accessibility in Colombia by Sabogal et al. (2018), World Bank studies of accessibility to jobs in Cox’s Bazar Bangladesh (World Bank, 2020), and even Google Maps’s Directions tool.

Geospatial cost-time models represent travel in terms of the minimum time to cross each cell in a grid (raster). These times are calculated based on some combination of the underlying roads and road speeds, landcover, walking speeds, terrain, and other factors (Zhu et al., 2016). The advantage of this approach is that grid cells can model travel as on-network, off-network (e.g. walking), or as a combination of the two (walk to the road and then take a bus). Relevant examples leveraging these off-road capabilities to analyze access in difficult contexts include the analysis of Kosmidou-Bradley and Blankespoor (2019) on accessibility to services in rural Afghanistan, the study by Ahlstr ̈om et al. (2011) on poverty’s relationship to accessibility in southern Sri Lanka, models of accessibility to markets in Africa by Harvest Choice and International Food Policy Research Institute (IFPRI) (2016), and global-scale analysis of wealth stratification by accessibility to urban centers by Weiss et al. (2018).

The accuracy with which models reflect seasonal access changes depends on the model and metrics employed. Transport geographers (Jafino et al., 2020; Rodrigue et al., 2016; Jenelius, 2009) and civil engineers 5
(Shrestha, 2018) have developed concepts of criticality and redundancy to explain the impact of seasonal disruptions on road network performance within a network analysis. Because these network-scale analyses approach seasonal impacts in terms of binary open-closed changes in roads’ status they obscure quantitative changes in network and road-scale performance from reduced speeds over damaged but still-functioning roads. Many are also data intensive and difficult to replicate in rural, developing world contexts. Where seasonal access is considered by social sciences researchers, they tend to rely on survey data, as in the model of seasonal market access in Ethiopia by Hirvonen et al. (2017). In Nepal, Huber (2015) adjusts speeds for major roads and airports for the monsoon based on expert guidance.

Walking travel must be modeled in rural areas of the developing world where lack of roads or simple poverty compel many to travel long distances on foot to reach services or transport networks. They can therefore represent the entire travel time to a service or be integrated with road transport for a multi-modal accessibility model. Representations of walking speeds vary in sophistication: while the hiking functions of Tobler (1993) and Van Wagtendonk and Benedict (1980) provide foundations for modeling walking speeds, they translate better to cost-time modeling, which treat walking cells like any other, than network analysis, which ignores off-network travel. In practice planners and researchers tend to ignore or simplify walking times in their analysis of rural roads given roads’ primacy in most economic and transport systems. In Nepal, Devkota et al. (2012) modeled walking as a primary transport modality when recommending rural trail bridge investments. To the authors’ knowledge however, the model we adapt here (from Banick and Kawasoe (2019)) remains the only published, scalable model of travel times which incorporates monsoon impacts and walking speeds in a rugged and sometimes high-altitude context.

# 2.3. Traditional rural transport valuation

Since available budgets for rural road building rarely match the observed needs, transportation planners and policy makers must choose the most productive subset of roads from a collection of potential investments. Valuation and prioritization exercises for rural roads investments traditionally define such productivity according to economic cost-benefit analysis (CBA). Van der Tak and Anandarup (1971) framed the classic method of evaluating rural roads construction benefits in terms of welfare gains within a CBA, as measured by society’s net savings from reductions in the cost of supplying goods, increased employment, and increases in commercial traffic linked to new roads. Improvements in travel times are principally used to measure changes in vehicle operating costs and opportunity costs of lost labor time. Lebo and Schelling (2001) updated this method to better emphasize year-round access to rural areas by incorporating seasonal access cost variations, the monetary value of improved access to services, and improved valuation of time savings into traditional cost-benefit analysis. As noted by Belli et al. (2001), the large budgets and timeframes required for these data-intensive methods make them difficult to scale to large sets of roads or road alternatives. Accordingly, Lebo and Schelling argued for analyzing roads’ cost-effectiveness – relative to stated development objectives, instead of economic outcomes – when evaluating lightly trafficked but locally critical rural transport infrastructure where comprehensive CBA may be prohibitively costly.

Accessibility indicators based on travel times may complement or outperform CBAs in rural areas as they present easily parsable decision criteria to lightly resourced rural governments, scale easily across large sets of roads, and readily translate to monetary opportunity costs of travel. Additionally, the travel time indicators generated by cost-time models have demonstrated correlations with changes in fields as varied as conservation (Nelson and Chomitz, 2011), poverty reduction (Porter, 2007; Ahlstr ̈om et al., 2011), trade (Schmitz et al., 2012), and disease prevention (Gilbert et al., 2014). For these reasons and the aforementioned difficulty of appropriately resourcing CBAs for many roads over large spatial scales, we evaluate roads according to their cost-effectiveness versus accessibility indicators in this paper.

# 2.4. Optimization approaches to (rural) transport planning

Previous sections detailed examples of criteria considered when planning roads development, and the manners in which the benefits of proposed projects may be quantified – specifically in a rural developingworld context, with a focus on accessibility. It is only natural that more than one potential approach (e.g. candidate development plan) for the upgrading of a roads network exist (the work of Scaparra and Church (2005) provides excellent examples of this), from which it is necessary to identify at least one which provides superior trade-offs (in cost, accessibility improvement, etc.) compared to the others. This section discusses 6
the optimization approaches which exist to identify these superior alternatives and how they have been employed in works concerning rural roads Optimizing across rural networks presents a unique and understudied challenge since traditional transportation optimization models are designed for urban, relatively developed settings and hence are likely to underperform in providing solutions for rural, sparsely populated settings (Shrestha, 2018). However, the optimization of rural roads development has not been entirely overlooked and has seen recent advances, building upon earlier foundational work in this context by Kumar and Tillotson (1991), Kumar and Kumar (1999), and Kumar and Jain (2000) – noteworthy is that these studies are all focused in South Asia.

The demand for transportation arises from the spatial mismatch between where people are and the locations of services they want to reach, so it is common for transportation network design studies to include the service locations in their evaluation process. Kumar and Tillotson (1991) investigated the use of a mathematical model that is capable of determining numerous high-quality road network layouts that provide trade-offs in cost and travel times to fixed service/facility locations – market centers in their case. They investigated a rural area in India, and the travel time to market centers (which serves as a proxy for other essential services) was investigated as the trade-off criterion against cost. Their objective was to provide allweather access to every village in their study area, achieved by minimizing the cumulative costs of upgrades to existing roads and the construction of new ones, while minimizing the sum of travel costs required from each village to reach a selected service/facility location. This work was extended by Kumar and Kumar (1999) and Kumar and Jain (2000), in which the same model was extended to be capable of determining trade-offs for three accessibility criteria (educational institutions in this instance, but possible to consider others) measured against cost.

Scaparra and Church (2005) introduced a model that is capable of determining candidate road network development approaches in a rural setting, with consideration given to the improvement of all-season connectivity between villages and the efficiency of the routes between them – given a fixed budget. Their work delves deeper into heuristic approaches when compared to previous works, which is a necessity as roads development projects increase in complexity (discussed in more detail later). Their model did not, however, consider access to specific service locations. Murawski and Church (2009) proposed an approach which determines solutions that simultaneously upgrade the road network’s accessibility to health care locations, while minimizing the associated financial costs. Their model was solved using commercial optimization software and was used to search for optimal solutions at different maximum budget levels. They went on to show that treating existing facility locations as fixed and upgrading transport network links to all-weather roads can substantially increase all-season access to health services – even with modest investments. Unfortunately, their model only considered one service type, which is not practical in a real-world environment where the building of roads should consider accessibility to more than just one service.

Specifically in the context of Nepal, Shrestha et al. (2014) explored a bi-objective model for rural road network construction and upgrading in hilly regions of Nepal. Their objectives were to minimize the overall user operating costs (which can be thought of as a roads usage difficulty measure) and to maximize the population covered (serviced) by the network. The model then approximates solutions which provide optimal trade-offs in these objectives, determined for different maximum budget values. Similarly, Shrestha (2018) presented a multi-objective decision support model for rural road networks that suggests road network links for improvement or new construction. Using a similar approach to Shrestha et al. (2014) and with the objectives minimizing four population- and distance-based criteria, optimal trade-off solutions were approximated at different budget levels.

In this paper we implement two solution approaches that are popular for roads planning, and which were used in the aforementioned literature. Heuristics are considered because they are easily compatible with rural roads planning (Ma et al., 2014; Scaparra and Church, 2005; Kumar and Kumar, 1999) and can obtain numerous well-performing solutions within reasonable computation times when the complexity of the problem is too overwhelming for traditional methods. An integer-linear programming (ILP) approach is the second method that we implement, because it provides a simpler way to solve optimization problems compared to our heuristic approach and has been used in rural roads planning before (Murawski and Church, 2009; Shrestha et al., 2014; Shrestha, 2018). An ILP approach is, however, more sensitive to computational complexity and the size of problems which it can solve, and returns fewer solutions when compared to a heuristic approach – resulting in less data and less insightful solution-analyses.

