# Optimal low emission zones scheduling as an example of transport policy backcasting

Asmae Alami, Vinith Lakshmanan, Antonio Sciarretta

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Asmae Alami, Vinith Lakshmanan, Antonio Sciarretta. Optimal low emission zones scheduling as an example of transport policy backcasting. 9th International Conference on Models and Technologies for Intelligent Transportation Systems, Institute of Electrical and Electronics Engineers Intelligent Transportation Systems Society Membership, Sep 2025, Luxembourg, Luxembourg. hal-05416495

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Distributed under a Creative Commons Attribution 4.0 International License
Optimal low emission zones scheduling as an
example of transport policy backcasting

Asmae ALAMI

IFP Energies Nouvelles

Rueil-Malmaison, France

asmae.alami-ouazzani@ifpen.fr

Vinith LAKSHMANAN

IFP Energies Nouvelles

Rueil-Malmaison, France

vinith-kumar.lakshmanan@ifpen.fr

Antonio SCIARRETTA

IFP Energies Nouvelles

Rueil-Malmaison, France

antonio.sciarretta@ifpen.fr

*Abstract*—This study presents a backcasting approach that considers the passenger car fleet dynamics to determine optimal policy roadmaps in transport systems. As opposed to the scenario-based approach, backcasting sets emission reduction targets first, then identifies policies that meet the constraint. The policy is the implementation of Low Emission Zones (LEZs), in the Île-de-France region as a case study. The aim is to minimize the number of scrapped vehicles due to LEZs under CO₂ emission targets and to deduce an interdiction schedule of polluting vehicles by 2050. To explore potential solutions, we use a genetic algorithm that provides a first insight into optimal policy pathways.

***Index Terms***—Backcasting, Optimization, Decision-making, mobility, Low Emission Zones, Optimal Control

# I. INTRODUCTION

Air pollution is responsible for exposing populations to
dangerous and toxic emissions significantly impacting their
health sometimes even leading to death [1]. Greenhouse gas
emissions (GHG) significantly contribute to global warming, a
key topic that remains at the heart of public debate in policy-
making and campaigning across Europe [2]. The European
Union has set an ambitious goal of achieving carbon neutrality
by 2050, requiring a massive reduction of transportation sector
emissions, as it remains one of the most polluting sectors and
one of the largest contributors to GHG emissions [3].

Many cities have been exploring numerous strategies to
reduce vehicle pollutant emissions and decrease GHG emis-
sions, mainly by reducing the use of private cars and lowering
congestion. Congestion pricing in urban areas introduces road
tolls to regulate traffic-flow and discourage unnecessary trips
during peak hours. In a study on Lyon (France) [4], it has
been shown that urban tolls generate revenue that can be
reinvested in public transport and sustainable infrastructure,
thereby improving accessibility and reducing CO₂ emissions.
Another study [5] highlights that urban tolls are more effective
when combined with public transport improvements while
acceptance remains a challenge.

Low Emission Zones (LEZ) have significantly spread across
Europe [6] and became one of the most popular measures in
terms of reducing GHG emissions and improving public health
[7]. Although LEZs have shown effectiveness in reducing
PM₁₀ and NO₂ concentrations in cities like Munich or Berlin
[8], the effectiveness in other areas such as London has shown
to be minimal [9]. In Madrid, a study [10] has shown that the

introduction of even a small LEZ entails scrapping old vehi-
cles, another study [11] highlights that LEZs encourage the
adoption of alternative-fuel vehicles, all of which inevitably
improves air quality. In spite of LEZs having great potential in
sustainable mobility, their implementation can lead to a decline
in people's well-being [12]. This is mainly due to restrictions
on individual mobility and common requirement to replace
forbidden vehicles with costly alternatives, often with little or
no government support [13]. Therefore, it is important that
policymakers also conduct thorough studies to assess LEZs
impacts on the population to make an informed decision.

More generally, it is crucial to assess the effectiveness of
different policies aimed at reducing air pollutants and GHG
emissions, guiding the transport sector towards carbon neutral-
ity. A large body of literature [14], [15], [16], uses agent-based
simulation to forecast the performance of the decisions to be
made in terms of improvement of air quality and/or reduction
of GHG emissions through prospective scenarios. Either by
selecting the best scenario among the designed ones or trying
to explore a broader range of possibilities through a surrogate
model (Forecasting) and then refine with an optimization
process, the agent-based approach shows its limitations due to
the numerous uncertainties that must be addressed to validate
the outcomes.

