Decomposition-based multi-objective evolutionary algorithm for vehicle routing problem with stochastic demands

Vehicle routing problem with stochastic demands (VRPSD) is a famous and challenging optimization problem which is similar to many real world problems. To resemble the real world scenario, total traveling distance, total driver remuneration, the number of vehicles used and the difference between driver remuneration are considered and formulated in the multi-objective optimization perspective. This paper aims to solve multi-objective VRPSD under the constraints of available time window and vehicle capacity using decomposition-based multi-objective evolutionary algorithm (MOEA/D) with diversity-loss-based selection method incorporates with local search and multi-mode mutation heuristics. We have also compared the optimization performance of the decomposition-based approach with the domination-based approach to study the difference between these two well-known evolutionary multi-objective algorithm frameworks. The simulation results have showed that the decomposition-based approach with diversity-loss-based selection method is able to maintain diverse output solutions.     

A decomposition based memetic algorithm for multi-objective vehicle routing problem with time windows

Multi-objective evolutionary algorithm based on decomposition (MOEA/D) provides an excellent algorithmic framework for solving multi-objective optimization problems. It decomposes a target problem into a set of scalar sub-problems and optimizes them simultaneously. Due to its simplicity and outstanding performance, MOEA/D has been widely studied and applied. However, for solving the multi-objective vehicle routing problem with time windows (MO-VRPTW), MOEA/D faces a difficulty that many sub-problems have duplicated best solutions. It is well-known that MO-VRPTW is a challenging problem and has very few Pareto optimal solutions. To address this problem, a novel selection operator is designed in this work to enhance the original MOEA/D for dealing with MO-VRPTW. Moreover, three local search methods are introduced into the enhanced algorithm. Experimental results indicate that the proposed algorithm can obtain highly competitive results on Solomon׳s benchmark problems. Especially for instances with long time windows, the proposed algorithm can obtain more diverse set of non-dominated solutions than the other algorithms. The effectiveness of the proposed selection operator is also demonstrated by further analysis.     

A penalty-based edge assembly memetic algorithm for the vehicle routing problem with time windows

In this paper, we present an effective memetic algorithm for the vehicle routing problem with time windows (VRPTW). The paper builds upon an existing edge assembly crossover (EAX) developed for the capacitated VRP. The adjustments of the EAX operator and the introduction of a novel penalty function to eliminate violations of the time window constraint as well as the capacity constraint from offspring solutions generated by the EAX operator have proven essential to the heuristic's performance. Experimental results on Solomon's and Gehring and Homberger benchmarks demonstrate that our algorithm outperforms previous approaches and is able to improve 184 best-known solutions out of 356 instances.     

An effective memetic algorithm for the cumulative capacitated vehicle routing problem

The cumulative capacitated vehicle routing problem (CCVRP) is a transportation problem which occurs when the objective is to minimize the sum of arrival times at customers, instead of the classical route length, subject to vehicle capacity constraints. This type of challenges arises whenever priority is given to the satisfaction of the customer need, e.g. vital goods supply or rescue after a natural disaster. The CCVRP generalizes the NP-hard traveling repairman problem (TRP), by adding capacity constraints and a homogeneous vehicle fleet. This paper presents the first upper and lower bounding procedures for this new problem. The lower bounds are derived from CCVRP properties. Upper bounds are given by a memetic algorithm using non-trivial evaluations of cost variations in the local search. Good results are obtained not only on the CCVRP, but also on the special case of the TRP, outperforming the only TRP metaheuristic published.     

Adaptive memetic algorithm for minimizing distance in the vehicle routing problem with time windows

This paper presents an adaptive memetic algorithm to solve the vehicle routing problem with time windows (VRPTW). It is a well-known NP-hard discrete optimization problem with two objectives—to minimize the number of vehicles serving a set of geographically dispersed customers, and to minimize the total distance traveled in the routing plan. Although memetic algorithms have been proven to be extremely efficient in solving the VRPTW, their main drawback is an unclear tuning of their numerous parameters. Here, we introduce the adaptive memetic algorithm (AMA-VRPTW) for minimizing the total travel distance. In AMA-VRPTW, a population of solutions evolves with time. The parameters of the algorithm, including the selection scheme, population size and the number of child solutions generated for each pair of parents, are adjusted dynamically during the search. We propose a new adaptive selection scheme to balance the exploration and exploitation of the solution space. Extensive experimental study performed on the well-known Solomon’s and Gehring and Homberger’s benchmark sets confirms the efficacy and convergence capabilities of the proposed AMA-VRPTW. We show that it is very competitive compared with other state-of-the-art techniques. Finally, the influence of the proposed adaptive schemes on the AMA-VRPTW behavior and performance is investigated in a thorough sensitivity analysis. This analysis is complemented with the two-tailed Wilcoxon test for verifying the statistical significance of the results.     

