Optimal Placement and Cost Analysis of Electric Vehicle Charging Stations Using Metaheuristic Optimization

Abstract

The rapid adoption of electric vehicles (EVs) has made the strategic deployment of charging infrastructure a critical task for sustainable mobility. This study formulates the siting of EV charging stations as a p-median problem and applies two metaheuristic approaches—genetic algorithm (GA) and ant colony optimization (ACO)—to solve it. The cost function, defined as the combination of transportation and installation costs, was analyzed in various scenarios. The results show that ACO consistently outperforms GA, offering lower total costs and shorter solution times. Crucially, the work uses optimization results published in the literature to expand the comparison beyond GA, using GA as a typical baseline. The suggested framework is adaptable and can be used to solve different spatial planning and facility location issues. This paper offers a data-driven, scientifically based approach for EV charging infrastructure development by combining cost effectiveness and service accessibility. In addition to providing decision-makers with useful tactics for creating dependable and sustainable charging networks, it helps handle the temporal and geographical coordination issues in EV charging.

1. Introduction

The increase in the usage of electric vehicles is strategically significant for urban transportation planning, spatial resource allocation, and energy infrastructure. Because of this, choosing the best site for charging stations is essential for sustainable urban growth. The literature looks at the infrastructure needs for charging electric cars (EVs) as they become more common. For the creation of effective and sustainable charging infrastructure, important elements such as station locations, network load modeling, and scheduling strategies are examined, and optimization techniques are suggested [1]. In this context, they developed a two-stage model considering distributed energy resources and electric vehicle penetration. This model determines the location and capacity of charging stations and aims to incorporate grid operating costs, user behavior, and uncertainties related to renewable energy [2]. Electric vehicles have been increasingly popular in recent years due to the negative effects of fossil fuel usage on performance and the expense of lowering CO₂ emissions. However, these developments are severely hampered by the dearth of charging facilities required for the effective use of electric products, unequal access to charging stations, and high installation prices [3,4]. Limited driving range, and particularly range anxiety, directly impacts consumers’ preferences for electric vehicles. A well-planned charging network has been suggested as a solution to this problem [3]. Various optimization methods have been proposed in the literature for the optimal location and capacity allocation of charging stations. These studies have considered various factors such as time and space-based demand modeling, distribution network impact, carbon emissions, social equity, user behavior, and infrastructure costs [5,6,7,8]. Some studies have attempted to achieve a uniform distribution of fast charging stations on major road networks using models supported by geographic information systems (GIS) [3]. Others have attempted to find solutions in large-scale systems using metaheuristic methods such as genetic algorithm (GA), ant colony optimization (ACO), particle swarm optimization (PSO), and, more recently, heuristic algorithms supported by deep learning [5,7,9,10]. Two-stage planning models aim to optimize both user behavior and grid operating conditions with frameworks that consider renewable energy integration (DER) and uncertainties [4,7,11]. Attempts have been made to develop models that evaluate social, environmental, and economic impacts using multi-criteria decision-making methods [6,12,13]. Some studies have tested the impact of planned settlements using a simulation infrastructure based on real road networks and open city-level data sources. The goal is to improve system performance by optimizing load density distribution [5,14,15]. This study aims to contribute to the location selection of electric vehicle charging stations by proposing a p-median multi-objective model that considers transportation and installation costs. The novelty of this study is the integration of transportation and installation costs into a p-median-based multi-objective model and a scenario-based comparison of GA and ACO. Thus, it provides a transferable framework for planning sustainable charging infrastructures for electric vehicles. GA and ACO algorithms are compared on a scenario basis, and the results are compared with other optimization approaches in the literature; GA is presented as a representative example. ACO is determined to be more efficient under budget-constrained planning conditions. The developed model aims to provide a general solution framework that can be adapted not only to electric vehicle infrastructure but also to other spatial decision-making problems. Furthermore, a data-driven planning approach can provide novel contributions to addressing gaps in the literature on the development of sustainable and viable electric vehicle infrastructure.

The key features of the metaheuristic algorithms proposed in our study can be summarized as follows. GA is an evolutionary search method inspired by natural selection and genetic principles, exploring the solution space through operators such as selection, crossover, and mutation. ACO is a method based on ant nests, stimulated by their foraging behavior. In it, artificial agents constantly generate solutions and directly search for the best locations through pheromones. Both methods are particularly suitable for solving complex spatial problems, such as nonlinear, multi-objective, and large-scale development systems. The remainder of the paper is organized as follows: Section 2 describes the materials and methods, including the mathematical formulation and development of the implemented algorithms. Section 3 presents and discusses the simulation results and the comparative performance analysis of GA and ACO. Section 4 concludes the paper with conclusions and main suggestions for future research.

2. Materials and Methods

The increasing prevalence of EV infrastructure necessitates the strategic location of charging stations. The optimal location should be determined by considering the distance between demand points and stations, as well as installation costs. This study mathematically formulates the EV charging station placement problem and utilizes ACO and GA optimization methods to solve it. GA represents an evolutionary algorithm inspired by the principles of natural selection. ACO reflects a swarm intelligence-based approach inspired by the foraging behavior of ants. Both algorithms are frequently used in facility location selection and electric vehicle charging station placement problems, and successful results have been achieved [16,17].