7
# 2.5. Existing techniques of rural road planning in Nepal

Nepal’s forbidding terrain, low level of development, and underdeveloped data ecosystem complicate effective measurement of economic gains or accessibility changes from planned roads investments, let alone the implementation of advanced optimization models. Moreover, models built for planners must balance technical sophistication with communicative efficiency to policy makers and the public.

As such, policy makers in Nepal and India have favored rough, easily calculable measures of accessibility to set policy and measure progress. Nepali policy makers traditionally have measured accessibility policy goals in travel times, e.g. “85% of children should live within 30 minutes walking distance of a school” (Ministry of Education, Nepal and UNESCO Office Kathmandu, 2015). These figures are typically collected by interviews with local administrators or in one-off survey instruments, making them prone to manipulation and impossible to scale. Other accessibility metrics include reaching target dates for all villages of certain population sizes to be connected by all-weather roads (Kumar and Tillotson, 1991) or connecting a given percentage of key population groups (caste, ethnic, or age-based) to roads (LAHURNIP and IWGIA, 2014).

Accessibility models are rarely applied in the planning of Nepalese roadworks, where the level of methodological sophistication falls sharply from major to minor roads. Central authorities and collaborating donors typically evaluate major proposed “strategic” roads using welfare-based economic valuation methods. For instance, the World Bank’s forthcoming Strategic Road Connectivity and Trade Improvement Project (SRTIC) prepared a cost-benefit analysis of 12 road segments evaluating with- and without-project scenarios on the basis of combined vehicle operating cost and travel time savings (World Bank, 2019). But in practice this rigor is unusual and at a local level little to no proper evaluation is done (Coburn, 2020); in interviews in August 2018 and March 2019, staff at the Rural Access Programme spoke of how municipal authorities keen to demonstrate progress but lacking planning capacity frequently plowed roads into hillsides with little regard for environmental outcomes, investment efficiency, or even basic engineering principles.

Some efforts are underway to equip local authorities with access-based planning tools that accommodate their limited data collection and analysis capacity. Over the last 15 years the Rural Access Programme has worked with local governments in Nepal to design and implement Transport Master Plans that provide a measurable, data-driven basis for prioritizing proposed roads. The most recent iteration is the Provincial Transport Master Plan, a standardized tool for provincial governments to prioritize roads based on a spreadsheet matrix of cost projections, one day traffic density studies, policy priority, and the population totals of administrative centers touched by roads (Rural Access Programme (RAP3), 2019). An extract of the prioritization tool within Karnali’s draft Provincial Transport Master Plan is shown in Figure 4.

Figure 4: Ranking road building options in Karnali’s draft Provincial Transport Master Plan (Rural Access Programme (RAP3), 2019).

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# 3. Data and methods

# 3.1. Inputs

The conditions of data production in Nepal mirror the physical conditions of the roads themselves: fragmented, incomplete, and least comprehensive for the most remote areas (Bikas Udhyami, 2018). In this environment, gathering sufficient primary data to accurately assess travel times and accessibility is difficult. Our model manages these issues by using global and freely available datasets – Shuttle Radar Topology Mission (SRTM) 30 m terrain elevation model, High Resolution Settlement Layer (HRSL) raster population data sets, OpenStreetMap, national land cover products (ICIMOD 2013) – and core governmental datasets like roads, health care, government offices, and financial institutions that a partner government agency can be reasonably expected to possess. We employ the HRSL data set instead of the WorldPop data set used in Banick and Kawasoe (2019) because it represents uninhabited areas as “Null” instead of fractional values as in WorldPop, and thus better capture Karnali’s unpopulated expanses, illustrated in Figure 3(b). In all cases OpenStreetMap data can provide a suitable “backstop” data set for missing or inaccurate governmental datasets. The data sources that were used to model accessibility to services are summarized in Table 1.

Table 1: Data sources used in this research.

|Data|Source|Date|Resolution<br>or Type|
|---|---|---|---|
|Ofcial road network of Nepal|Survey Department of Nepal|2019|Vector (Lines)|
|Road and path network of Nepal|OpenStreetMap|Dec 2019|Vector (Lines)|
|Trail bridges|Trail Bridge Infrastructure<br>Support Program (TBIS)|Aug 2019|Vector (Points)|
|Proposed roads in Karnali province|Karnali provincial government<br>(via RAP)|Aug 2019|Vector (Lines)|
|Terrain|NASA Shuttle Radar<br>Topology Mission|Global|1 arc-second<br>(≈30m × 30m)|
|Landcover of Nepal|Integrated Center for Mountain<br>Development (ICIMOD)|2020|1km × 1km|
|Rivers of Nepal|OpenStreetMap|Dec 2019|Vector (Lines)|
|Health facilities|Nepal Ministry of Health|2016|Vector (Points)|
|Karnali municipal headquarters|World Bank|2019|Vector (Points)|
|Formal fnancial institutions<br>(classes A - D)|Nepal Rastra Bank<br>(central bank)|2017|Vector (Points)|
|High Resolution Settlement|CIESINdFbk|2018|1 arc-second|
|Layer Maps (HRSL)|an aceoo||(≈30m × 30m)|

Geospatial data for health services and formal financial institutions were sourced from the Ministry of Health (2016) and Nepal Rastra Bank (2017), respectively, while municipal headquarters were compiled from assorted Nepali-language policy documents and then geolocated with reference to OpenStreetMap. This basket of services was selected as a representative of a cross-section of developmental, economic, and political needs; Figure 3(a) shows their current distribution versus existing roads. Effective health care is an essential input to human development, particularly in the region of Nepal most afflicted by food insecurity and consequent malnutrition. Formal financial institutions (hereafter referred to as financial institutions) contribute to economic development by enabling the growth of local small to medium enterprises (SMEs) – unfortunately, no suitably comprehensive data set of informal financial institutions exists. Finally, municipal headquarters not only provide essential administrative services but are acceptable proxies for principal local markets. Education was considered for inclusion but a suitably comprehensive geospatial data set could not be located.

The Rural Access Programme (RAP), a donor-funded infrastructure support program active in Karnali, shared shapefiles for the 92 individual proposed road segments specified in Karnali’s draft Provincial Transport Master Plan as of early 2019 and the average per-kilometer budget charge associated with the different 9
physio-geographic regions in Karnali: Low Hills, Middle Hills, High Hills, and Mountains. These charges aggregate materials, labor, management, and administrative expenses. We followed the government’s practice as described by RAP in an August 2018 interview, allocating per-kilometer budget charges to road segments based on their length and the majority geography of the district they primarily fell within. Thus Mountain roads were 33% more expensive than Low Hill roads. The values that were used are provided in Table 2.

Table 2: Average per-kilometer budget charge associated with different physio-geographic regions. Values were provided in NPR and converted to USD using an exchange rate of 120 NPR to 1 USD (2 May 2020).

|Geography|Road cost<br>(NPR / km)|Road cost<br>(USD / km)|
|---|---|---|
|Low Hills|15 million|126 thousand|
|Middle Hills|17 million|143 thousand|
|High Hills|18 million|151 thousand|
|Mountains|20 million|168 thousand|

# 3.2. Roads vs. road sequences

Roads do not exist in isolation, but as part of networks. As such, proposed roads may implicitly depend on the construction of other roads linking them to the existing road network. We reviewed the proposed roads and grouped them into combination sets with internal hierarchies (tiers) reflecting these spatial dependencies. Thus a tier 2 road enables a tier 3 road to be built but depends in turn on a tier 1 road being built. Applying these hierarchical concepts to generate all plausible combinations of road tiers expands the number of candidates from 92 roads to 261 combinations – called sequences – and corresponding GIS files were created from visually observable hierarchies. In a real-world scenario, such hierarchies would be identified by experts in road construction and regional accessibility; the priority here was to illustrate our process and its accommodation of such hierarchies. The accessibility improvement modeling process was then run for these sequences as well. The notion of such tiers that form part of the sequences identification process is illustrated in Figure 5 for a number of connecting roads ranked into three tiers. For narrative simplicity, in the remainder of this paper all potential additions to a candidate layout are referred to as a road sequence – whether a standalone road or a combination of roads.

