# Payment Maintenance Decision Making Based on Optimization Models
## 1 Introduction
GAs and traditional mathematical programming are often used to solve road M&P planning problems based on multiobjective optimization (MOO), but they also have their limitations. [PERSON] et al. [12] proposed a two-objective optimization model balancing minimum action costs and maximum conditions for used road networks and developed a GA-based procedure for solving the MOO problem. [PERSON] et al. [13] described the development of a genetic algorithm based on multiobjective programming for pavement and investigated the optimal maintenance strategy options applied as function of road surface distress conditions with a lack of information related to monitoring data and evaluation. [PERSON] and [PERSON] [14] explored the expected accuracy rates of network treatment options through a multiobjective optimization methodology that utilized a GA and mixed-integer programming; their method was capable of effectively assigning pavement maintenance tasks under certain conditions. [PERSON] et al. [15] performed large-scale optimization to compare the existing maintenance policy with an alternative strategy. Specifically, they incorporated a GA into the optimization model to address the issues associated with specific optimization constraints and the limitations related to low-volume roads during the optimization process. [PERSON] et al. offered a new multiobjective stochastic algorithm called the integer search algorithm (ISA) [1]. The ISA and GA were applied to improve the performance condition rating (PCR) of pavement in developing countries and achieved this by maximizing the condition of the pavement with minimum costs at specified constraints. [PERSON] et al. [3] proposed a novel adaptive hybrid GA that incorporated local search techniques to improve the overall efficiency and effectiveness of the search. [PERSON] et al. [16] proposed two multiobjective evolutionary approaches to solve problems of road construction within a reasonable time. These approaches were combinations of different techniques, such as GA, NSGA-II, the Frank-Wolfe algorithm, and the ordered logit model. The NSGA-II and its improved algorithms are popular for solving MOO problems [17; 18]. To address the high computation complexity associated with pavement maintenance at the network level, [PERSON] et al. [19] developed a model to reduce the search space and formulated the original problem as a generalized assignment problem, which was a well-known problem in mathematical optimization. [PERSON] et al. [20] proposed a chaotic particle swarm optimization algorithm to find the optimal solution for pavement maintenance. This algorithm could effectively resolve the maintenance and rehabilitation issues associated with flexible pavements. [PERSON] and [PERSON] [21] used condition indicators in the form of normalized values and developed technical constraints in a linear integer programming model to improve network-level pavement maintenance and rehabilitation planning. [PERSON] et al. [22] proposed a network-level pavement maintenance and rehabilitation optimization model considering the costs of user travel time and vehicle fuel consumption. The model optimized the asphalt pavement performance evaluation method, including 11 different combinations, which could be easily extended to the study of more complex road networks considering other factors. [PERSON] et al. [23] proposed a model based on the cloud decision tree (CDT) theory, which included a general decision-making model and various decision trees for every province of the country. As evident from the foregoing discussion, considerable research has been conducted to improve GAs and to utilize them for decision making in pavement maintenance because of their effectiveness in resolving multiobjective optimization problems. In this study, the pavement maintenance problem was introduced and formulated as a multiobjective decision-making problem. Subsequently, two optimization models were developed based on actual road conditions and applied to a real-world case.