In this paper, we are pursuing the research conducted by Lakshmanan et al. [17] that explores a new paradigm where backcasting is defined as a quantitative optimal control-based approach. While [17] focuses on electric vehicle purchase incentives, this work concentrates on LEZs and their acceptability among users. The subsystem considered in this study, includes the evolution of a passenger vehicle fleet, its impact on GHG emissions, and individuals' responses to LEZ policies. The decision variable corresponds to the detailed schedule of vehicles' age to forbid from present to 2050 within a certain perimeter. This paper is organised as follows: Section II introduces the revised model that incorporates LEZs and formulates the optimal control problem. Section III presents our case study covering the Parisian Region (Île-de-France). In Section IV we present and discuss the results, including the optimal schedules. Finally, Section V concludes the paper and outlines perspectives for future work.
## II. BACKCASTING MODEL

### A. Vehicle fleet model

We use the time variable $t \in [0, T]$ representing a discrete time horizon from the present until 2050 with $T$ denoting the total number of years in the period.<fnref n="1" /> The vehicle stock $S(t)$ is composed of two types of vehicles: ICE ($v = 1$) and electric ($v = 2$), and we use the discrete age variable $a \in [0, A]$ where $A = 30$ is the maximum vehicle age. The study area (cf. section III) is divided into $Z$ distinct zones, indexed by the disaggregation variable $z \in [1, Z]$. Vehicle-kilometer (vkm) is a measure of the transport demand $G(t)$, which is segmented by zones, while the mileage $M(t)$ is the average distance traveled across all zones, per vehicle per year (km/veh/y). The number of new vehicles ($a = 0$) required to meet the total demand is $N(t)$, which is also segmented by zones and expressed as follows

$$N_z(t) = \frac{G_z(t)}{M(t)} - \sum_{va} O_{vaz}(t) \quad (1)$$

with $O(t)$ being the total number of old vehicles ($a > 0$) at year $t$, segmented into type, age and zone: $O_{vaz}(t)$. Due to LEZs, many vehicle owners dispose of their vehicle if it has been or is close to being forbidden. Let $R(t)$ be the number of vehicles that were disposed of because of the LEZs, by type, age and zone, and $\sigma$ the disposal ratio that depends on the LEZ schedule. Just as established in [17], the $\eta$ represents the survival rate of a vehicle from a year to the next, depending on its age $a$. Figure 1 shows that among the previous available stock $S(t-1)$, the vehicles that survive, are either disposed of ($R(t)$) or become part of the old stock ($O(t)$). The vehicles that do not survive leave the fleet and are not quantified.

<figure><img src="image_2.png" /><figcaption>Fig. 1. Schematic representation of the relationship between $S$, $O$ and $R$</figcaption></figure>

The expressions of old and disposed vehicles are valid for each type and zone, $\forall t \in [1, T]$, and are expressed as follows

$$O_{vaz}(t) = \eta_a(1 - \sigma_{vaz}(t))S_{v,a-1,z}(t-1) \quad \forall a \in [1, A-1] \\ O_{vAz}(t) = \eta_A(1 - \sigma_{vAz}(t))[S_{v,A-1,z}(t-1) + S_{vAz}(t-1)] \quad (2)$$

$$R_{vaz}(t) = \eta_a \sigma_{vaz}(t) S_{v,a-1,z}(t-1) \quad \forall a \in [1, A-1] \quad (3)$$

$$R_{vAz}(t) = \eta_A \sigma_{vAz}(t) [S_{v,A-1,z}(t-1) + S_{vAz}(t-1)].$$

The disposal ratio $\sigma_{vaz}(t)$ depends on the LEZ and will be discussed in subsection II-B. In this paper, we assume that the only vehicles that can be disposed of are ICE vehicles, which implies that $\sigma_{2az}(t) = 0 \ \forall t$ and $\forall z$.