# 3.3. Geospatial cost-time analyses

A recently released geospatial model of Nepal representing distances in units of time offers a scalable, replicable solution to the problem of modeling travel in Karnali (Banick and Kawasoe, 2019).<sup>2</sup> The model calculates the minimum travel time to cross every 30 m<sup>2</sup> of Nepal’s two dimensional surface based on the underlying terrain, landcover, altitude, roads, and road conditions; an accompanying monsoon model adjusts these factors and resulting travel times for monsoon conditions. The two dimensional output is packaged into a 30 m<sup>2</sup> gridded (“raster”) friction surface that can be used to calculate accessibility to various services from any place on the grid. These accessibility rasters can be aggregated into descriptive statistics at almost any useful level of analysis – administrative areas, catchments for specific markets or hospitals, or catchments for individual roads.

Applying the friction surface to services of interest allowed us to specify the precise accessibility gains associated with each planned road or sequence of roads in Karnali province. We measured the increase in accessibility associated with specific proposed roads by generating a friction surface for every proposed road incorporating its projected travel time improvements, then using said model to calculate accessibility to selected nearby services. Comparing these to similar measures from a reference data set based on the existing road network yielded the accessibility improvement associated with an individual road.

> 2Readers with a deeper interest in the process of cost-time modeling and subsequent accessibility analysis in Nepal are encouraged to refer to Banick and Kawasoe (2019), where the modeling process and parameters are discussed at length.

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# Off Road Speeds Road Speeds

<!-- Start of picture text --> Off Road Speeds Road Speeds On Road Speeds<br>BM verge Oo _<br>co Coe. bel<br><!-- End of picture text --> <!-- Start of picture text --> Mesh Speed<br>Fastest of each<br><!-- End of picture text --> Cost-Distance Linear distance + vertical distance <!-- Start of picture text --> FastestMeshesh ofSpeed each<br>Ze on<br>oS<br><!-- End of picture text --> Generic friction surface bel Friction surface (time to cross) per 30 meters <!-- Start of picture text --> 01<br>hours -005 S<br>hours Sz<br><!-- End of picture text --> Friction surface Large scale | im a Times per 30m add up from service to each cell

<!-- Start of picture text --> Access time<br>Total at pop. center<br>~~<br>| | | thr<br>[<br>:<br>ee | °<br>as: Se<br>Nearest service<br>(healthcare / bank/ muni. HQ)<br><!-- End of picture text -->
<!-- Start of picture text --> Dolpo Karnali<br>Access to health facilities<br>with current roads i~<br>Monsoon season (i. =<br>——/—Proposed road ae| BX<br>Main existing :<br>Road Trail es 4<br>Settlements (of any size) PEE i<br>|| P Peag<br>Health “ee Ras<br>facilties (any type) iG Myr Brg a 3<br>Hours to health facilities J i Be FiiN é<br>° 12 24+ fig ah KK % mad ‘<br>Nea)3 (A yyeohi? 4<br>: om GO" 4 iy an x<br>4 by hie hes SM Wry<br>_0 20km CDEe pea : yh : OswyyetAn SourcesiDept, RAPNASA: DOR,S RSL<br><!-- End of picture text -->

<!-- Start of picture text --> Dolpo Karnali<br>Access to health facilities<br>with sequence 44 -<br>MonsProp o sedon seasonroad cepe =” ie i 2 Th<br>Senuctets Other <} , o.<br>Main existing rh pus<br>—=_———Road Trail S24® s y a Aya«<br>Settlements (of any size) hie Soul j > y i<br>a wy Vs Re | A,<br>Health facilties (any type) E yn Le ee Mj, Zp g WZ<br>jours cc) | Why vV OO wk Ms<br>to health facilities ce 4h F thizs % Uy 4 LHS Ae LB<br>0 12 24+ farWO il <i % Hi) a“te %,ba fiFat OB iz Z<br>) fee 7) s7 gigas<br>‘i A E77SaBile)Li Sya (<br>—. > /ae<br>() 20km CA "Clay “OF ; Sources: NASA,S<br><!-- End of picture text -->
<!-- Start of picture text --> é<br>Access toDolpohealth facilities ; Karnali<br>with sequence 44 y<br>Monsoon season ex<br>Nae<br>Proposed road " OX<br>Sequence44 Other \<br>Main existing<br>[————nRoad I Trail<br>Settlements (of any size)<br>a<br>Health facilties (any type)<br>Hours saved to health facilities<br>0) =D 3<br>12 24+ A<br>4° a (<br>= re 4<br>P a wi AR es ‘<br>0 20km ame A Sources: NASA, Survey<br>Dept., RAP, DOR, HRSL<br><!-- End of picture text -->
<!-- Start of picture text --> Dry season Dry season Dry season<br>Existing Road n, affected area Road n, all Karnali<br>| | | || ||<br>< 7 M th o a<br>3© lerge wii | ———===>><br>fe)<br>hn<br>BS Monsoon season Monsoon season Monsoon season<br>wn Existing Road n, affected area Road n, all Karnali<br>O|<br>o<br>g°Merge with, of 7 | ———==> =H<br><!-- End of picture text -->

<!-- Start of picture text --> Dry season Healthcare Financial Municipal HO<br>Friction surface access time access time access time<br>From pop. place From pop. place From pop. place<br>| | a Ha 6m (o| a | Hn 6<br>¢ | | | Hi a | a | fot<br>3 “i + | _— oe PO | Nearest muni.<br>gas - | {9 | on |_| peer -_ =<br>)= .earest healthcare- iGy facilitye e- au e----<br>3 Monsoon season Healthcare Financial Municipal HO<br>ry”) Friction surface access time access time access time<br>re) From pop. place From pop. place From pop. place<br>2. | | a (o| i | (o| i | (o| a |<br>o | EG om H oO H__o lol<br>& i. Ss wseoes<br>Pt : Hk > EE : Hk<br>| | | Be - Be Be - fn: -<br>Nearest healthcare facility<br><!-- End of picture text -->
<!-- Start of picture text --> Access time Population density Person - hours<br>per 30 meters per 30 meters per 30 meters<br>1 1 )<br>hours 3E O pop p-h p-h<br>bel<br>x =<br>4 5 30<br>pop p-h p-h<br><!-- End of picture text --> <!-- Start of picture text --> Person - hours Person - hours Access improvement<br>Existing roads e, service s Road r, service s Road r, service s<br>4 1 E 1 1 3<br>p-h p-h & p-h p-h p-h<br>= |nl=<br>5 30 5 30<br>p-h p-h p-h p-h<br><!-- End of picture text -->

<!-- Start of picture text --> Proposed Proposed Proposed<br>Road 1 Road 2 coe Road n<br>Dry Monsoon Dry Monsoon Dry Monsoon<br>i on is oon i on i on i ol is oon<br>Patt a =o CH Pat ia<br>—t— —t— —t— —t+— —t— —t—<br>meet MMos ST OTST Bap ETT OTST Mag OTST Saal tt Sad ETT OTT Saad<br>afin of af oe oe eB ee od Be oe afQat of of of of<br>41'1<br>aa | a a a | | a a a | | a a a a a<br><!-- End of picture text -->

|||Prop<br>Ro|osed<br>ad 1||Prop<br>Roa|osed<br>d 2<br>coe||Prop<br>Roa|osed<br>d n|
|---|---|---|---|---|---|---|---|---|---|
||Dry||M|onsoon|Dry|Monsoon|Dry||Monsoon|
||i on<br>Patt<br>|||isoon<br>a<br>|i on<br>=o<br>|i on<br>CH<br>|i ol<br>Pat<br>||isoon<br>ia<br>|
|me<br>af|t<br>et<br>in|MMos<br>of|ST<br>af|t—<br>OTST<br>Bap<br>oe<br>oe|—t—<br>ETT<br>OTST<br>Mag<br>eB<br>ee<br>od|—t+—<br>OTST<br>Saal<br>Be<br>oe|—t<br>tt<br>afQat|Sad<br>of|—t—<br>ETT<br>OTT<br>Saad<br>of<br>of<br>of|
|||||||||||
||a|||a|a<br>a||<br>|<br>a|a<br>a<br>|||<br>a|a|a<br>a<br>a|
||RoadSe|quence|Name|Season|Service<br>Acce|ssibilityImprovement (p-h)|Budget(NPR|)|P-h/ NPR|
|1108<br>:T10_3|ccc|eeecc|eeeeee|eeeeeeee<br>OM<br>en|eeeeeeeeeeee<br>ble**a**lthFacili**ti**es<br>|ecceecceneeeeeeseeeee<br>495,01|0<br>......62|**00**0000|2**.**407**3**6**E-06**|
|||||iDry|<br><br>‘Fin ncial Ins<br>tutions|<br>5284.9:|<br><br>621|0<br>000|8 510 7|
|M103||||Monsoon<br><br>|{HealthFacilities0<br>|)<br>2869.9!6<br> <br>|210000<br>|00.<br>|3.81623E-06<br>|
|||1||0<br>Monsoon.|<br>0<br>iFinancialInstitutionsj|<br><br>o<br>0804.4!|21000|00|1.73984E-05|
|{T15_1.<br> <br>|1<br> <br>|||<br>iDry<br>|<br>:HealthFacilities<br>|<br><br>8181.7:<br> <br>|527<br> <br>|000000<br> <br>|1.55251E-05<br>|
|TUS <br>1T15_1_|d<br>|cccec|ceseeseeeesee|eee(DIV...|<br>fFinancialinstitutions|fo<br>63262.2!|o<br>527000|<br>00.|0.000119852|
|<br>|<br> <sup>1</sup>|||<br>:Dr|<br>{Municipal headquarter.|<br><br>5574.9:|<br><br>527|<br><br>000000|1.05786E-05|
|{T15_1.<br>|1<br>|||{Monsoon_ <br>|Financial Institutions<br>|116589.6:<br> <br>|527<br>|000000<br>|0.000221233<br>|
|TIS|4|4||Monsoon|jMunicipalheadquarter§|0<br>5725.2E|270000|00.|1.08637E-05|
Our approach considers a maximum and minimum budget specification and candidate plans therefore provide alternatives within this range. A benefit of following such an approach is that it allows for policy makers to examine trade-offs in construction costs and avoid unnecessary spending. For example, if a plan that costs 5% less than a plan at the maximum budget, yet achieves accessibility improvements that are similar to those which may be achieved at the maximum budget, then the 5% in savings could be allocated to other development projects.