2.1. Problem Formulation

The aim of our study is to minimize access costs by locating EV charging stations in convenient locations. This minimizes the installation costs of the stations, thus reducing overall costs.

Equations (1) and (2) give the expression of decision variables to place electric vehicle charging stations in suitable locations [18].

$$f_j=\left\{\begin{array}{l}1 \mathrm{if} \mathrm{station} \mathrm{j}. \mathrm{is} \mathrm{active}\\ 0 \mathrm{in} \mathrm{other} \mathrm{cases}\end{array}\right.$$

(1)

f_j ∈ {0, 1}, j ∈ {1,…,M}

(2)

2.1.1. Objective Function

Heuristic algorithms for optimal placement of electric vehicle charging stations use Equation (3) as the objective function.

$$\min z={\omega }_1.z_1+{\omega }_2.z_2$$

(3)

In Equation (3), z represents the total cost (the value to be optimized). z₁ and z₂ represent the transportation cost based on the distance to the stations where the demand points are assigned and the installation cost of the selected stations, respectively. w1 is the coefficient of the distance cost. w₂ is the coefficient of the cost of opening a station. In Equation (3), the cost function was tested under four different weight combinations $(w_1, w_2)$ to represent varying priorities between transportation and installation costs. The equal-weight case $(w_1=1.0, w_2=1.0)$ reflects a balanced scenario, while $(w_1=0.9, w_2=1.1)$ emphasizes budget constraints, and $(w_1=1.1, w_2=0.9)$ moderately prioritizes user accessibility. The extreme case $(w_1=1.2, w_2=0.8)$ assigns the highest importance to transportation costs, simulating planning conditions where minimizing user travel distances is critical. These weight settings are consistent with sensitivity analysis approaches commonly found in the literature [19,20,21], and they demonstrate the adaptability of the proposed model to different planning priorities.

The weighted cost of transportation is calculated by multiplying the distance from each demand point to the nearest open station by the demand at that point. The transportation cost is given in Equation (4).

$$z_1={\displaystyle \sum _{i=1}^N{d}_i.D_{\min }^{(i)}}$$

(4)

In Equation (4), N represents the number of demand points, di represents the demand quantity for the ith demand point, and $D_{\min }^{(i)}$ represents the distance to the nearest open station for the ith demand point. Equation (4) calculates the weighted transportation cost by multiplying the distance from each demand point to the nearest open station ($dis{t}_i$) with its associated demand quantity ($d_i$). Here, $d_i$ reflects the estimated daily charging demand at point $i$, derived from local traffic density, residential/commercial land-use, and EV ownership distribution. This formulation ensures that both demand magnitude and spatial accessibility are captured in the cost evaluation.

Equation (5) gives the station installation cost [18].

$$z_2={\displaystyle \sum _{j=1}^M{f}_j. c_j}$$

(5)

In Equation (5), M represents the number of all potential station points, fj ∈ {0,1} is the decision variable indicating whether the jth station is open (1) or closed (0), and c_j represents the fixed installation cost of the jth station. Only the costs of open stations are calculated in this study. The total setup cost is created by multiplying the setup cost by the decision variable.

2.1.2. Constraints

The minimum station constraint equation is given in Equation (6). The number of open stations must be at least H.

$${\displaystyle \sum _{j=1}^M{f}_j}\ge H$$

(6)

f_j ∈ {0, 1}

(7)

In Equation (7), the binary expression of the decision variables is given.

2.2. Mathematical Modeling of the P-Median Facility Location Selection Problem

The p-median facility location problem was first formulated by Revelle and Swain. The objective of this model is to minimize the total weighted distance from all demand points to the facilities to which they are assigned [22]. The objective function used in this problem aims to maximize service efficiency by minimizing the access distance between facilities and demand points.

$$\min {\displaystyle \sum _{i=1}^n{\displaystyle \sum _{j=1}^n{\omega }_i{d}_{ij}{x}_{ij}}}$$

(8)

$${\displaystyle \sum _{j=1}^n{x}_{ij}}=1 \forall ij i,j=1,2,.....,n$$

(9)

$$x_{ij}\le y_j \forall ij i,j=1,2,.....,n$$

(10)

$${\displaystyle \sum _{j=1}^n{y}_j}=p$$

(11)

$$x_{ij},y_j \in \left\{0\left.,1\right\}\right. i,j=1,2,......,n$$

(12)

$$x_{ij}\{\begin{array}{l}1 \mathrm{if} \mathrm{customer} \mathrm{i} \mathrm{is} \mathrm{assigned} \mathrm{to} \mathrm{facility} \mathrm{j}\\ 0 \mathrm{in} \mathrm{other} \mathrm{cases}\end{array} \}$$

