Transport Optimization in the Supply Chain Using the Ant Colony Algorithm ^†

Abstract

The shortest path problem is algorithmic and involves finding the least costly path (in terms of distance, time, cost, or other criteria) between two nodes in a graph. This problem is fundamental in graph theory and has applications in logistics, networks, mapping, and more. Several methods have been used to solve this problem. In this paper, we applied the ant colony algorithm to optimize the travel path of product quality technicians in a textile company specializing in washing and dyeing denim items. The company aims to minimize distances and costs between its subcontractors. The method has demonstrated a significant impact on distance and cost reduction while contributing to the reduction of the environmental effects.

1. Introduction

The path-finding problem is determining the optimal path from a starting point to a destination, considering specific conditions. These problems arise in networks such as highway systems, railroads, logistics, and communication networks, and they cover a wide range of applications [1]. In the literature, various studies are concerned with this topic in several fields, but few studies have been published in the textile and apparel field. Shin and Young used a heuristic algorithm in the fashion apparel industry to solve the problem of restocking and distribution. They used this approach to reduce the distribution lead time between manufacturers and retailers [2]. Guo et al. used a hybrid intelligent algorithm to optimize production and delivery operations in the apparel supply chain. This approach was used to minimize the total transport and penalty costs [3]. A genetic algorithm was used by Yu and Lu to optimize the cutting path of an automatic garment cutter [4]. In addition, other scientific works dealing with this problem in the manufacturing field are numerous. In this section, we present some of them to highlight the wide variety of applications. Koopahi applied a linear programming model for a material replenishing, manufacturing, and distribution network to obtain the optimal transportation pattern for a food processing company to minimize transportation costs [5].

Clement explores the use of AI-based predictive analytics to optimize the textile industry’s supply chain, addressing challenges such as fluctuating demand and logistical inefficiencies. He proposes a hybrid framework combining deep learning, reinforcement learning, and time series forecasting, validated by real-world data. The results show that this approach can reduce lead times, improve resource allocation, and minimize waste, thereby contributing to profitability and sustainability [6]. Wang et al. developed a flexible scheduling strategy to optimize task allocation on automated production lines by introducing an improved genetic algorithm. This algorithm dynamically adjusts crossover and mutation rates and sorts individuals based on their fitness, thereby improving solution quality. Simulations show that this approach reduces production time by 26% compared to traditional methods, while providing faster convergence and increased optimization capabilities [7]. Sun et al. examined freight route optimization for multimodal transportation, a key solution for reducing international logistics costs, which represent 30–50% of companies’ total production costs. Their study provides a systematic review of optimization models and solution algorithms, distinguishing model formulation characteristics and identifying recent approaches. Emphasis is placed on heuristic algorithms to solve these models and improve the efficiency of multimodal transportation [8]. Farahmand and Afrasyabi developed a multi-objective quantum particle swarm optimization (MOQPSO) approach to address routing problems in urban transportation networks. Their method aims to reduce route length while improving system efficiency, through the integration of quantum techniques and specific modifications. The results obtained demonstrate that the MOQPSO algorithm outperforms classical approaches by providing optimal solutions faster [9]. After a thorough literature search, several studies were found to solve the shortest path problem; however, research studies in the clothing industry are still limited. In this paper, an ant colony algorithm was used to optimize the transportation of technicians between laundry subcontractors with minimum distance and cost. This approach aims to minimize the distances traveled, reduce fuel costs, and limit the company’s carbon footprint. By streamlining travel and promoting more efficient logistics, this project is part of a sustainable development dynamic. It also reflects a strong commitment to supporting the textile sector in its ecological transition, by adopting responsible practices that combine optimization of resources and reduction of environmental impacts.

2. Materials and Methods

2.1. Materials and Software Used

In this research, we used a high-performance laptop (Micro-Star International, New Taipei City, Taiwan) equipped with a 2.60 GHz Intel Core i7-9750H processor, 16 GB of RAM, and an NVIDIA GTX 1650 graphics card. A 512 GB SSD ensures fast data access, thus optimizing loading times. All calculations were performed using MATLAB software version 2017.

2.2. Method

Ant Colony Algorithm

Dorigo proposed the ant colony in 1996 [10]. Ant colony algorithms are inspired by the cooperative behavior of ants. They have developed very complex mechanisms to find the shortest path between their anthill and a food source. Ants release a trail of pheromones on their path that attracts their fellow ants passing nearby. The pheromone trails weaken over time, and we see that if there are several paths between the anthill and the food source, the shortest path will tend to strengthen and become more and more attractive to the detriment of the other paths where the pheromones will gradually become weaker and weaker and finally disappear. Dorigo applied ant colony to solve the traveling salesman problem [11]. The flowchart of the ant colony algorithm is presented in Figure 1.

3. Results and Discussion

3.1. Evaluation Test

In this study, we applied the Ant Colony Optimization (ACO) algorithm to optimize technician routes, a complex task that requires the consideration of several logistical factors. The algorithm was used to determine the shortest path connecting all laundry subcontractors while aiming to minimize not only the distance traveled but also the costs associated with technician travel. This optimization process is essential to improve operational efficiency and reduce operating costs.

Table 1. Distance between subcontractors.

	A	B	C	D	E
A	0	2	10	8	3
B	1	0	2	5	7
C	9	1	0	3	6
D	10	4	3	0	2
E	2	7	5	1	0

details the locations of laundry subcontractors and the distances between them, providing the basic data needed for route modeling.