Our approach does not allow for the same road to be selected for inclusion in a candidate plan more than once – when a candidate plan is configured during the optimization process, sequences that share roads with those already included in the plan are excluded from consideration. For example, if multiple sequences include road DR5007, then a candidate development plan can only include one of these road sequences and all the others (and the standalone use of DR5007) are excluded from consideration. As more sequences are added to a potential plan, the list of exclusions grows. The constraint on duplicate roads selection as discussed here is an important factor to consider during the mathematical problem formulation and optimization processes so that practical solutions are obtained, and is further elucidated in the remainder of this section, where relevant.

Finally, our approach considers 6 accessibility maximization objectives (3 services per season) in this study alone and potentially more in future work. Depending on the solution approach followed, the criterion of cost may be considered either as a budgetary constraint (enforcing that a candidate plan’s costs are between maximum and minimum limits) or as an additional cost minimization objective.

# 3.6.1. Candidate solutions and evaluation

In multi-objective optimization, a candidate solution (roads plan) is evaluated by multiple objective functions – mathematical functions which calculate the plan’s performance with respect to each of the objectives. In our approach the objective functions determine the sum of the accessibility improvements (in personhours) of all the sequences in a plan, for each service per season. Similarly, based on feedback from key RAP staff during a December 2019 interview with key staff, the cost of a plan is the sum of the estimated cost of all its constituent sequences. The objective function values of a candidate plan correspond to a single point in objective function space – this is illustrated in Figure 13 by (hypothetical) example candidate plans represented as points and evaluated with respect to two accessibility maximization objectives (plotted on the axes). This example figure shows the solutions evaluated with respect to only two objectives, but the same principles apply for 3 or more objectives. Minimizing cost is often considered as a maximization objective, by maximizing 1/cost.

In multi-objective optimization, solutions such as those in Figure 13 are classified either as non-dominated (superior) or dominated (inferior) (Zitzler et al., 2004). The set of non-dominated solutions exhibit superior trade-off alternatives when compared to the dominated solutions, and form what is commonly known as the Pareto-optimal front, or simply the Pareto front, as may be observed in the figure (Zitzler et al., 2003). Only the solutions in the Pareto front need to be presented to decision makers because of their superior quality; that is, dominated solutions are avoided. The Pareto front is determined using the same principles of domination for problems involving more than two objectives, and the notion of Pareto optimality remains applicable, albeit harder to visualize.

# 3.6.2. Heuristic solution approach

The search for the exact (true) Pareto front for optimization problems that include multiple objectives involves a significant computational challenge and may become prohibitively large to solve within realistic computation times (Jia et al., 2007; Owen and Daskin, 1998; ReVelle and Eiselt, 2005; Tong et al., 2009; Xiao et al., 2002). In such instances, powerful heuristics are often employed in order to approximate the set of solutions on the Pareto front (Xiao et al., 2002; Zitzler et al., 2004; Heyns and van Vuuren, 2018). These heuristics target and explore promising regions of the solution space<sup>3</sup> in order to arrive at solutions that are approximated to be Pareto-optimal, and in the process avoid the computationally expensive consideration of solutions in inferior regions of the solution space. It has been demonstrated that heuristics are well capable

> 3The solution space in the context of this paper is the set of all feasible plans, e.g. all the combinations of sequences that avoid road repetitions (the exclusions) and with costs that fall within the monetary budget.

17
<!-- Start of picture text --> Candidate solution (roads plan)<br>N<br>oO<br>YL<br>e<br>®<br>wn<br>£ bad e @<br>9<br>o e<br>&<br>©<br>5<br>7 e<br>£ sg<br>& © e@ = Pareto front of<br>ie!wn @ non-dominated solutions<br>3 Dominated solutions e<br>N & ‘<br>2g e<br>RE _ e<br>Ss XX e<br>Qo ‘<br>OF<br>Objective 1<br>Maximise accessibility improvement to service 1<br><!-- End of picture text --> Objective 1 Maximise accessibility improvement to service 1
# ONE-POINT CROSSOVER

parent 1(35 [60 [23] 261193| (35 [60 [23] 166] 50] 207) ofpring crossover point UNIFORM CROSSOVER rarer 1(35 [60 [125] vee] 95] 05] 2] 258 Ofspring N. a, Nee _ rarer 2(27 [100] 125] 190] 20] 207) 23] 35 [205] 80 [146] 254) ofpring2
# MUTATION

randomly selected entry parent (55 [oo [i]s 5|| 5] 29) mutated ortepring (35 | 23] so [05] 2] 250] 25] 09
STEP 1 <!-- Start of picture text --> Identify and remove duplicates<br>(55 [20] 95] 05] 259<br>duplicate<br>STEP 2<br>Remove exclusions<br>Cs [oo [re] oo] aos =a) (7 [roo] es fivo] 9<br>eee Oe ee ee P<br>excluded<br>STEP 3<br>Identify and remove weakest (Repeat)<br>(35 [80 [125] esf9af205] 2212] 27 [125] 209) Offering 1<br>weakest<br>C55] o0 [ress [mse] [25] 29) oftprng 2<br>weakest<br>(5 [565] oes [PH] ]AS) ofteprng 3<br>Repeat until minimum budget reached<br><!-- End of picture text -->
<!-- Start of picture text --> mutate entry 1<br>parent (35] 60 [125] vce]z0s 22] 254] 125] 209<br>aN \ I / LO<br>Bins<br>random select] )\ot excluded<br>Cor [20 [125] 05] 21] 254] 25] 29) New offspring - keep improvement<br>Parent (35 [60]yrutate 125] entry5] 05] 2 221] 254] 125]285)<br>ae \\ | / Loe<br>Bens<br>random select! \jot excluded<br>Cas [os [a3] 165205 [221] 254] 125] 209) New offspring - keep itimproverent<br>Repeat for each entry<br><!-- End of picture text -->
<!-- Start of picture text -->
*START*<br>'Generate N solutions ;<br>(ooo ee<br>1<br>1<br>Current population | No<br>size N<br>Crossovers<br>and drops Select N best Converge?<br>Combined solutions<br>New solutions current and<br>Offspring population offspring Yes<br>populations<br>Multimutation swap Improvedsolutions DONE<br><!-- End of picture text -->
<!-- Start of picture text --> corner<br>Obj 3 max<br>bd<br>°<br>; ® corner<br>a: pst : Obj 1 max<br>Maximize to<br>Objective corner @ . : ' '<br>3 Obj 2 max : Maximize<br>, Objective 2<br>Maximize<br>Objective 1<br><!-- End of picture text -->
<!-- Start of picture text --> corner<br>Obj 3 max<br>bd<br>@ corner<br>: Obj 1 max<br>100k p-h<br>Maximize ‘<br>oo corner @ desired solution '<br>Objective 3 Obj 2 max | region<br>250k p-h | Maximize<br>Objective 2<br>Maximize<br>Objective 1<br><!-- End of picture text -->
each criterion are already determined in stage 1 of the ILP approach, in (2), and are rescaled to a value of one. The minimum value with respect to each objective function is rescaled to zero – these minimum values remain to be determined. However, this process is not overly sophisticated since the values may be found at the corner points not associated with the objective.