(13)

$$y_j\{\begin{array}{l}1 \mathrm{if} \mathrm{a} \mathrm{facility} \mathrm{is} \mathrm{opened} \mathrm{at} \mathrm{point} \mathrm{j}\\ 0 \mathrm{in} \mathrm{other} \mathrm{cases}\end{array} \}$$

(14)

In Equations (8)–(14), wi represents the demand at point i, n represents the total number of demand points, d_ij represents the shortest distance between point i and point j, and p represents the median number (number of facilities). In Equation (8), in the objective function, ${\omega }_i$ represents the demand quantity at demand point i, and $d_{ij}$ represents the distance between demand point i and potential facility j. $x_{ij}$ represents a binary decision variable that takes the value 1 if demand point i is assigned to facility j, and 0 otherwise. Equation (8) aims to minimize the weighted total distance of all demand points to assigned facilities. In this way, the model aims to reduce user access distances while increasing the overall cost-effectiveness of the system. The objective function of the p-median facility location selection problem is defined by Equation (8), and the main objective of the model is to minimize the total service cost between served facilities and demand points. The requirement that each demand point be assigned to only one facility is a fundamental constraint that ensures the integrity of the model and is expressed in Equation (9). Equation (9), the binary variable $x_{ij}$, represents the assignment of demand point $i$ to facility $j$. This constraint aims to ensure that each demand point is served by a single facility. This prevents unassigned demand points and multiple assignments to different facilities. By implementing this constraint, the model reflects realistic facility planning conditions where each demand must be met uniquely and completely. The constraint that a demand point can only be assigned to open facilities is defined to ensure the applicability of the model, and this dependency is illustrated in Equation (10). In Equation (11), $y_j$ is a binary decision variable that takes the value 1 if facility $j$ is selected and 0 if it is not. $p$ represents the specified number of facilities to be opened. This constraint ensures that the model selects exactly $p$ facilities from all candidates. Thus, it represents a planning condition where the number of facilities is limited for budgetary or strategic reasons. Finally, the fact that the number of active facilities is limited by p represents a capacity constraint on the system and is mathematically modeled in Equation (11) [22,23,24,25,26].

2.3. Genetic Algorithm Modeling

In this study, GA, an evolutionary approach suitable for the electric vehicle charging station location selection problem, was used due to the complexity of the solution space and the multitude of possible solution combinations.

2.3.1. Individual (Solution) Representation

$$f=\left[f_1,f_2,....,f_M\right]$$

(15)

In Equation (15), everyone is defined as a binary vector f. If each element is 1, that station is active; if it is 0, that station is inactive.

2.3.2. Initial Population

The initial population is given in Equation (16). H random stations are tried to be created so that individuals are active.

$$po{p}_i= Random Binary Vector Where{\displaystyle \sum f_j}\ge H$$

(16)

2.3.3. Selection

In our study, we used the Roulette Wheel Method and the Tournament Selection Metod.

$$P_i={\displaystyle \frac{e^{-\beta .z_i/x_{max}}}{{\displaystyle {\sum }_{k=1}^{nPop}{e}^{-\beta .z_k/x_{max}}}}}$$

(17)

In Equation (17), zi represents the cost of the ith individual, while β represents the selective pressure parameter.

In the Tournament Selection method, m individuals are randomly selected, and the lowest cost individual is chosen as the parent.

2.3.4. Crossover

The expression for Simple Single Point Crossing is given in Equations (18) and (19). The expression cc in Equations (18) and (19) represents the crossover point (randomly selected).

$$y_1=\left[x_1(1:cc), x_2(cc+1:end)\right]$$

(18)

$$y_2=\left[x_2(1:cc), x_1(cc+1:end)\right]$$

(19)

$$y_1=\left[x_1(1:c_1), x_2(c_1+1:c_2),x_1(c_2+1:end)\right]$$

(20)

$$y_2=\left[x_2(1:c_1), x_1(c_1+1:c_2),x_2(c_2+1:end)\right]$$

(21)

$${\alpha }_j\sim \left\{0,\left.1\right\}\right.\Rightarrow \left\{\begin{array}{l}{y}_1=\alpha .x_1+(1-\alpha ).x_2\\ y_2=\alpha .x_2+(1-\alpha ).x_1\end{array}\right.$$

(22)

The expression for double-point crossing is given in Equations (20) and (21). The expression for regular crossover is given in Equation (22). After the crossover process, Equation (16) is checked again.

2.3.5. Mutation

The equation for the mutation process is given in Equation (23). In Equation (23), some bits (station status) of everyone are randomly changed at a certain rate. However, after the mutation, Equation (16) check is repeated.

$$y_j=\left\{\begin{array}{l}1-x_j \mathrm{if} j \in \mathrm{selected} \mathrm{positions}\\ x_j \mathrm{other} \end{array}\right.$$

(23)

2.3.6. Elitism and the New Population

The expression for the Elitism equation is given in Equation (24). In our study, the lowest cost nPop individual is selected while preserving the best solutions.