LEZs also change the course of purchase of ICE vehicles. Indeed, if a LEZ forbids access to a certain vehicle, its owner is less likely to replace it with a new ICE vehicle. In this

paper, we consider that if a vehicle has been denied access to because of a LEZ, then the probability of replacing it with an ICE vehicle is null. The number of new vehicles has also been disaggregated by type and is expressed as follows

$$N_{1z}(t) = (N_z(t) - \sum_a R_{1az}(t))P_{1z}(t) \quad (4a)$$

$$N_{2z}(t) = \sum_{a} R_{1az}(t) + (N_z(t) - \sum_{a} R_{1az}(t))P_{2z}(t). \quad (4b)$$

where $P_{1z}(t)$ and $P_{2z}(t)$ are the ratios of ICE and electric vehicle purchase. Expressions for $P_{vz}(t)$ as a function of fixed and variable costs will be introduced in subsection II-B.

The evolution of vehicle stock by vehicle type, age and zone at year $t$ is expressed as

$$S_{vaz}(t) = \begin{cases} N_{vz}(t) & a = 0 \\ O_{vaz}(t) & a > 0. \end{cases} \quad (5)$$

From (5), CO₂ emissions are evaluated using emission factor $\varepsilon_{1a}$ (gCO₂/km) such that $\varepsilon_{2a} = 0$ for electric vehicles.

$$E(t) = M(t) \sum_{a} \varepsilon_{1a}(t) \sum_{z} S_{1az}(t). \quad (6)$$

### B. Decision Variable and disposal function

#### 1) Age restriction variable:

Let us introduce the age restriction variable $I \in \mathbb{N}^{T \times Z}$, such that $0 \le I_z(t) \le A$. Each element $I_z(t)$ defines the maximum age allowed for vehicles. If $I_z(t) = a$, all vehicles of age $a$ and more are forbidden in zone $z$ at time $t$. The initial value $I_z(0)$ reflects the current vehicle restrictions in the study area, as detailed in table I. As only ICE vehicles are assumed to be forbidden, the subscript $v$ is dropped in $I$. We impose that $I$ verifies certain constraints moving from a year to the next. Our first constraint consists of not allowing a forbidden vehicle to be authorized again. This means we impose that for the same zone, $I_z(t) \le I_z(t-1) + 1 \ \forall t \in [1, T]$. If no new restriction is applied moving from a year $t$ to the next, $I_z(t) = I_z(t-1) + 1$. The second constraint is ensuring that the ban remains reasonably restrictive. Therefore, we define a parameter $D \in \mathbb{N}^Z$, that represents the maximum allowable ban rate for each zone, between consecutive years. This parameter is intended to be determined by decision makers. However, for the purposes of this study, specific reference values for $D$ have been provided in Table I. The second constraint is illustrated as $I_z(t-1) - D_z \le I_z(t) \ \forall t \in [1, T]$. Both constraints depend on the previous value of $I$; thus, we introduce a decision variable $J \in \mathbb{Z}^{T \times Z}$, such that

$$I_z(t-1) - I_z(t) = J_z(t). \quad (7)$$

The resulting constraint for the decision variable is

$$-1 \le J_z(t) \le D_z, \quad (8)$$

and the state variable $I$ is further constraint by

$$0 \le I_z(t) \le A. \quad (9)$$

The decision variable $J$ explicitly shows how many additional ages will be forbidden at time $t$ compared to ones forbidden

<footnote n="1">¹In this paper, $[a, b]$ refers to the discrete interval $\mathbb{N} \cap [a, b]$ where $a, b \in \mathbb{N}$</footnote>
at time $t-1$. This makes $J$ a suitable control variable for the optimal control problem and $I$ one of its state variables.

In addition, $\Pi_{az}(t)$ is a variable that indicates if vehicles of age $a$ are forbidden in zone $z$ at time $t$. It equals 1 if vehicles are forbidden or 0 if they are not, and is defined as

$$ \Pi_{az}(t) = \mathbf{1}_{\{I_z(t) \le a\}} = \begin{cases} 1 & \text{if } I_z(t) \le a \\ 0 & \text{if not.} \end{cases} \quad (10) $$

## 2) Disposal function and probability of purchase:

The disposal function $\sigma_{az}(t)$ can be simply defined as being equal to 1 if the vehicle is banned and 0 otherwise. However, to reflect realistic behaviour of vehicle owners —who may not always dispose of a banned vehicle or may get rid of it even before it is banned— we introduce two factors $K_M < 1$ and $K_m > 0$, whose values can be estimated more accurately through further studies. Figure 2 shows the three different pathways of vehicles’ disposal considered for our study. For banned vehicles ($\Pi = 1$), the fraction of those that are disposed of is $K_M$. For vehicles that are not banned in zone $z$, two pathways are feasible depending on the number of bans in neighbouring areas.