Consider Figure 20 once more, where we aim to find a solution between the corners of objective 1 and objective 2. The minimum value that may be achieved with respect to objective 1 is simply found at the corner of objective 2, and the minimum of objective 2 is found at the corner of objective 1 – when considering objectives 1 and 2 only. Using the minimum and maximum values for each objective function, values determined between these values may be scaled to between zero (at the minimum) and one (at the maximum). In this manner, the effect of objective function magnitudes on a weighted-sum may be eliminated and the search for solutions is directed by the weights in the weighted-sum. If we were to search for solutions between all three corners, the minimum of each objective still lies at one of the other corners, and the value at each corner needs to be compared to the others before the minimum may be identified. For example, when only considering objectives 1 and 2, the minimum for objective 2 lies at the corner of objective 1. Now, if objective 3 is also considered, then the minimum of objective 2 may be found at either the corner of objective 1 or objective 3. If we look at the figure and the projections of the corner points onto the obj1/obj2-plane, then the minimum for objective 2 is now found at the corner of objective 3 and this minimum value becomes zero relative to other values.

Let A ⊆{1, . . . , Na} denote the set of criteria for which a weighted objective function is sought, with the weights of the selected criteria adding to 1. Furthermore, let va,max denote the maximum value of accessibility criterion a ∈ A, determined in ILP stage 1. Similarly, let va,min denote the minimum value of accessibility criterion a ∈ A, which is pre-determined as the lowest value found with respect to the objective at the Pareto corner points of the criteria included in A. The normalized objective function is then to maximize The objective in (6) is subject to the same constraints (3) to (5).

# 3.7. Optimization process setup

The accessibility improvement in person-hours was determined for each of the 261 sequences, for each season and with respect to health facilities, financial institutions, and municipal headquarters – therefore 6 accessibility criteria in total. Minimum and maximum budget limits of 6 and 13 billion NPR were specified. We used 13 billion NPR as the upper bound because this was the budget for the roads that were eventually selected by the provincial government. The much lower limit of 6 billion NPR provided a large budget span, which allows us to compare rates of accessibility improvement that may be achieved for different services at different budget ranges, and to compare how improvements between services relate to each other across the budget range (e.g. linear or exponential). The objectives in both the ILP and heuristic approaches were to find solutions so that person-hour accessibility improvements with respect to all 6 criteria are maximized.

# 3.7.1. Heuristic

Cost was implemented as an additional, seventh objective by the heuristic, with the aim of minimizing total cost – implemented as a maximization objective, maximizing 1/cost. By adding the cost minimization objective, the heuristic is forced to not only find solutions that maximize the accessibility objectives, but also to explore the maximization of these objectives at lower cost levels, from 13 down to 6 billion NPR. Because of the stochastic nature of the heuristic’s Pareto-front approximation process, the solutions returned by different optimization runs will generally vary in quality. It is therefore standard practice to repeat the process multiple times (Knowles et al., 2006; Kim et al., 2008; Heyns et al., 2019). The results of all the runs are then combined and a final attainment front – essentially the Pareto front of all the combined Pareto front approximations – is identified. We repeated our process 40 times, from which a final attainment front of 5,000 solutions that are approximately Pareto optimal with respect to all 7 objectives was identified. The authors’ personal optimization code was used for the heuristic runs, executed in MATLAB.

26
# 3.7.2. ILP weighted-sum

In the weighted-sum ILP approach, cost was considered as a maximum constraint and solutions were sought for various weight combinations at maximum cost levels beginning at 6 billion NPR and increasing in increments of 1 billion NPR up to 13 billion NPR, resulting in eight cost levels. In the first ILP stage, no weights are assigned because the objective in (2) is repeated for each individual accessibility criterion, at each cost level in order to determine the corner points on the Pareto front. In the second stage, equal weights were assigned with respect to all pairs of two criteria that can be compared from the six, e.g. w1 = 0.5 and w2 = 0.5, then w1 = 0.5 and w3 = 0.5, and so forth for each pair, resulting in twenty such weight combinations at each cost level. Then, all combinations of three criteria were equally weighted together, e.g. w1 = 0.33, w2 = 0.33, and w3 = 0.33, and so forth, resulting in 15 such weight combinations at each cost level. No more weight combinations were investigated, as these were primarily used for visual comparison to the heuristic results and visualizing solutions with respect to more than three objectives is challenging. The six runs from the first stage together with the thirty five weighted runs from the second stage totaled 41 runs at each of the eight cost levels, resulting in a global number of 328 weighted-sum runs. The runs were all executed with CPLEX and called from within MATLAB. This is because data preparation was done in MATLAB, and for each CPLEX run a different set of variables (depending on the criteria for which weights are assigned) are selected and provided as input – this was managed by MATLAB.

# 4. Results

# 4.1. Pareto fronts

The solutions obtained by the heuristic and weighted-sum runs are presented in this section. It was possible to determine each set of heuristic and ILP results (for all heuristic runs and weight combinations) within one day.<sup>5</sup> The 40 heuristic runs each terminated in around 10 minutes or less, while the ILP run times showed more variation because of different weight sets and budget limits in each run, but averaged at 13 minutes. Figure 21 visualizes the results of our heuristic runs in the form of the 5,000 solutions plotted simultaneously in 3D objective space for both seasons. It should be noted that these 5,000 solutions are the same solutions in both these 3D plots – although all solutions were determined with consideration given to 7 objectives, they are plotted against different axes because plotting them with respect to more than 4 objectives (3 accessibility axes and cost in color as in Figure 21) is visually challenging. The same 5,000 solutions are examined in the remainder of this paper.

The cost of the solutions in Figure 21 are indicated as increasing in darkness from light gray at 6 billion NPR, to dark gray at 13 billion NPR. Solutions number 4,845 and 3,449 are explicitly linked between their solution “dots” and their roads layouts show representative examples of optimal solutions at various budget ranges. These layouts are shown alongside the layout and corresponding objective function values of the actual roads selected by Karnali’s provincial government. Figure 21 exemplifies how solutions may be presented to decision-makers to assist their analysis of options. A more evolved presentation might provide this data in interactive form. These results are analyzed in more detail in the following section.

In Figure 22(a)–(c), the 5,000 solutions are now presented in 2D, along axes which are pairs of accessibility improvements in person-hours with respect to different services, for the dry season. A legend to describe the colors and markers used in Figure 22(a)–(c) is provided in (d). Selected solutions are indicated in the colors orange, magenta, blue, and red, which represent solutions at budget levels of 7, 9, 11 and 13 billion NPR, respectively. When examining the color solutions at each level, it may be observed that three are larger circles – these are the ILP solutions that were determined with the budget set at the indicated maximum value. Of these three ILP solutions at each budget level, the two outer points at each budget level are the values determined by single-objective optimization, while the middle solutions were determined by the weighted-sum with respect to the two objectives in each plot (i.e. determined with two equal weights for the two objectives).

The smaller color circles are heuristic solutions that are determined at each budget level and collectively form a Pareto front extracted with respect to the two objectives in each plot. To aid in understanding these

> 5All optimization processes in this paper were run on a Dell 7820 Precision desktop PC, running Windows 10 Pro with an Intel Xeon Silver 4110 processor and 64 GB memory.

27
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<!-- Start of picture text --> 75 x10 5<br>°<br>«a 7- 9°.‘2. °,Ue OeoYe,<br>2 rn oe.<br>is} ° Foot - fe 0<br>5 65> eet lag, TT) FE<br>£ se CCN. Ae RE<br>B 6 . F Je Se BEEP<br>8 BE QE ee Sa been ESE °<br>E ig SE EE ekg: 6 Dag<br>rs NS tos ARDe ene a oe eR RN<br>255+ tgbyne 0h 2m Po me ey<br>S Te Ser heel OO<br>< Sere eAe Boe 5 Cat Lume<br>5 5> ee i Bae ae ee oo ts<br>E Paget tS : Loe<br>g mp Bae ot Se yee<br>£45- ‘s Shoe<br>@a<br>7)<br>8 4-<br>g<br>3.5<br>0.6 0.8 1 1.2 1.4 1.6 1.8<br>Access improvement (p-h) to Health Facilities (DRY) 10°<br><!-- End of picture text --> <!-- Start of picture text --> 35 x105<br>><br>Q3 ne<br>= cat ae é . °o.;- 8<br>oO O22 PEA Pry eS cue<br>& ° Or "aga". oA * am =. 4 aM<br>c 7 SS eh get ede re<br>=2 ° . : vo ayeUTR, Tayeot SEa GesNaa rga oPme)<br>=G2 Lengreeog gasaaeeingBeots A,tte Ta:<br>g Rae 2ihe Ae PEELE Sb <3." J<br>Bis. ee<br><1S} ; < by<br>;<br>Access improvement (p-h) to Financial Institutions (DRY) 10°<br><!-- End of picture text --> <!-- Start of picture text --> 35 x10 5<br>in> 7he eatf<br>SB 3- ot! Ps<br>a @: ore ~ ee O<br>So af . . ;<br>g a See eee<br>8 ety ei et<br>5 25> are a Rae vende<br>= ° pee oe Fe ae<br>= sae Yel Ro URS eee<br>ray oe AEP 0.6 : pe Leges<br>& CE bee ee eae | BERET TS<br>Pd cae Ow gshee | eek<br>E int £3 ota pais °°<br>3 13 aig APE.<br>£ beg ecg, pease<br>7 ts ier: AL)<br>B15>8 ; WeeWee.<br>rs s ae<br>ed de<br>Peas<br>a<br>0.4 0.6 0.8 1 1.2 1.4 1.6 1.8<br>Access improvement (p-h) to Health Facilities (DRY) 10°<br><!-- End of picture text -->