(New Pop = Parents + Offspring + Mutants)

(24)

GA is applied as a population-based evolutionary search method that uses the standard steps of representation, selection, crossover, mutation, and elitism. Its implementation for EV charging-station placement follows conventional formulations in the literature; a schematic diagram and the pseudocode of the GA procedure are provided in Figure 1.

2.4. Modeling Ant Colony Optimization

In this study, ant colony optimization (ACO), a heuristic method inspired by the behavior of ants in nature, was applied to improve the solution quality in charging station location selection and to reach the global optimum without getting stuck in the local minimum [27,28,29,30,31,32,33]. The aim is to find the optimum station locations (vector f) to minimize the total cost (z) defined in Equation (3).

2.4.1. Pheromone Matrix (τ)

The pheromone matrix equation is given in Equation (25). Initially, it is assigned equally for all stations.

$${\tau }_j=1 \forall j \in \left\{1,.....,\left.M\right\}\right.$$

(25)

$${\tau }_j=(1-\rho ). {\tau }_j+{\displaystyle \sum _{k=1}^n\frac{\phi }{z_k}}+{\displaystyle \sum _{elit}\frac{{\phi }^{\prime }}{z_{elit}}}$$

(26)

Equation (26) gives the update expression at each iteration. In Equations (25) and (26), ρ represents the pheromone evaporation rate, zk represents the cost of the solution created by the kth ant, φ represents the pheromone contribution coefficient, and elite solutions: the best-found solutions represent the solutions that receive additional pheromone contribution [29].

2.4.2. Intuitive Knowledge (ƞ)

The heuristic information equation is given in Equation (27). It is used to give lower selection probability to high-cost stations and is then normalized.

$${\eta }_j={\displaystyle \frac{1}{c_j^2+\epsilon }}$$

(27)

2.4.3. Probability Calculation (P)

The probability (P) equation is given in Equation (28). The probability vector in Equation (28) determines which points the ants will prefer when selecting stations. Ants make their choice stochastically according to the probability distribution in Equation (28).

$$P_j={\displaystyle \frac{{({\tau }_j)}^{\alpha }. {({\eta }_j)}^{\beta }}{{\displaystyle {\sum }_{l=1}^M{({\tau }_l)}^{\alpha }. {({\eta }_l)}^{\beta }}}}$$

(28)

In Equation (28), α represents the pheromone effect and β represents the heuristic information effect. A curve showing the change in total cost is created using the best cost values obtained through iterations.

(ACO) is employed as a swarm intelligence-based metaheuristic inspired by the foraging behavior of ants, where pheromone trails guide the probabilistic construction of solutions. The main steps and pseudocode include pheromone initialization, solution construction, pheromone updating, and stochastic selection, as illustrated in Figure 2.

3. Results & Discussion

This study was conducted in Dadaşkent, Aziziye District, Erzurum Province, using two scenarios with 1035 and 1535 demand points, respectively. The different search densities provided a comparative assessment of the consistency and flexibility of the optimization models. The primary objective of the study is to develop a feasible roadmap for optimal planning of the location and capacity of electric vehicle charging infrastructure at the regional level. The total cost function is evaluated under different weighting combinations: (w₁ = 0.9; w₂ = 1.1), (w₁ = 1; w₂ = 1), (w₁ = 1.1; w₂ = 0.9), and (w₁ = 1.2; w₂ = 0.8). These scenarios reflect the trade-off between transportation and installation costs at different levels and allow comparison of algorithm performance under multiple conditions. For this purpose, genetic algorithm (GA) and ant colony optimization (ACO) methods were used, and their performances were compared. Both metaheuristic approaches proved effective in solving the inherently NP-hard p-median location problem. The comparison results demonstrate the methods’ success in minimizing total service costs and access distances, as well as their adaptability to different demand scenarios and weighting combinations.

3.1. GA and ACO Results for 1035 Demand Points and 40 Station Locations

In this scenario, 1035 demand points and 40 station locations were considered. Optimization was performed using GA and ACO algorithms, and both methods successfully solved the p-median problem. The results showed that station locations are critical in determining total costs and range.

While solving the problems, the population size for the GA was set as nPop = 100, the maximum iteration number as MaxIt = 100, the crossover percentage as pc = 0.8, and the number of offspring as nc = 2 × round (pc × nPop/2) according to this relationship. The mutation percentage was taken as pm = 0.3, and the number of mutated individuals was calculated using nm = round (pm × nPop). In addition, the mutation rate was set as μ = 0.05 [34,35].

The following parameters were used for ACO: maximum iteration number of 100, ant population of 100, pheromone evaporation rate of 0.05, pheromone weighting factor of 1, fitness weighting factor of 2, and initial pheromone concentration of 1. For ACO, parameters such as the number of ants, pheromone evaporation rate, and heuristic coefficients ($\alpha ,\beta$) were also adopted from the literature and fine-tuned through preliminary tests to achieve stable convergence [36,37]. The results of the optimization performed with these parameters are presented in

Table 1. GA-based station positioning results (1035 demand points).