* If no bans are enforced in $z$'s neighboring zones, the disposal ratio is $K_m$.

* If neighbouring zones enforce bans, the ratio becomes $K_\nu(t)$, and is adjusted based on the number of neighbouring zones with bans.

Let $\nu(z)$ represent the number of $z$'s neighbours and $\nu_z = \mathbf{1}_{\{\nu(z)=0\}}$. The disposal ratio $K_\nu(t)$ increases with the number of neighbouring zones where the vehicle is forbidden, within the range $K_m < K_\nu(t) < K_M$. and is calculated as

$$ K_{\nu}(t) = \min \left( K_{lim} \sum_{z' \in \nu(z)} \Pi_{az'}(t), K_{lim,max} \right). \quad (11) $$

This formula scales the contribution of restrictive neighbors by multiplying the number of forbidden neighboring zones by $K_{lim}$. To ensure $K_\nu(t)$ does not exceed $K_M$, it is capped by $K_{lim,max}$, such that $K_m < K_{lim} < K_{lim,max} < K_M$.

<figure><img src="image_3.png" /><figcaption>Fig. 2. Schematic representing the three pathways to vehicle disposal</figcaption></figure>

Finally, the formulation of the disposal function is

$$ \sigma_{az}(t) = K_M \Pi_{az}(t) + (\nu_z K_m + (1 - \nu_z) K_\nu(t))(1 - \Pi_{az}(t)). \quad (12) $$

In order to determine the values of both probabilities of purchase (ICE and electric) (cf. (13)), we use the utility functions $U_1$ and $U_2$ deployed in [17] (cf. Equation (6)) and a logit discrete choice model (cf. Equation (5) in [17]). We would not allow the purchase of ICE vehicles for zone $z$ if all ICE vehicles have been definitively forbidden for all ages, i.e. if $\Pi_{0z}(t) = 1$. Here are the expressions of such ratios

$$ P_{1z}(t) = \frac{e^{\mu U_1(t)}}{\sum_v e^{\mu U_v(t)}} (1 - \Pi_{0z}(t)), \quad (13a) $$

$$ P_{2z}(t) = \frac{e^{\mu U_2(t)}}{\sum_v e^{\mu U_v(t)}} (1 - \Pi_{0z}(t)) + \Pi_{0z}(t). \quad (13b) $$

## C. Optimal Control Problem (OCP)

In order to account for citizen well-being and acceptance of LEZ implementation, we use a constrained optimization framework. The aim is to find the optimal decision variable $J$ that minimizes the total number of vehicles that were disposed of because of the LEZ throughout the years, $R$, while ensuring that $CO_2$ emissions at horizon time $T$ stay below a decision-maker-defined threshold $\bar{E}$, aligned with the European Commission's target for 2050.

Through (1), (2), (3), (4), (5), (7), (10), (12) and (13), we express the state variables $S_{vaz}(t)$ and $J_z(t)$ as

$$ S_{vaz}(t) = f_S(J_z(t), S_{vaz}(t-1), I_z(t-1), t), \quad (14a) $$

$$ I_z(t) = f_I(J_z(t), I_z(t-1)). \quad (14b) $$

Similarly, through (3), (10) and (12), $R_{vaz}(t)$ is expressed as

$$ R_{vaz}(t) = f_R(J_z(t), I_z(t-1), S_{vaz}(t-1)), \quad (15) $$

Finally, through (6) and (14a), the emissions are expressed as

$$ E(t) = f_E(J_z(t), I_z(t-1), S_{vaz}(t-1), t). \quad (16) $$

In summary, the OCP is formulated as follows

**Objective function**

$$ \min_J R = \sum_{1 \le t \le T} \sum_{az} f_R(J_z(t), I_z(t-1), S_{1az}(t-1)) $$