<!-- Start of picture text --> Solution type<br>Heuristic ILP<br>Budget levels<br>7 9 1 13<br>-- 5-5 - ee ee eee ee<br>6 Cost (billion NPR) 13<br><!-- End of picture text -->
additional “sub”-fronts, one can consider the 5,000 heuristic solutions as a subset of the entire solution space of all possible solutions, and which have been identified to return optimal trade-offs with respect to the 6 accessibility criteria, and cost (i.e. a 7-dimensional Pareto front of 5,000 solutions). Then, similar to the process of determining a Pareto front from the entire solution space with respect to some objectives (see Section 3.6.1), we are now determining sub-fronts from the 5,000-solution space with respect to selected objective pairs. In Figure 23, the results are presented in the same manner as in Figure 22, for accessibility improvements during monsoon season.

The same 5,000 heuristic solutions and selected weighted-sum solutions are now presented in Figure 24, with the axes in each graph representing accessibility improvements for each service with respect to the two seasons – (a) for health facilities, (b) for financial institutions, and (c) for municipal headquarters. The same legend in Figures 22 and 23 is again used here, for budget levels and ILP and heuristic solutions.

# 4.2. Analysis

When analyzing the Pareto fronts in Figures 22 and 23, the trade-offs between improving accessibility to services become clear. At each budget level, moving along solutions that improve in quality with respect to one objective causes a degradation in solution quality with respect to another objective. This provides insight into the decision-making process, as it is clear that the objectives are conflicting and that the trade-offs should be examined. The solutions exhibit constant improvement in the objective function values when moving from one budget level to the next, indicating a relatively linear relationship between cost and accessibility improvement. Particularly encouraging is that the heuristic solutions at each budget level are similar in solution quality to those yielded by the ILP approach. This is significant, since the heuristic solutions are determined thousands at a time, while each of the ILP solutions are determined separately (and our results were determined within similar computation times for heuristic and ILP solutions). The fact that our heuristic returns solutions of similar quality and which follow the shape of the sub-fronts returned by the ILP solutions indicates that the heuristic solution process is powerful and returns solutions of very strong quality.

When analyzing the Pareto fronts in Figure 24, the trade-offs between improving accessibility to the same services during different seasons reveals interesting characteristics. The trade-offs in the objective function values are small – indicating that gains in accessibility in one season scale favorably to gains in another season. This is particularly noteworthy for the comparison of health facilities in Figure 24(a), in which the improvements in health access is highly linear, possibly due to the wider spatial distribution and higher absolute number of health facilities, which reduces the occurrence of relatively extreme accessibility gains for any specific road sequence. Such observations may lead to improved decision-making processes. In this case, it may be possible to eliminate the consideration of seasons in health care access.

In Figures 25 and 26, the heuristic solutions are plotted with respect to each individual accessibility objective during dry and monsoon season, respectively. The horizontal axis represents each solution number from 1 to 5,000, which were sorted to increase in cost. Therefore, as may be seen in the figures, the budget levels intervals along the solution numbers is non-uniform and displayed by vertical lines where the solutions crossed a budget interval value. The reason for the non-uniformity in cost distribution lies with the heuristic solution methodology, which appears to struggle to find more solutions between 9 and 12 billion NPR – yet manages to obtain solutions of high quality despite the lower distribution. Such restrictions may, nevertheless, be improved in future versions of the heuristic. Also displayed in the figures are the ILP solutions determined at each budget level – these are the single-objective solutions determined with respect to the single accessibility objective in each plot. Finally, the accessibility improvement achieved by the actual roads selected by the Karnali provincial government are also displayed in each plot in red – since their roads plan was selected at a budget of 13 billion NPR, it is located along the corresponding budget line at the right of each plot.

Comparing the heuristic solution quality to that of the ILP once more reveals that the heuristic solutions return high-quality solutions that nearly match the quality of the ILP solutions. An example of interesting observations that may be made when analyzing these plots for decision-making purposes is when the solutions for health facilities and municipal headquarters are compared in the dry season. For health facilities, between 9 and 12 billion NPR, a number of solutions are concentrated “lower” along the vertical axis. This indicates that a number of solutions do not perform well with respect to health facilities in this budget range, and this is clarified when examining the municipal headquarters solutions. Here, these solutions are clustered to perform well with respect to municipal access – solutions between 9 and 12 billion NPR are therefore generally more beneficial to municipal access than health facilities, while the improvements to financial institutions in 30
<!-- Start of picture text --> 41x10 5<br>10- - B., 38y ©<br>= Osis! MN CEE.<br>Sa5 ° TegSpot g,2 |ke DECTO. .-he8ag,<br>9p Qe pee 7 eS<br>a oy pete 99% 2 ee OO Ake<br>= ORE Poe Be ad a<br>S9 gt LE Ce,Bhs Oe ee ee<br>& ae ceBee G é i rye)<br>Q@7- 1. SBy aleeed“oe 89.aness “ OQ, :<br>— ee gti met<br>i= 6b ee ig [owe<br>6<br>3<br>5 5}<br>8<br><8[s} 4p<br> Ce<br>1 1.5 2 2.5 3<br>Access improvement (p-h)to Health Facilities (MSN) 10°<br><!-- End of picture text -->

<!-- Start of picture text --> 452105<br>°<br>. Oe 2<br>fe}n a. MERE) he okSen heree8Sy<br>835+ A See ot =. Byte<br>32 ° CeBe. Bar Aad eeSah"eeaeme<br>=2 3 i eh oarseeeCEN Pe¢ MTSee Oeet 0<br>z ee ess<br>ig Pehacend<br>a : é ae &<br>£ ; pe Bed Se. OF<br>g Spe Rae<br>ee?Bo.8 ; : .<br>a<br>Access improvement (p-h) to Financial Institutions (MSN)x 10°<br><!-- End of picture text --> <!-- Start of picture text --> 452105<br>7 “Ee satigh eo °<br>@ 4) - aids Piet ee 8<br>=~ Greeo we rrpe. fs ee<br>fe} a sige As Te Outset<br>o Ops. wee are came.<br>23.55 me “a daa wo Be<br>xe oe oi Do 3 ka O<br>e 3 ro eeraere? a<br>‘2& 3poO =vee: Aa n St Berwaelee 9. .<br>= 50 ra<br>g | ee ee RGN .<br>ic] Bg<br>Q ‘ ARIES es<br>‘ : ne GHEE. ae<br>8 2- He fee<br>< , Q<br>4.5<br>1 1.5 2 2.5 3<br>Access improvement (p-h)to Health Facilities (MSN) 10°<br><!-- End of picture text -->

<!-- Start of picture text --> Solution type<br>Heuristic ILP<br>- oo ee eee eee eee<br>Budget levels<br>7 9 11 13<br>Sete BAS sete Fee ss<br>6 Cost (billion NPR) 13<br><!-- End of picture text -->
<!-- Start of picture text --> 182105<br>%<br>owFSatéD aeaASsggtie®44<br>=: aeaf bis<br>Q exe<br>Q4° Aeser<br>5 ee<br>2 al<br>® reg<br>gS) ee<br>al<br>0.6<br>1 1.5 2 2.5 3<br>Access improvement (p-h) to Health Facilities (MSN) 10°<br><!-- End of picture text --> <!-- Start of picture text --> 35 «10 5<br>_~ °<br>> ° °<br>Oog 3 grEenon,<br>w De % ee<br>& ate 5 “9 . ost<br>3 owe sie<br>2 “Ogee<br>z@ 2 ahgh PstOT BAetees?<br>ie) ma : ae e t?<br>B15; 28 gh aaa<br>x sek et<br>oe<br>Access improvement (p-h) to Municipal HQs (MSN) — 10°<br><!-- End of picture text --> <!-- Start of picture text --> 75 105<br>%<br>Le56526 ekafveeloe 8e.oe.heote 2%.0 9-.P8<br>aot: GESyASSes oFIG BS:a sat Ries<br>€ 5 ba BADR AF<br>iso 5 ¥ SLEI ess -angsheweWO<br>3 i cy re ><br>£ oi rea<br>a a : ‘<br>3<br>8<br>3.5<br>3 4 5 6 7 8 9 10 11<br>Access improvement (p-h) to Finanical Institutions (MSN)x 10°<br><!-- End of picture text --> <!-- Start of picture text --> Solution type<br>O<br>Heuristic ILP<br>Budget levels<br>7 9 1 13<br>A. oe ee ee<br>6 Cost (billion NPR) 13<br><!-- End of picture text -->
this budget range is more universal during the dry season. Performing a similar analysis in the same budget range for the monsoon season in Figure 26, it is interesting to observe that financial institutions are more sensitive to the effects of the monsoon season, as these solutions now exhibit similar clustering in the “lower” objective function value range which was not observed for the dry season. Besides the implications for road building solutions, these findings suggest to decision-makers that seasonal accessibility may impact financial inclusion or access to finance policy objectives.