Weights	Method	Number of Stations	Best Cost (Unit)	Time (Sec)
w1 = 0.9 w2 = 1.1	Roulette Wheel Method	5	528,423.8403	18.755
		10	1,507,898.3917	19.3474
		15	2,600,142.952	21.4276
		20	3,910,835.8669	21.7708
		25	6,095,324.9715	20.4426
		30	9,153,610.4172	20.2904
	Tournament Selection Method	5	528,423.8403	18.8981
		10	1,507,898.3917	21.0609
		15	2,600,142.952	24.5617
		20	3,910,835.8669	19.8669
		25	6,095,324.9715	21.6699
		30	9,153,610.4172	26.1362
	Random Solution Method	5	528,423.8403	20.7837
		10	1,507,898.3917	21.1595
		15	2,600,142.952	22.0567
		20	3,910,835.8669	20.296
		25	6,095,324.9715	19.9503
		30	9,153,610.4172	19.657
[13,26] w1 = 1 w2 = 1	Roulette Wheel Method	5	480,387.6003	21.0337
		10	1,370,818.2130	24.1918
		15	2,363,767.7244	23.8657
		20	3,555,306.5187	25.2528
		25	5,541,205.5238	21.0406
		30	8,321,464.908	22.2517
	Tournament Selection Method	5	480,387.6003	22.0521
		10	1,370,818.2130	21.6374
		15	2,363,767.7244	21.0744
		20	3,555,306.5187	20.9676
		25	5,541,205.5238	21.3158
		30	8,321,464.908	21.5167
	Random Solution Method	5	480,387.6003	20.6076
		10	1,370,818.2130	20.8197
		15	2,363,767.7244	20.4193
		20	3,555,306.5187	20.6475
		25	5,541,205.5238	20.216
		30	8,321,464.908	21.1915
w1 = 1.1 w2 = 0.9	Roulette Wheel Method	5	432,351.3604	20.7088
		10	1,233,738.0343	25.7194
		15	2,127,392.4969	26.8998
		20	3,199,777.1706	24.7711
		25	4,987,086.0762	24.0061
		30	7,489,319.3988	25.4554
	Tournament Selection Method	5	432,351.3604	21.9336
		10	1,233,738.0343	22.3719
		15	2,127,392.4969	28.4227
		20	3,199,777.1706	28.3149
		25	4,987,086.0762	25.8091
		30	7,489,319.3988	22.1446
	Random Solution Method	5	432,351.3604	23.8509
		10	1,233,738.0343	21.2729
		15	2,127,392.4969	21.0781
		20	3,199,777.1706	25.4831
		25	4,987,086.0762	24.1565
		30	7,489,319.3988	21.4968
w1 = 1.2 w2 = 0.8	Roulette Wheel Method	5	384,315.1204	21.8645
		10	1,096,657.8556	20.2901
		15	1,891,017.2693	21.8783
		20	2,844,247.8225	23.1534
		25	4,432,966.6286	25.4719
		30	6,657,173.8895	26.0406
	Tournament Selection Method	5	384,315.1204	21.9265
		10	1,096,657.8556	25.0044
		15	1,891,017.2693	25.1768
		20	2,844,247.8225	22.6945
		25	4,432,966.6286	22.5757
		30	6,657,173.8895	26.8153
	Random Solution Method	5	384,315.1204	25.1584
		10	1,096,657.8556	22.2908
		15	1,891,017.2693	26.7027
		20	28,44,247.8225	21.6301
		25	4,432,966.6286	22.5041
		30	6,657,173.8895	22.3328

and

Table 2. ACO-based station positioning results (1035 demand points).

Weights	Number of Stations	Best Cost (Unit)	Time (Sec)
w1 = 0.9 w2 = 1.1	5	406,480.4864	10.2387
	10	1,333,409.1116	10.854
	15	2,590,965.6989	11.9365
	20	4,016,561.4344	13.1641
	25	5,783,681.077	16.5156
	30	7,713,389.9023	17.3751
w1 = 1 w2 = 1	5	369,528.9233	9.6294
	10	1,133,334.7828	10.0508
	15	2,434,284.3612	10.8504
	20	3,651,420.4174	11.4383
	25	5,179,035.0467	11.5601
	30	6,706,650.1152	11.7645
w1 = 1.1 w2 = 0.9	5	332,578.141	9.853
	10	1,020,001.2934	10.0143
	15	2,048,911.8862	10.3737
	20	3,219,765.9901	11.7497
	25	4,661,132.634	11.8491
	30	6,310,956.8056	11.959
w1 = 1.2 w2 = 0.8	5	295,627.0157	10.8451
	10	906,670.2993	11.4015
	15	1,884,342.1174	11.7966
	20	3,106,433.4264	12.8718
	25	4,021,020.3409	12.9210
	30	5,609,740.2526	13.8997

.