**State equations**

$$ \begin{pmatrix} S_{vaz}(t) \\ I_z(t) \end{pmatrix} = \begin{pmatrix} f_S(J_z(t), S_{vaz}(t-1), I_z(t-1), t) \\ f_I(J_z(t), I_z(t-1)) \end{pmatrix} $$

**State constraints**

$$ \begin{aligned} S_{vaz}(t) &> 0 \\ 0 &\le I_z(t) \le A \end{aligned} $$

**Control constraint**

$$ -1 \le J_z(t) \le D_z $$

**Terminal constraint**

$$ E(T) = f_E(J_z(T), I_z(T-1), S_{vaz}(T-1), T) \le \bar{E} $$

**Initial conditions**

$S(0)$ (cf. Subsection III-B and Table I)

$I(0)$ (cf. Table I)

(17)
### D. Resolution method

Due to the problem's complexity and state constraints, the solution is obtained using a numerical approach, namely a genetic algorithm (cf. Section IV). The latter evolves a population of candidate solutions through selection, crossover, and mutation to progressively converge toward an optimal solution.

## III. CASE STUDY : ÎLE-DE-FRANCE REGION

This paper examines the evolution of the vehicle fleet and the implementation of LEZs in the Île-de-France region. For this study, the region is divided into six successive rings expanding outward from Paris. The first zone corresponds to Paris itself. The second zone includes the intermunicipalities bordering Paris. The third zone contains the intermunicipalities neighbouring those in the second zone, and so on, as illustrated in Fig 3. This zoning approach simplifies the implementation of distinct LEZ policies for each ring.

<figure><img src="image_4.png" /><figcaption>Fig. 3. Boundries for the 6 chosen rings of the Île-de-France region (red), for the 63 intermunicipalities (white) and for the current LEZ in the Parisian region (blue)</figcaption></figure>

### A. The initial schedule for 2025

The Greater Paris Metropolis has implemented LEZs since 2019 to improve air quality, starting with banning pre-1998 vehicles. Restrictions have progressively tightened as the vehicle fleet modernizes to meet European emissions standards (Euro Norms). As of January 1, 2025, the latest policy [18] prohibits diesel cars over 14 years old and gasoline cars over 19 years old (i.e. Crit'Air 3 vehicles) in the current Parisian LEZ (LEZ-m) (cf. [14]). Since shares of diesel (49.7%) and gasoline (48.2%) vehicles in Île-de-France are similar (2021), we can consider that the average banned vehicle age is approximately 16 or 17 years. Future studies will refine this estimate by segmenting ICE vehicles by fuel type. The current Parisian LEZ roughly overlaps with rings 1 and 2 of this paper's zoning.

Table I presents the chosen initial values of the state variable $I_z(t)$ and the maximum allowed ban rate $D_z$ for each ring $z$, which serve as numerical references for this study. $I_z(0) = A$ indicates that only vehicles of age $A$ and more are banned. Since the oldest existing vehicles are assumed to be of age $A-1$, setting $A$ means no bans are applied in that ring.

<table><caption>TABLE I
INITIAL VALUES OF THE STATE VARIABLES FOR YEAR 2025 AND THE CHOSEN MAXIMUM BAN RATE $D_z$ FOR EACH RING</caption><thead><tr><th></th><th>Ring 1</th><th>Ring 2</th><th>Ring 3</th><th>Ring 4</th><th>Ring 5</th><th>Ring 6</th></tr></thead><tbody><tr><th>$I_z(0)$</th><td>16</td><td>17</td><td>A</td><td>A</td><td>A</td><td>A</td></tr><tr><th>$D_z$</th><td>4</td><td>3</td><td>3</td><td>2</td><td>2</td><td>1</td></tr><tr><th>$S_1(0)$</th><td>1.15M</td><td>2.09M</td><td>1.95M</td><td>0.89M</td><td>0.43M</td><td>0.16M</td></tr><tr><th>$S_2(0)$</th><td>8.99K</td><td>16.31K</td><td>15.18K</td><td>6.95K</td><td>3.37K</td><td>1.23K</td></tr></tbody></table>