The capacitated vehicle routing problem with stochastic demands and time windows

The capacitated vehicle routing problem with stochastic demands and time windows is an extension of the capacitated vehicle routing problem with stochastic demands, in which demands are stochastic and a time window is imposed on each vertex. A vertex failure occurring when the realized demand exceeds the vehicle capacity may trigger a chain reaction of failures on the remaining vertices in the same route, as a result of time windows. This paper models this problem as a stochastic program with recourse, and proposes an adaptive large neighborhood search heuristic for its solution. Modified Solomon benchmark instances are used in the experiments. Computational results clearly show the superiority of the proposed heuristic over an alternative solution approach.     

A self-adaptive memeplexes robust search scheme for solving stochastic demands vehicle routing problem

In this article, we proposed a self-adaptive memeplex robust search (SAMRS) for finding robust and reliable solutions that are less sensitive to stochastic behaviours of customer demands and have low probability of route failures, respectively, in vehicle routing problem with stochastic demands (VRPSD). In particular, the contribution of this article is three-fold. First, the proposed SAMRS employs the robust solution search scheme (RS ³) as an approximation of the computationally intensive Monte Carlo simulation, thus reducing the computation cost of fitness evaluation in VRPSD, while directing the search towards robust and reliable solutions. Furthermore, a self-adaptive individual learning based on the conceptual modelling of memeplex is introduced in the SAMRS. Finally, SAMRS incorporates a gene-meme co-evolution model with genetic and memetic representation to effectively manage the search for solutions in VRPSD. Extensive experimental results are then presented for benchmark problems to demonstrate that the proposed SAMRS serves as an efficable means of generating high-quality robust and reliable solutions in VRPSD.     

A hybrid algorithm for vehicle routing problem with time windows

Vehicle routing problem with time windows (VRPTW) is a well-known combinatorial problem. Many researches have presented meta-heuristics are effective approaches for VRPTW. This paper proposes a hybrid approach, which consists of ant colony optimization (ACO) and Tabu search, to solve the problem. To improve the performance of ACO, a neighborhood search is introduced. Furthermore, when ACO is close to the convergence Tabu search is used to maintain the diversity of ACO and explore new solutions. Computational experiments are reported for a set of the Solomon’s 56 VRPTW and the approach is compared with some meta-heuristic published in literature. Results show that considering the tradeoff of quality and computation time, the hybrid algorithm is a competitive approach for VRPTW.     

The memetic self-organizing map approach to the vehicle routing problem

The paper presents an extension of the self- organizing map (SOM) by embedding it into an evolutionary algorithm to solve the Vehicle Routing Problem (VRP). We call it the memetic SOM. The approach is based on the standard SOM algorithm used as a main operator in a population based search. This operator is combined with other derived operators specifically dedicated for greedy insertion moves, a fitness evaluation and a selection operator. The main operators have a similar structure based on the closest point findings and local moves performed in the plane. They can be interpreted as performing parallels and massive insertions, simulating the behavior of agents which interact continuously, having localized and limited abilities. This self-organizing process is intended to allow adaptation to noisy data as well as to confer robustness according to demand fluctuation. Selection is intended to guide the population based search toward useful solution compromises. We show that the approach performs better, with respect to solution quality and/or computation time, than other neural network applications to the VRP presented in the literature. As well, it substantially reduces the gap to classical Operations Research heuristics, specifically on the large VRP instances with time duration constraint.     

A parallel evolutionary algorithm for the vehicle routing problem with heterogeneous fleet

Nowadays genetic algorithms stand as a trend to solve NP-complete and NP-hard problems. In this paper, we present a new hybrid metaheuristic which uses parallel genetic algorithms and scatter search coupled with a decomposition-into-petals procedure for solving a class of vehicle routing and scheduling problems. The parallel genetic algorithm presented is based on the island model and its performance is evaluated for a heterogeneous fleet problem, which is considered a problem much harder to solve than the homogeneous vehicle routing problem.     