A combined analysis of Table 1 and Table 2 reveals significant differences in cost, solution time, and number of functions. From a cost perspective, the total cost of GA results increased steadily as the number of stations increased, reaching approximately 9.15 million units at 30 stations. In contrast, ACO achieved lower costs under the same conditions at 7.71 million units, yielding approximately 15–20% better results than GA, particularly with fewer stations.

Whereas ACOs took 10 to 17 s to solve, GAs took 20 to 26 s. This illustrates the increased time efficiency of ACO. ACO ran 5095 functions per trial, whereas GA ran 11,100 functions. This implies that ACO can accomplish comparable or superior outcomes with less computing work.

The findings demonstrate that ACO performs better than GA in terms of cost, solution time, and computing effort. This is in line with research findings and implies that ACO can offer more effective solutions, particularly in urban planning scenarios with limited funding. While GA inherently offers more flexible selection methods (roulette, tournament, random), it lags ACO in terms of solution quality and speed. Therefore, ACO can be considered a more rational choice for low-capacity station planning problems, both in terms of cost and time efficiency.

Comparative cost graphs for 30 station locations with GA and ACO solution methods are given in Figure 3.

Looking at the graphs in Figure 3, the ACO method achieves lower costs and faster convergence compared to the GA method for 1035 demand points across all weighting combinations. While the GA methods stabilized after a certain number of iterations, the ACO method provided more efficient solutions and gradually reduced costs.

Figure 3a–d show the cost convergence comparison graphs of the GA and ACO algorithms for 30 charging stations and 1035 demand points under four different weight combinations: (w₁, w₂) = (0.9; 1.1), (1.0; 1.0), (1.1; 0.9), and (1.2; 0.8). The results show a sharp decline in the initial iterations for GA (roulette, tournament, and random solution methods). However, the equilibrium is reached after approximately 2000 iterations. ACO consistently outperforms GA in all scenarios. It also achieves lower final cost values and demonstrates gradual improvements throughout the iteration process. Comparing the weighting configurations, it is found that (w₁ = 1.2, w₂ = 0.8) yields the most efficient results. In this scenario, ACO achieves a final cost of approximately 5.5 × 10⁶, which is significantly lower than the cost levels achieved in the other cases. More critically, significantly fewer function evaluations are required to reach convergence. Because the algorithms’ calculations are unpredictable, the shapes begin at different points. ACO finds better outcomes with just 5095 function evaluations, whereas GA needs about 11,100 function evaluations to identify the ideal answers. It is understood that ACO uses greater processing power to accomplish these goals in addition to offering reduced total expenses. This implies that ACO is especially well-suited for large-scale electric vehicle charging infrastructure development, where time and computational resources are crucial. The focus on transportation expenses (w₁) and the slight decrease in setup costs (w₂) is responsible for this efficiency, which results in more balanced solutions that reduce user trip distances and enhance accessibility. ACO’s distributed search mechanism enables adaptive exploration and exploitation of the solution space, requiring fewer convergence evaluations compared to GA’s evolutionary operators. The superiority of the ACO (w1 = 1.2, w2 = 0.8) configuration demonstrates strong performance in addressing large-scale facility location and transportation planning problems thanks to the adaptive and distributed search mechanisms of ant colony-based approaches [19,20,21]. These results suggest that incorporating higher weights for transportation costs not only minimizes user access distances but also leads to lower overall costs through improved computational efficiency. Thus, they provide evidence supporting more sustainable and practical electric vehicle charging infrastructure planning. Figure 4 shows a concentration and some imbalance in the central areas of the station distribution obtained with GA (random solution). However, Figure 5 shows that ACO distributes demand points more evenly and homogeneously across stations, particularly by minimizing access distances. While both methods solved the p-median problem, ACO provided a more even station distribution and more cost-effective solutions.

Figure 6a–d compare the performance of the GA under two different mutation rates ($pm=0.1$ and $pm=0.3$) for 30 charging station locations and 1035 demand points. The results show that both parameter settings achieve convergence within the first 2000 iterations, but they differ in convergence speed and stability. A lower mutation rate ($pm=0.1$) is consistent with commonly reported ranges in the literature and leads to faster convergence, while a higher mutation rate ($pm=0.3$) enhances solution diversity and prevents premature convergence, resulting in more stable outcomes across multiple runs. These findings indicate that parameter settings can influence convergence behavior, although the overall cost levels remain comparable in both scenarios. In addition, the results obtained with $pm=0.3$ are presented in Table 1, and the same values were also achieved with $pm=0.1$, though the solution time was longer in the $pm=0.1$ case. Furthermore, when considering the effect of the weight coefficients, the combination $(w_1=1.2,w_2=0.8)$ yields the lowest total cost and significantly reduces user access distances. This result suggests that assigning a higher weight to transportation costs relative to installation costs ensures more effective service coverage for demand nodes and enhances the practical applicability of station placement strategies in urban planning.

3.2. GA and ACO Results for 1535 Demand Points and 40 Station Locations

In this scenario, 1535 demand points and 40 station locations were considered. Both methods, optimized with the GA and ACO algorithms, effectively solved the p-median problem and demonstrated the impact of station locations on costs and access distances as demand density increases. Optimization results are presented in

Table 3. GA-based station positioning results (1535 demand points).