### B. Parameters and exogenous inputs

The state variable $S$, was initialized for ICE ($S_1(0)$) and electric ($S_2(0)$) vehicles using french national level stock data from the French Ministry for the ecological Transition and Territorial Cohesion [20], with an additional segmentation to only account for the specified rings of the Île-de-France region by applying the appropriate proportion of the population (cf. Table I). Parameters such as the survival rate $\eta_a$, the emission factors $\epsilon_{va}(t)$ and $M(t)$ employed in (6) are explicitly estimated using data sources provided in [17]. However, instead of considering a time-dependent annual mileage $M(t)$, we use a fixed average mileage $M_0 = 13500$ Km/veh/year uniformaly for all years from present until 2050. The demand $G(t)$, used in (1) and other exogenous parameters of the utility functions ($U_1$ and $U_2$) and $\mu$ used in the logit model (13) are based on the DRIVE<sup>RS</sup> fleet model of the French Agency of Ecological Transition (ADEME) (cf. [17]). The numerical values chosen for the disposal ratios are $K_M = 0.75$, $K_m = 0.05$, $K_{lim} = 0.2$, and $K_{lim,max} = 0.6$.

### C. Genetic algorithm

The genetic algorithm was run with 50 individuals over 1000 generations, using crossover and mutation rates of 0.5 and 0.3.

## IV. RESULTS

For the backcasting runs, we have chosen a set of different scenarios:

* A "No LEZs" scenario where we suppose that LEZs have never been implemented in the Paris Region.

* A "reference" scenario, where no additional restrictions are introduced after 2025. This means that all the restriction rules up to 2025 will stay the same, but no new restrictions will be added after that. The final emissions in this reference scenario are noted as $\bar{E}_{ref}$.

* An "optimized" scenario, representing the solutions of OCP (17) for six different targets $\bar{E}^{(i)}$. For each target $i$, the terminal constraint is required to satisfy

$$E(T) \leq \bar{E}^{(i)} = \bar{E}_{ref}(1 - \beta^{(i)}) \quad (18)$$

Table II shows the decrease percentages $\beta^{(i)}$ for each target. The emissions shown in Figure 4 highlight the differences between the scenarios over time. The "No LEZs" scenario (blue line) follows a trend similar to that observed in [17], but specific to the Île-de-France region rather than the whole of France. The reference scenario (black line) shows a steady decline in emissions, reflecting the impact of policies already
<table><caption>TABLE II
DESIRED DECREASE PERCENTAGE FOR EACH TARGET</caption><thead><tr><th>Targets</th><th>1</th><th>2</th><th>3</th><th>4</th><th>5</th><th>6</th></tr></thead><tbody><tr><th>β<sup>(2)</sup></th><td>35%</td><td>45%</td><td>55%</td><td>65%</td><td>75%</td><td>85%</td></tr></tbody></table>

in place. For the optimized scenarios, emissions remain close to the reference scenario until around 2040. This could suggest that the GA considered the natural fleet renewal process was sufficient to sustain the moderate decline in emissions without introducing new policies. However, after 2040, the algorithm accounted for the constraints and began enforcing stricter measures to meet the predefined emission targets for 2050.

<figure><img src="image_5.png" /><figcaption>Fig. 4. Annual Emissions from 2026 to 2050</figcaption></figure>

Figure 5 shows the cumulative number of vehicles disposed of across different scenarios. The final value for $T$ (year 2050) corresponds to the running total of $R(t)$ throughout the years and represents the minimization criterion. In the "No LEZs"

<figure><img src="image_6.png" /><figcaption>Fig. 5. Number of vehicles that were disposed of because of the LEZ</figcaption></figure>

scenario (blue line), no vehicles are phased out (i.e. $R(t) = 0 \forall t$). The reference scenario (black line) shows the lowest possible values for $R(t)$ but is not null as people continue to dispose of their vehicles even if they are not banned. The optimized scenario targets demonstrate that the higher $R$ is, the lower $E(T)$ will be, emphasizing the trade-off between stricter vehicle disposal policies and their environmental impact.