Continuing the analysis of Figures 25 and 26, conspicuous improvement in solution quality is observed when comparing the heuristic solutions to the actual roads plan selected by the Karnali provincial government. The maximum accessibility improvements for solutions at or near the maximum 13 billion NPR budget are approximately 3, 3, and 1.5 times those yielded by the actual selected roads for health facilities, financial institutions, and municipal headquarters, respectively. Even at half the budget the mean accessibility improvement is double that of the actual roads selected for health services and financial institutions and roughly equal for municipal headquarters.

Assessing solution accessibility results in the aggregate reveals important differences in the potential accessibility gains to each type of service. Figure 27(a) plots the mean per NPR gain in accessibility for each service in each season across all 5,000 approximately Pareto-optimal heuristic solutions at different budget levels. Across all solutions, it is observed that mean accessibility gain per NPR is highest for financial institutions and weakest for health facilities. However, this likely reflects the over-concentration of financial institutions in Karnali’s major towns where most profitable businesses reside and the comparative dispersion of public services like health facilities and municipal headquarters. To account for these spatial patterns we compute each service’s nearest neighbor index, a spatial statistic that describes the distribution of a point feature set relative to a completely spatially random process as clustered (approaching 0), random (1), or regular (exceeding 1) (Cover and Hart, 1967), using a common geographic extent. We multiply each service’s index by its mean accessibility figure to establish a dispersion-adjusted accessibility index, with the results presented in Figure 27(b). So adjusted, health facilities retain the lowest accessibility gain per NPR while municipal headquarters gain two times more efficiently than other services. However, the continued upward trend in accessibility per NPR at the maximum budget levels in Figures 25 and 26 suggests that additional budgetary investments would continue significantly improving accessibility to the studied services.

The charts in Figures 28 reveal a considerable disparity in investment efficiency amongst proposed roads. These charts visualize the person-hours improvements per 100,000 NPR associated with each road sequence, as generated by the cost-time modeling and analysis routine, with sequences ascending in efficiency from left to right. Sequences are colored from light to dark depending on the frequency of their selection within the 5,000 heuristic solution sets to illustrate the relationship between efficiency and solution selection. Setting aside extreme values outside the 5th and 95th percentiles, the most efficient road during the dry season is approximately 6.6, 18.3, and 9.3 times more efficient than the least efficient road for health facilities, financial institutions, and municipal headquarters respectively. The same pattern holds for the monsoon season, where the most efficient road or sequence is 9.0, 28.1, and 9.0 times more efficient than the least efficient road. Although the most efficient roads are generally the most frequently selected, certain efficient combinations are not selected often and certain less efficient roads are frequently selected. Efficient combinations may be superseded by even more efficient combinations using the same road sequences, and cheap but less efficient roads may be useful complements to more efficient roads and combinations. The last point underlines the utility of our method: judging roads in isolation ignores the significant complementarities that exist between choices.

# 5. Discussion

# 5.1. Summary

The marked gains in cost-effectiveness from our methods justify their additional complexity, time investment, and expense. Our methods substantially outperform current planning approaches in simultaneously improving accessibility to all services studied. Geospatial cost-time models accurately quantify mean accessibility improvements in a challenging environment and heuristic optimization models efficiently process and highlight the most promising combinations of rural roads based on the provided objectives (accessibility improvements) and constraints (budget). The system provides flexibility to policy makers and analysts by proposing solutions at various budget levels and accommodating additional objectives, accessibility-related 33
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<!-- Start of picture text --> Mean accessibility gains per NPR<br>Municipal HO<br>(monsoon)<br>Municipal HO<br>(dry)<br>Health facilities<br>(monsoon)<br>Health facilities<br>(dry)<br>Financial institutions<br>(monsoon)<br>Financial institutions<br>(dry)<br>0.00 0.02 0.04 0.06 0.08<br>Mean accessibility (person-hour) improvement (per NPR)<br><!-- End of picture text --> <!-- Start of picture text --> Mean accessibility gains vs. dispersion<br>Municipal HO<br>(monsoon)<br>Municipal HO<br>(dry)<br>Health facilities<br>(monsoon)<br>Health facilities<br>(dry)<br>Financial institutions<br>(monsoon)<br>Financial institutions<br>(dry)<br>0.00 0.05 0.10<br>Mean accessibility improvement (per NPR)<br>relative to service and population dispersion<br><!-- End of picture text -->
Road sequence investment efficiency vs. solution selection frequency Access improvement per 100,000 NPR <!-- Start of picture text --> Dry Monsoon<br>30 30<br>2<br>3°fe) 20<br>z<br>A=<br>LL<br>E100 poor il mill | | | 10o il UTI | |<br>4<br>3 4<br>So<br>Ww<br><=<br>22<br>o<br>——<br>9 15<br>a<br>fe}<br>x=<br>3 6 10<br>YL<br>=<br>0 1! WT MULE ll 0 TL ou OLLI i<br>Roads Roads<br>Selection frequency<br>—<br>0 1K 2K 3K<br><!-- End of picture text -->
<!-- Start of picture text --> eg ae Access improvements<br>pf fA,<br>CA?) Monsoon | Municipal headquarters<br>‘\. <i i of SR Solution #4845<br>inchs X“ oy ore EVCEe 12.9 billion NPR | 46 municiplities<br>ed f oe 4 ry 4)A £9» 2.4 million p-h savings<br>Ceies Zraysete Ome:<br>Se UNGwiry inBOEGe: © OD O®<br>Ree gia UP EG eS Sis 4pears<br>Pesees Bee PS:CCM SLE ers<br>Pot ri Gee Ee Cy eg!MLE<br>gii. Lek ¥& = ByAe, Vii Br, ye<br>” i heey Ms fo ry Age { ya tO oe he tig<br>WAY,io ILA Dea SeNs ig aes | 5Sie<br>OS% TIEIeA<br>eeTM,Mee “rca @ Municipal HO Proposed road<br>eyion Cpe.pe NsgeUeA Hours saved to municipal headquarters<br>0 GIR,dt Miah 0 6 12+<br>"= 50 km "ay nae Sources: NASA, Survey Dept., RAP, DOR, HRSL<br><!-- End of picture text -->

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explicitly to development objectives than prevailing Nepali practitioner models of infrastructure project evaluation, which typically simplify around administrative aggregates (i.e. x schools per ward), focus exclusively on one specific service type, or disregard services entirely. More rigorous cost-benefit evaluation methods may similarly disregard services, despite their developmental importance, while presupposing data inputs (e.g. international roughness index, traffic flows per segment) that are prohibitively expensive to collect accurately at scale for large numbers of rural roads. Finally, both approaches either ignore, simplify, or require painstaking effort to measure the effects of seasonal changes on transport speeds and overlaps in proposed road accessibility improvements.

Vector-based geospatial models offer comparable scalability to cost-time models but fail to manage the inherent complexity of rural, mountainous contexts. Where network models lack geospatial data on walking paths (as is common in Nepal) they must simplify considerably; in Nepal such simplifications are likely to route travelers over difficult or impassable terrain. By contrast, raster-based models explicitly record travel times across every surface, allowing accurate modeling of walking via least-cost paths to the nearest destination or road. Modeling walking also enables walking-specific speed reductions at high altitudes.

Furthermore, raster-based travel models can measure improvements in accessibility more accurately and specifically by pinpointing the precise improvement for households in a grid cell via interaction with rasterbased population models. This is advantageous in Nepal’s sparsely populated hills where administrative aggregates can mask extremes. Beyond making the analysis more accurate, this specificity allows policy makers to compare roads that best reduce travel times for the most remote populations to roads that improve travel times for the greatest overall population, weighting them according to policy objectives if so desired.