Weights	Method	Number of Stations	Best Cost (Unit)	Time (Sec)
w1 = 0.9 w2 = 1.1	Roulette Wheel Method	5	528,435.4063	29.5066
		10	1,507,905.9205	28.0497
		15	2,600,149.8967	28.839
		20	3,910,842.096	29.194
		25	6,095,330.6585	29.2244
		30	9,153,615.466	28.6504
	Tournament Selection Method	5	528,435.4063	29.2393
		10	1,507,905.9205	29.2085
		15	2,600,149.8967	29.8672
		20	3,910,842.096	29.2407
		25	6,095,330.6585	29.9993
		30	9,153,615.466	29.9799
	Random Solution Method	5	528,435.4063	29.5284
		10	1,507,905.9205	31.9647
		15	2,600,149.8967	31.2996
		20	3,910,842.096	30.0185
		25	6,095,330.6585	30.9585
		30	9,153,615.466	29.8658
w1 = 1 w2 = 1	Roulette Wheel Method	5	480,400.4515	29.408
		10	1,370,826.5783	29.0725
		15	2,363,775.4407	35.4018
		20	3,555,313.44	31.4103
		25	5,541,211.8428	30.1009
		30	8,321,470.5178	35.8789
	Tournament Selection Method	5	480,400.4515	33.5891
		10	1,370,826.5783	31.2243
		15	2,363,775.4407	36.3428
		20	3,555,313.44	34.5482
		25	5,541,211.8428	36.9039
		30	8,321,470.5178	30.2614
	Random Solution Method	5	480,400.4515	31.0121
		10	1,370,826.5783	32.1508
		15	2,363,775.4407	29.3197
		20	3,555,313.44	30.0639
		25	5,541,211.8428	29.647
		30	8,321,470.5178	29.9319
w1 = 1.1 w2 = 0.9	Roulette Wheel Method	5	432,365.4966	37.7539
		10	1,233,747.2361	38.1092
		15	2,127,400.9848	38.5319
		20	3,199,784.784	37.9094
		25	4,987,093.0271	38.2969
		30	7,489,325.5696	37.9782
	Tournament Selection Method	5	432,365.4966	38.4997
		10	1,233,747.2361	39.2898
		15	2,127,400.9848	38.8148
		20	3,199,784.784	39.4417
		25	4,987,093.0271	39.2178
		30	7,489,325.5696	38.8487
	Random Solution Method	5	432,365.4966	37.9232
		10	1,233,747.2361	37.6347
		15	2,127,400.9848	38.6011
		20	3,199,784.784	38.6867
		25	4,987,093.0271	38.2548
		30	7,489,325.5696	38.5946
w1 = 1.2 w2 = 0.8	Roulette Wheel Method	5	384,330.5418	38.1012
		10	1,096,667.894	38.7382
		15	1,891,026.5289	39.512
		20	2,844,256.128	37.9886
		25	4,432,974.2114	39.8795
		30	6,657,180.6214	38.2015
	Tournament Selection Method	5	384,330.5418	39.5944
		10	1,096,667.894	37.7204
		15	1,891,026.5289	38.8818
		20	2,844,256.128	39.9965
		25	4,432,974.2114	39.7603
		30	6,657,180.6214	38.4045
	Random Solution Method	5	384,330.5418	38.9016
		10	1,096,667.894	39.0349
		15	1,891,026.5289	39.6881
		20	2,844,256.128	38.4648
		25	4,432,974.2114	39.4757
		30	6,657,180.6214	38.3501

and

Table 4. ACO-based station positioning results (1535 demand points).

Weights	Number of Stations	Best Cost (unit)	Time (sec)
w1 = 0.9 w2 = 1.1	5	406,488.7741	20.0761
	10	1,333,415.3007	14.9639
	15	2,672,268.1518	15.1818
	20	4,520,678.9273	16.211
	25	6,033,017.8028	14.7424
	30	7,968,174.7858	15.5618
w1 = 1 w2 = 1	5	369,540.5805	16.0451
	10	1,364,960.011	15.4051
	15	2,508,192.4685	14.7589
	20	3,651,425.6321	15.6658
	25	5,331,801.4459	15.1888
	30	6,859,416.1255	15.8235
w1 = 1.1 w2 = 0.9	5	332,588.9296	15.3857
	10	1,090,981.566	16.7759
	15	2,119,891.1625	16.8678
	20	3,494,742.5288	18.2357
	25	4,869,595.171	17.399
	30	6,310,961.8369	15.7726
w1 = 1.2 w2 = 0.8	5	295,641.0043	15.7086
	10	969,768.8204	15.8662
	15	1,884,349.0268	17.7192
	20	3,106,439.1265	14.669
	25	4,328,531.7447	17.0717
	30	5,672,831.9384	15.7802

.