In our case study, we used the following parameters:

• The number of ants is equal to the number of subcontractors equal to 5;
• The parameters α and β are equal to 1;
• The initial pheromone is τi,j(0) = 2; Q = 100.

We chose the parameter values (α = β = 1, initial pheromone τ = 2, Q = 100) based on classical recommendations from the ant colony algorithm (ACA) literature, which suggest that these values are often effective in simple scenarios and achieve good convergence in vehicle routing problems.

• Step 1: Calculate the paths taken for each ant.

In this step, we started the first iteration, in which each ant traveled through all the subcontractors. The results obtained, including the total distance traveled and the amount of pheromones deposited by each ant, are summarized in

Table 2. The traveled length and the pheromone for each ant (k).

k	Lk	Δτi,jk
1	11	9.1
2	9	11.1
3	9	11.1
4	11	9.1
5	9	11.1

.

• Step 2: Update the pheromones by applying the following formula:

$$\tau ij(t+1)=(1-\rho )\tau ij(t)+{\sum }_{k=1}^m\Delta {\tau }_{ij}^k(t); \mathrm{with} \rho =0.5$$

(1)

The pheromone update is presented in

Table 3. Pheromone update.

	A	B	C	D	E
A	0	19.2	1	1	34.3
B	34.3	0	19.2	1	1
C	1	34.3	0	3	1
D	1	1	34.3	0	19.2
E	19.2	1	1	34.3	0

.

Once the pheromones were updated, we performed a second iteration for each ant. At the end of this iteration, the paths traveled by each ant, as well as the distances associated with each of these paths, were determined and are presented in

Table 4. The second iteration for the five ants.

The Path Traveled by Each Ant	Length Path (KM)
A, E, D, C, B, A	9
B, A, E, D, C, B	9
C, B, A, E, D, C	9
D, C, B, A, E, D	9
E, D, C, B, A, E	9

.

In another part, we determined the pheromone heat map, as presented in Figure 2.

Figure 2 represents the pheromone matrix obtained at the 100th iteration of the ant colony algorithm (ACO). Each cell of the matrix indicates the quantity of pheromone deposited on the path connecting two subcontractors. Brighter colors (yellow) indicate a high concentration of pheromones, corresponding to the paths most frequently taken by virtual ants, while darker shades (blue) indicate less frequently used paths.

Analysis of this matrix highlights a high intensity of pheromones on paths A→B, B→C, C→D, D→E, and E→A, which forms an optimal closed circuit passing successively through all the subcontractors before returning to the starting point. This indicates that the algorithm has converged to an optimum. The low intensity of the other cells suggests that alternative paths were explored but ultimately abandoned in favor of this preferred route. Thus, Figure 2 clearly illustrates the ACO algorithm’s ability to learn and reinforce the best paths through the selective accumulation of pheromones, leading to a stable and efficient solution.

According to Table 4, the ant colony algorithm has concluded that all ants have followed the same path and completed the same number of iterations.

To evaluate our work, we take five paths taken by the technician as a test sample to compare the results found by the ant colony and others registered by the technician, as presented in

Table 5. Traveled paths.

	Technician’s Results			Ant Colony Results
Path	The Path Traveled by a Technician	Path Length (KM)	Cost (dt)	The Path Traveled by Each Ant	Path Length (KM)	Cost
A→A	A, B, E, C, D, A	27	25.37	A, E, D, C, B, A	9	22.44
B→B	B, D, C, A, E, B	27	25.37	B, A, E, D, C, B	9	22.44
C→C	C, A, D, E, B, C	28	25.37	C, B, A, E, D, C	9	22.44
D→D	D, A, C, B, E, D	29	25.37	D, C, B, A, E, D	9	22.44
E→E	E, B, D, A, C, E	28	25.37	E, D, C, B, A, E	9	22.44

.

3.2. Statistical Study and Analysis Results

Based on Table 5, we conducted a comparative statistical analysis of technicians vs. ACO, as presented in

Table 6. Comparative statistical analysis.

Indicator	Technician	ACO (Ant Colony Optimization)
Average Distance (km)	27.8 km	9 km
Average Cost (dt)	25.37 dt	22.44 dt
Standard Deviation (Distance)	≈0.748 km	0 km
Standard Deviation (Cost)	0 dt (fixed cost)	0 dt (same for all ants)
Min/Max Distance	27 km/29 km	9 km/9 km
Min/Max Cost	25.37 dt/25.37 dt	22.44 dt/22.44 dt
Performance Gain	—	+67.6% (distance), +11.55% (cost)

.

The comparative statistical study between the routes planned by the technicians and those proposed by the ant colony algorithm (ACO) presented in Table 6 and Figure 3 shows a clear improvement in terms of performance. On average, the distance traveled was reduced by 67.6%, from 27.8 km to only 9 km, while the cost was reduced by 11.55%, offering a solution that is both more economical and more efficient. In addition, the results produced by the ACO present perfect regularity (zero standard deviation), reflecting a convergence towards a reproducible optimal solution.

4. Conclusions

This paper shows that the ant colony algorithm is particularly effective in finding the shortest path while optimizing both the distance traveled and the associated cost. On average, the distance is reduced by 67.6% and the cost by 11.55%. This optimization has significant impacts on the environment, particularly by reducing the carbon footprint. By reducing distances and costs, this algorithm contributes to a decrease in greenhouse gas emissions, thus promoting a positive impact on environmental sustainability.