An improved ant colony optimization algorithm for the multi-depot green vehicle routing problem with multiple objectives
Introduction
A key component of every distribution system is the routing of vehicles to service customers (Osaba et al., 2017). Accordingly, research in mathematical modelling of transport systems and network optimization has received additional momentum over the last three decades in optimizing such systems (Laporte, 1992; Ho et al., 2008; Braekers et al., 2016). In particular, a large number of studies have shown that the use of operations research and computerized procedures for designing and planning of distribution networks will not only reduce transportation costs, but also assists the decision makers to achieve desired service levels (Chebbi and Chaouachi, 2016; Lai et al., 2016; Soleimani et al., 2018). The success of operation research techniques in this area is considerably owed to the advancement of computers (both hardware and software) and applications of information and communications technology (ICT) in design, management and monitoring of transportation systems (Toth and Vigo, 2002).
In this context, vehicle routing problem (VRP) is one of the most researched combinatorial optimization problem that deals with the optimal allocation of vehicles in a fleet to the desired destinations. VRP was formally introduced by Dantzig and Ramser (1959) as the truck dispatching problem, and since then, several variations have emerged, including capacitated VRP (CVRP), VRP with time window (VRPTM), VRP with pickup and delivery (VRPPD), VRP with multiple trips (VRPMT) and open VRP (OVRP). As the result of mounting transportation costs, limited resources and increasing customer expectations, VRP models have been playing an essential role in providing practical solutions to management and operations of physical distribution systems (Soleimani et al., 2018; Zohal and Soleimani, 2016). Govindan et al. (2014) proposed a multi-objective optimization model for a two-echelon location–routing problem with time-windows for sustainable supply chain network design.
The issue of organizing the routing is of the core strategic decisions in a transport and logistics business (Kahfi and Tavakkoli-Moghaddam, 2015). Since the strategic goals of transportation companies differ from one to another, the structure, objectives and constraints of VRPs become extremely diverse and complex.
Thus, it is important to acknowledge real-world distribution networks are far more complex and multifaceted when meeting operational, tactical and strategic objectives (Melián-Batista et al., 2014; Darbari et al., 2019) While the classic VRP is suitable to solve single depot problems, predominantly, supply chain networks consist of multi-depots and multiple delivery points, which require more robust and all-inclusive approaches such as multi-depot vehicle routing problem (MDVRP). Furthermore, there exists a mounting pressure on transportation and logistics businesses to minimize their environmental footprints. Recognizing this increasing complexity, development of models that are capable to address economic, social and environmental challenges associated with management and operations of supply chain networks is on soaring demand.
Therefore, considering a double-tier distribution chain, this paper presents a multi-depot green vehicle routing problem (MDGVRP) to simultaneously satisfying multiple objectives of cost minimization, profit maximization, travel time minimization and emission reduction. To solve the problem, an improved ant colony optimization (IACO) approach was applied and compared with other methods. The main contribution of this research is observed in development of the model which considers four conflicting objectives into a single integrated function, including green criteria. Also, this paper applies an improved ACO, into a VRP domain, which is based on a new method of updating pheromone that produce slightly better solutions. The remaining of this paper is as follows. Section 2 present a brief review of the literature on MDVRP, GVRP and use of ACO in similar problems. The mathematical model is formulated in Section 3 and the algorithm is presented and tested in Section 4. Experimental results are summarized in Section 5. Finally, concluding remarks and direction for future research are drawn in Section 6.
Section snippets
Literature
This review of literature first aims to provide a summary on the development of VRP research necessary to understand the development of MDVRP. It then summarizes the most relevant works in terms of objective and solution approach. Next, some of the recent and influential research in the area of GVRP are reported. Finally, a brief review of literature on the applications of ACO in VRP research is presented.
To overcome the increasing complexity associated with design and management of
Problem description and formulation
Organizations that deal with the delivery, collection, and movement of objects and humans face unique challenges when designing their transport network. As noted, VRP is one of the most practical and common issues in transportation systems. Over time, VRP has been developed and several different branches exist, which was discussed in the literature. In particular, businesses involved in distribution of goods are keen to reduce the total kilometers traveled by vehicles when serving customers
Solution approach
ACO is a meta-heuristic method that has been successfully used in solving a large number of optimization problems. ACO algorithm was introduced as a tool for solving the traveling salesman problem (TSP) by Dorigo and Stutzle in 1999. This algorithm, which is a multi-agent system, has been inspired by the food searching mechanism of ants, so that each agent is an artificial ant. The algorithm is also a successful example of a group's intelligent systems in which each agent performs a simple
Experimental results
This section presents the procedures used to validate reliability of the IACO using parameters obtained and tuned from experimental results. Taguchi and Wu (1979) method of robust design is adopted to find the optimum combination of parameters in the IACO. To enhance the performance of the model, the parameters values are considered in three levels of instances and the means are reported. Table 2 provides the levels of parameters values for tuning process.
Accordingly, Qualitek-4 software was
Conclusion and future research
Due to increasing transportation costs and greater legislative requirements, many retailers and manufacturing organizations are under pressure to improve the efficiency of their distribution network. When researching the topic of efficiency in transport systems, traditionally, a great amount of effort was devoted to the issues of cost reduction. However, in the contemporary business environments, there are other major factors that not only play a critical role in the success of a transport
Acknowledgements
The work funded by National Social Science Foundation of China. Grant Number: 14BJL045; Shandong provincial social science planning research project. Grant Number: 18BCXJ03; Qingdao social science planning project. Grant Number: QDSKL1801043; Shandong university humanities and social science research project. Grant Number: J18RB189.
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