In constrained optimization, visualizing the Pareto front is essential for decision-making as it highlights these trade-offs. Decision-makers can make more informed decisions by choosing to relax or tighten constraints and observing their impact on the objective function. The Pareto front in Fig. 6 illustrates this balance for the reference scenario and the six targets, where $E(T)$ is a function of the objective $R$.

<figure><img src="image_7.png" /><figcaption>Fig. 6. The Pareto front showing final emissions as a function of the total number of disposed vehicles, for the reference and the optimized scenarios</figcaption></figure>

The reference scenario (black line in Figs. 4 and 5) results in the highest emissions, corresponding to the lowest $R$ value. In contrast, target 6 (red line in Figs. 4 and 5) achieves the lowest emissions, linked to the highest $R$ value. The two breaking points in Fig. 6 represent targets 3 (light blue) and 4 (green). Both targets have nearly identical $R$ values (cf. Figs. 5 and 6) with a difference of 0.7%. However, target 4 achieves lower final emissions compared to target 3 (cf. Figs. 4 and 6) with a 22% decrease in emissions relative to target 3.

Figure 7 illustrates the policy of target 4, detailing the scheduled restrictions over the years for the six designated rings. The years of vehicles production, ranging from 1995 to 2050, are shown as a function of the corresponding years of ban. According to this policy, no restrictions are applied in

<figure><img src="image_8.png" /><figcaption>Fig. 7. Policy schedule suggested by the decision variable of scenario 4</figcaption></figure>

ring 6 while restrictions in ring 5 are delayed until 2048, in ring 4 until 2045, and in ring 3 until 2040. No new restrictions are scheduled between 2026 and 2040 for ring 1 and between
2026 and 2039 for ring 2. The restriction policies for rings 2 and 3 are at their highest rate : $D_2 = D_3 = 3$ from 2040 to 2048. Meanwhile, ring 1's restrictions reach their highest rate $D_1 = 4$ slightly later, from 2042 to 2049, ultimately achieving the highest restriction level by 2050. Overall, the policy imposes stricter restrictions on rings closer to Paris. For target 4, the schedule proposed by the GA leads to a total vehicle disposal number of $R = 5.2 \times 10^6$, which represents 78% of $S_1(0)$. The corresponding final emissions are valued at $E(T) = 471 \text{ ktCO}_2$, representing a 92% reduction compared to the initial emissions value $E(0)$ in the year 2025.

## V. CONCLUSION AND PERSPECTIVES

Applying a backcasting framework allows policymakers to ask the right questions, prioritize key targets, and explore innovative strategies to address mobility challenges. By continuously refining methodologies and integrating diverse policy levers, we can move towards more sustainable and efficient urban transport systems that benefit both the environment and public health. This paper has demonstrated the feasibility of the backcasting approach. Applied to LEZ policies in the Île-de-France region, and resolved using a genetic algorithm, the run results suggest the proper schedule of LEZ implementation to reach chosen emission targets, while limiting impacts on individuals' mobility by minimizing the number of vehicles disposed of in response to LEZs introduction.

Future research can further enhance the backcasting approach in several ways. Introducing a finer geographical disaggregation than the rings proposed in this paper could better reflect local characteristics in the implementation of LEZs. Additionally, incorporating ICE vehicle types, such as diesel, gasoline and plug-in hybrid vehicles, would provide a more accurate representation of the vehicle fleet and its evolution. Investigating user behaviour and refining disposal ratio $\sigma$ models with additional studies would also improve the framework's robustness. Beyond greenhouse gas emission reductions, future work should consider air quality indicators such as nitrogen oxides ($NO_x$) and particulate matter (PM), given their significant health impacts. Combining LEZs with complementary measures, such as incentives for electric vehicle adoption, improvements in public transport infrastructure, or urban planning strategies that promote active mobility (e.g., cycling infrastructure and safety measures), could provide a more comprehensive and effective policy roadmap. A diversified approach would not only optimize environmental benefits but also enhance economic feasibility and social acceptance. The genetic algorithm has provided initial results, but further validation is necessary. Exploring alternative optimization methods, such as parametric optimization, could offer valuable perspectives and improve problem-solving efficacy.

## ACKNOWLEDGMENT

This research benefited from aid managed by the Agence nationale de la recherche (ANR), under France 2030, within the project FORBAC bearing the reference ANR-23-PEMO-0002.

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