The outcomes of the GA and ACO algorithms for the 1535 demand point scenario are shown in Table 3 and Table 4, respectively. The findings indicate that while both algorithms’ costs rise as demand density rises, their performance varies significantly.

In terms of expenses, ACO was able to lower expenditure to 7.96 million units under the same circumstances, whereas GA reached a peak value of 9.15 million units for 30 stations. At fewer stations, a similar pattern was seen; for instance, in the five-station scenario, GA obtained a value of 528,435 units while ACO obtained a value of 406,488 units, resulting in about 23% cost reduction. This shows that even when demand rises, ACO can optimize costs more successfully.

ACO computations normally take 14 to 20 s to complete, whereas GA computations usually take 29 to 39 s. This suggests that ACO can provide solutions 40–50% more quickly than GA.

ACO obtained more effective solutions with just 5095 functions, whereas GA performed 11,100 functions per test. This distinction shows that ACO requires less computing power to get better outcomes.

Looking at the cost diagrams shown in Figure 7, the ACO method achieved lower costs than the GA method for all weighting combinations for 1535 demand points. While GA methods achieved rapid convergence in the first few iterations and remained fixed at a certain point, ACO achieved more efficient results by gradually reducing costs throughout the iterations. The results obtained with different weight combinations (w₁, w₂) illustrate the impact of the parameters on total costs. Increasing the value of w₁ (more weighting of transportation costs) shortens travel distances and significantly reduces total costs. In particular, the scenario (w₁ = 1.2, w₂ = 0.8) stands out among the other scenarios, offering the most efficient solution with final costs of approximately 5.5 × 10⁶. ACO also outperforms GA in terms of computational performance. The shapes start from different starting points due to the random calculations of the algorithms. While GA reaches a solution in approximately 11,100 function evaluations, ACO achieves faster and more cost-effective results in only 5095 evaluations. These results are consistent with studies in the literature showing that ACO is superior in terms of computational performance and solution quality for large-scale facility layout problems [16,17,21].

Figure 8 shows the locations of 30 stations identified using a stochastic GA solution. While stations are concentrated in high-demand areas, some areas are overconcentrated, leading to load imbalances among stations. Specifically, some central stations serve many demand points, while stations in peripheral areas experience relatively lower demand.

Figure 9 shows the layout of 30 stations determined using the ACO method. The ACO method better captured the demand distribution, resulting in a more balanced distribution of supply and contributing to the homogenization of station usage. Furthermore, the ACO results resulted in shorter access routes and less congestion, particularly in densely populated areas.

In the scenario with 1035 demand points in Figure 4 and Figure 5, excessive concentration and imbalances were observed in some regions among the 30 station locations determined using the GA random solution method. In contrast, the ACO method distributed the stations more evenly, shortening commuting distances and providing a more balanced load distribution.

The differences are more pronounced in the scenario with 1535 demand points in Figure 8 and Figure 9. In the GA solutions, imbalances increased with increasing size, and while some central stations had high utilization rates, stations in peripheral areas were considered relatively underutilized. ACO more accurately captured the distribution of demand points, resulting in a more balanced supply distribution and shorter distances between stations, even with increased density.

When the 1035 and 1535 demand point scenarios were analyzed holistically, it was determined that the ACO method was more advantageous than GA in terms of scalability and efficiency.

Figure 10a–d compare the performance of the GA with two different mutation rates ($pm=0.1$ and $pm=0.3$) for 30 charging station locations and 1535 demand points. The results confirm that both settings converge within the first 2000 iterations, but they show variations in speed and stability. While $pm=0.1$ is consistent with commonly reported parameter ranges in the literature and yields faster initial convergence, $pm=0.3$ enhances solution diversity and reduces the risk of premature convergence, leading to more stable performance across repeated runs. These findings suggest that parameter choices affect convergence dynamics, while the final cost values remain broadly comparable. In addition, GA-based station positioning results obtained with $pm=0.3$ are presented in Table 3, and the same values were also achieved with $pm=0.1$; however, the solution time was longer in the $pm=0.1$ case. Furthermore, the analysis of weight coefficients highlights the advantage of the $\left(w_1=1.2,w_2=0.8\right)$ scenario. This setting results in reduced overall costs and shorter access distances by giving transportation expenses more weight than installation costs. Such a weighting scheme improves the practical application of charging station placement tactics in urban situations and offers more efficient service coverage for demand points.

4. Conclusions

Using a p-median modeling technique, this study investigated the location and capacity planning of EV charging stations in Erzurum. Genetic algorithm (GA) and ant colony optimization (ACO) were used to generate solutions. According to the comparison findings, ACO constantly outperforms GA in terms of cost, quality, and computational efficiency. After 60–80 iterations, GA often stabilizes with output fluctuations of roughly ±8–10%, while ACO reduces costs by 15–25% and yields more consistent results with a smaller variance of ±3–4%. These results highlight the applicability of ACO for planning sustainable EV charging infrastructure and offer a reliable point of reference for future research topics, such as hybrid metaheuristic techniques, dynamic demand modeling, and the incorporation of renewable energy.