Using Metaheuristics on the Multi-Depot Vehicle Routing Problem with Modified Optimization Criterion

Abstract

This article deals with the modified Multi-Depot Vehicle Routing Problem (MDVRP). The modification consists of altering the optimization criterion. The optimization criterion of the standard MDVRP is to minimize the total sum of routes of all vehicles, whereas the criterion of modified MDVRP (M-MDVRP) is to minimize the longest route of all vehicles, i.e., the time to conduct the routing operation is as short as possible. For this problem, a metaheuristic algorithm-based on the Ant Colony Optimization (ACO) theory and developed by the author for solving the classic MDVRP instances-has been modified and adapted for M-MDVRP. In this article, an additional deterministic optimization process which further enhances the original ACO algorithm has been proposed. For evaluation of results, Cordeau's benchmark instances are used.Algorithms 2018, 11, 74 2 of 14 was introduced by Montoya-Torres et al. [6], who consider papers published between 1988 and 2014. Several variants of MDVRP are studied in the article: time windows, split delivery, heterogeneous fleet, periodic deliveries, and pickup and delivery. Another survey of publications on VRP and its variants can be found in [7], where 277 articles published between 2009 and 2015 are classified.Popular metaheuristic algorithms for MDVRP are based on the tabu search approach. One of the first tabu search-based algorithms was published by Gillet and Johnson in 1976 [8]. The same approach is used by Chao, Golden and Vasil [9], or Renaud, Laporte and Boctor [10], and indeed, examples of new algorithms using the tabu search approach continue to be published [11,12].Other popular metaheuristic approaches for MDVRP are simulated annealing [13,14] and genetic algorithms [15]. A hybrid algorithm, based on both simulated annealing and the genetic approach, was proposed by Seidgar et al. [16]. An excellent survey of papers using genetic algorithms for MDVRP can be found in [17].More recently, bio-inspired algorithms have also been broadly used for MDVRP. Ant colony optimization algorithms are inspired by the behavior of ants when searching for food. There are many publications using this for MDVRP. Yu, Yang and Xie [18] proposed an algorithm which transfers the problem to VRP by inserting a virtual central depot (V-MDVRP). Another solution was proposed by Yao et al. [19], who applied the ACO algorithm to a seafood product delivery routing problem. The most recent works include algorithms by Yalian [20], Gao [21], and Ma et al. [22].In the last few years, hybrid metaheuristic methods have emerged. They combine features from various methodologies to take advantage of their different strengths. Ting and Chen [23] introduced a combination of the ant colony algorithm, and simulated annealing for MDVRP with time windows. Vidal et al. [24] proposed a method which combines the exploration breadth of population-based evolutionary searches, the aggressive-improvement capabilities of neighborhood-based metaheuristics, and advanced population-diversity management schemes. Oliveira et al. [25] de...

A Heuristic Solution Method for Multi-Depot Vehicle Routing-Based Waste Collection Problems

“…The arrows in the figure indicate the direction of segmentation. The sectors within the inner circle are: [10,7,1,3], [5], [12,8], the sectors within the outer circle sectors are: [6], [2,11], [4,9,13].…”

“…According to the above rules, a result of the sector arrangement of the depot A is shown in Figure 4a. The sector sequence is: [12,8], [4,9,13], [10,7,1,3], [6], [2,11], [5]. The rearranged order using CWS method.…”

“…As shown in Figure 4b, the total customer demand of the sector [12,8] is 29.0, the total customer demand of the sector [4,9,13] is 27.0, and the sum of two sectors is 56.0, which does not exceed the vehicle capacity, 80.0. Therefore, the two sectors are grouped into one sector [12,8,4,9,13]. The total customer demand of the next sector [10,7,1,3], 48.0, 56.0 + 48.0 = 104.0, exceeds the vehicle capacity, 80.0, so the customers in the sector [10,7,1,3] are selected to add to the sector [12,8,4,9,13] in order.…”

“…Therefore, the two sectors are grouped into one sector [12,8,4,9,13]. The total customer demand of the next sector [10,7,1,3], 48.0, 56.0 + 48.0 = 104.0, exceeds the vehicle capacity, 80.0, so the customers in the sector [10,7,1,3] are selected to add to the sector [12,8,4,9,13] in order. The result is that 10, 7, 1 have been added to the sector [12,8,4,9,13]; therefore, customers 12, 8, 4, 9 13, 10, 7, 1 are assigned to a vehicle and the sector [3] is left as the current sector, and so on.…”

“…Yu et al [3] presented a parallel improved ACO with a coarse-grain parallel strategy, ant-weight strategy and mutation operation for MDVRP. Stodola [4] dealt with the modified MDVRP (M-MDVRP) which altered the optimization criterion. The optimization criterion of the standard MDVRP is to minimize the total sum of routes of all vehicles, whereas the criterion of M-MDVRP is to minimize the longest route of all vehicles, i.e., the time traveled by the vehicle is as short as possible.…”