This research’s final contribution to geospatial analysis methods is to prove the utility and feasibility of producing and applying cost-time models at scale. Advances in parallel processing and computing power increasingly enable batch production of complex, multi-modal, multi-scenario (e.g. seasonal road speeds) geospatial accessibility models in reasonable timeframes. The advent of affordable cloud computing solutions places such methods within the reach of analysts in Nepal and similar contexts where relatively expensive computing power and internet speeds have traditionally constrained analysis possibilities. Producing multiple accessibility models for each proposed roadway has several advantages: a) it eases the modeling of interactions (overlapping improvements) between roads; b) the analysis can scale to exponentially greater numbers of roads, services, and seasonal scenarios given sufficient geospatial data and computing power; and c) because individual roads are discrete analytical elements they easily fit within the solution sets of optimization models.

# 5.4. Advances in optimization methods

Several novel optimization approaches were followed in this research. Most notable is the consideration of a budget span – instead of a fixed maximum value – which was achieved by novel variable-length chromosome representations of candidate roads plans in the heuristic. Furthermore, the heuristic is capable of determining thousands of solutions which exhibit optimality with respect to multiple conflicting objectives, in reasonable computation times. Seven objectives were considered by the heuristic here, which is an unusually large number even when compared to traditional methods in multi-objective optimization.

A significant benefit to obtaining such a large number of solutions that are optimal with respect to many objectives is that it provides decision-makers with rapid analysis capabilities. By determining a large number of solutions once-off with respect to many objectives, the behavior of solutions may later be examined with respect to only selected objectives and criteria. From the set of solutions determined by the heuristic, subfronts may simply be extracted (as was performed in Section 4), instead of having to re-perform heuristic or ILP optimization with respect to the selected objectives. Such capabilities may provide decision makers with rapid insight during the analysis process, and can aid in finalizing a budget and most significant objectives – which may then be followed by a final round of optimization to “fine-tune” solutions to these specifications. Other benefits to having a large number of solutions (which were discussed in Section 4), include added insight into a) the relative linearity or concavity of a specific service’s accessibility improvements versus cost increases, b) the trade-offs that exist between accessibility services and seasons, c) the roads’ investment efficiency and selection frequency, and d) the relative improvements to accessibility to different services in different seasons yield at various investment budget levels. Such analyses of large numbers of solutions have not been performed in the literature – most likely because methods capable of obtaining such solutions have not existed until now.

40
The analysis of road sequences’ gains, efficiency, and importance across solutions may help policy makers identify the key roadworks in potential plans. These strategies may further help compensate for the delays and inefficiencies inherent to Nepal’s capital infrastructure planning bureaucracy, by focusing policy makers’ attention on the roadworks most critical to success within an overall optimized portfolio.

# 5.5. Limitations

We must note certain limitations to our analysis. The most significant is that due to resource and data constraints, we present the accessibility gains as a simultaneous phenomenon instead of staggered over the provincial government’s 5-year road construction window. A deeper analysis would specify a yearly budgetary max within the overall budget max and stagger the solution roads across the time period, with gains appropriately discounted. Additionally, we employed flat per-kilometer road costs per geographic area due to lack of data, and to better align and compare with Nepali practitioners and academics (Shrestha, 2018); more specific road cost data would improve our method’s accuracy. Finally, this analysis treats population as spatially fixed, while in reality population is dynamic and new road construction can induce population movements; for example, in Nepal new markets often spring up at newly built roads heads. This could create additional unobserved objectives if the government speculatively selected roads to create new market hubs or connect underpopulated remote villages to reduce population outflows.

The complexity of the analysis routines described here places them effectively out of reach of even national government planning agencies in Nepal, let alone provincial or municipal ones. Thus government will need to employ universities and private sector companies with specialized expertise to replicate this analysis in new areas. Given that the studied investment planning exercise happens on a 5 year basis this seems a manageable extra expense. As stated above, care was taken to use free global or common national data sets to ease adoption and replication by other parties.

A further limitation is the difficulty of communicating our results to policy makers compared to traditional instruments. Welfare-based evaluation methods ease the cognitive burden on decision makers by measuring investment returns in terms of familiar NPR values or easily parsable rates of return. To compensate we have produced thorough explanatory visuals for our methods and results. Nevertheless, correctly interpreting a 3D bubble chart – itself a simplification of 6D results – of person-hours is inherently more challenging than a table of NPV or Internal Rate of Return (IRR) values. This erodes decision makers’ ability and willingness to use our results. Therefore real-world implementations will need to invest additional time and effort in correctly explaining results and guiding policy makers to use them appropriately.

# 5.6. Potential improvements and future research opportunities

Given the complexity of the multi-disciplinary analysis methods undertaken we employed a relatively straightforward series of inputs, metrics, and decision criteria for roads investment. Having proven the value of this work, we have several suggestions for enlarging its focus, improving its specificity, and aligning it better with traditional planning methods.

Additional georeferenced services would nuance the analysis, each one representing two (dry and monsoon season) additional objectives. For instance, the analysis could incorporate accessibility to schools, water points, agricultural extension services, or other important services, even at a village or household level. A variation on this theme is to differentiate qualitatively between services, for instance by separating hospitals from health posts or major from minor financial institutions and then re-running the analysis with each as an objective.

A more involved modification would involve calculating cumulative person-hours within service-specific constrained catchments that reflect travel time limits on the utility of services, both generally and for specific demographic groups. For instance, in an August 2018 interview RAP staff described how individuals might travel 8 hours for important health problems but never to bring produce to weekly markets and Nepalese women are typically warier of overnight travel (in excess of 4 hours one way). Accessibility indicators could also be calculated solely for target demographic groups (i.e. pregnant women to maternal health centers). Particularly ambitious would be replacing cumulative person-hours with more data intensive changes in gravity models of service access based on the quality (attractiveness) of services vs. the distance and size of reached populations.

Alternatively, the geospatial models could be adapted to provide inputs to a comprehensive cost-benefit analysis. While this paper has explored our methods as an alternative to CBA for planning remote rural roads, 41
given its difficulty and expense in this context, with additional investment in data production and analysis it could instead improve CBA. With information on annual trips per service, time elasticities of service usage, and/or economic benefits of service usage the economic benefits of time saved, increased health, and/or better access to markets and financing could be quantified and discounted within a time-bound cost-benefit analysis.

Sensitivity tests could be conducted on optimization results to verify the stability of preferred solutions to cost overruns or accessibility miscalculations. Recommending optimal solutions with the greatest degree of stability across reasonable cost overruns would help guard against the construction industry’s notoriously poor cost control. Similarly, the optimization routines could offset Nepal’s budgetary and planning inefficiencies by recommending which core road sequences to finish first.

# 6. Conclusion

This research has demonstrated the utility of a multidisciplinary approach to arrive at meaningful and substantially improved roadworks plans in a mountainous and data-poor environment characterized by walking as a primary transport modality. In doing so we provide an alternative to traditional planning tools for policy makers in Nepal and other similar contexts.

This research uses a cost-time model to measure travel time distances as it credibly manages walking speeds and off-road travel in Nepal’s rugged terrain, is computable with free or Nepali government-standard data sets, and returns intuitive travel times. While cost-time models are standard geospatial analysis tools, we were not able to find prior examples of deriving accessibility metrics for proposed construction via the batch production and comparison of road-specific cost-time models, let alone applications of this model in mountainous areas with walking as a primary travel modality.

Facility optimization models are similarly standard tools within the field of operations research, but to our knowledge none have previously incorporated the outputs of cost-time models, much less to analyze access improvements to rural roads. The optimization methods followed in this paper introduced a number of novel approaches that improve on previous roads optimization work and provide more intricate and insightful decision-making possibilities. Thus this research represents a methodological advance within both disciplines and the Nepali country context. To enable replication and adoption within Nepal we have employed open data and developed open source tools where possible; where not we have employed governmental data sources and industry standard software packages common in Nepal. As a result our models provide more precise estimates of populations’ accessibility to specific services in Nepal at a lower cost and greater scalability than available academic or practitioner alternatives.

# Acknowledgments

We are grateful to the UK Department for International Development in Nepal for funding this work via its Evidence for Development program. Hiroki Uematsu’s belief in a more data-driven approach to roads building in Nepal inspired this research and his guidance and review helped ensure its quality. Nethra Palaniswamy and Nandini Krishnan arranged crucial feedback sessions in Washington DC; the participants to these sessions are too many to name here, but their inputs greatly improved the “real world” applicability of this research. Benjamin Stewart, Tom Gertin, and Andres Chamorro of the World Bank’s Geospatial Operations Support Team and Walker Kosmidou-Bradley of the Poverty GP helped us validate and improve the technical modeling. Jonas Parby and Drs. Jagat Shresthra and Seth Appiah-Opoku generously reviewed the initial draft of this paper. The counsel, data, and documents provided by Diva Malla, Arjun Poudel, Michael Green, Kirsteen Merrilees, and Philippa Jeffries from IMC Worldwide’s Rural Access Programme 3 (RAP3) were crucial for enabling this research.

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