Efficient stochastic hybrid heuristics for the multi-depot vehicle routing problem

The paper addresses the problem of multi-depot vehicle routing in order to minimize the delivery time of vehicle objective. Three hybrid heuristics are presented to solve the multi-depot vehicle routing problem. Each hybrid heuristic combines elements from both constructive heuristic search and improvement techniques. The improvement techniques are deterministic, stochastic and simulated annealing (SA) methods. Experiments are run on a number of randomly generated test problems of varying depots and customer sizes. Our heuristics are shown to outperform one of the best-known existing heuristic. Statistical tests of significance are performed to substantiate the claims of improvement.     

A hybrid particle swarm optimization algorithm for the vehicle routing problem

This paper introduces a new hybrid algorithmic nature inspired approach based on particle swarm optimization, for successfully solving one of the most popular supply chain management problems, the vehicle routing problem. The vehicle routing problem is considered one of the most well studied problems in operations research. The proposed algorithm for the solution of the vehicle routing problem, the hybrid particle swarm optimization (HybPSO), combines a particle swarm optimization (PSO) algorithm, the multiple phase neighborhood search–greedy randomized adaptive search procedure (MPNS–GRASP) algorithm, the expanding neighborhood search (ENS) strategy and a path relinking (PR) strategy. The algorithm is suitable for solving very large-scale vehicle routing problems as well as other, more difficult combinatorial optimization problems, within short computational time. It is tested on a set of benchmark instances and produced very satisfactory results. The algorithm is ranked in the fifth place among the 39 most known and effective algorithms in the literature and in the first place among all nature inspired methods that have ever been used for this set of instances.     

A particle swarm optimization algorithm for open vehicle routing problem

This paper presents a real-value version of particle swarm optimization (PSO) for solving the open vehicle routing problem (OVRP) that is a well-known combinatorial optimization problem. In OVRP a vehicle does not return to the depot after servicing the last customer on a route. A particular decoding method is proposed for implementing PSO for OVRP. In the decoding method, a vector of the customer’s position is constructed in descending order. Then each customer is assigned to a route with taking into account feasibility conditions. Finally one-point move has been applied on constructed routes that seem promising to result in a better solution. Experimental evaluations on benchmark data sets demonstrate the competitiveness of the proposed algorithm.     

A hybrid algorithm for the capacitated vehicle routing problem with three-dimensional loading constraints

The capacitated vehicle routing problem with three-dimensional loading constraints combines capacitated vehicle routing and three-dimensional loading with additional packing constraints concerning, for example, unloading operations. An efficient hybrid algorithm including a tabu search algorithm for routing and a tree search algorithm for loading is introduced. Computational results are presented for all publicly available test instances. Most of the best solutions previously reported in literature have been improved while the computational effort is drastically reduced compared to other methods.     

A competitive neural network algorithm for solving vehicle routing problem

This paper describes a self organization Neural Network algorithm for a class of Vehicle Routing Problems. Motivated by the outstanding performance of adaptive Neural Network approach in the Traveling Salesman Problem, we devised an algorithm to extend the domain of applicability of this approach to more complex problems. First, relevant adaptation is proposed to refine the model for the Multiple Traveling Salesman Problem. Then, an additional mechanism to satisfy further constraints are embodied into the algorithm. The effectiveness of the proposed algorithm is evaluated by considering a series of standard problems from the literature. The results show that the algorithm can yield solutions within a few percent of optimality.     

随机需求多车辆路径问题的神经网络算法

目前国内外对随机需求多车辆路径问题的研究还很少,本文针对标准hopfield神经网络容易陷入局部极值点等问题,以总路程最短和总使用车辆数最少为目标,提出了一种基于退火策略的混沌神经网络的求解随机需求多车辆路径问题的算法,该算法既可以使混沌运动有足够长的进程以提高粗搜索性能,又可以随混沌动态的减弱使收敛速度加快。实验结果表明,该算法优化车辆路径更佳,是解决随机需求多车辆路径问题的有效方法。     

多车场满载车辆路径优化算法

针对多车场满载车辆路径问题(MDVRPFL),结合节约法提出了一种依次对车场、配送中心、用户进行循环调整直到最优的迭代算法.该算法具有使总费用随迭代次数逐渐降低的特点,其运算结果能同时得到最优车辆分配方案和车辆行驶路径.最后用该算法对不同规模的算例进行试验.试验结果表明,该算法对多车场车辆路径问题有效适用.     

车辆路径问题的改进的双种群遗传算法

提出了一种基于车辆路径问题的改进双种群遗传算法.该改进双种群遗传算法主要通过两个种群同时进行进化操作,并结合新交叉算子和种群交叉策略,以克服传统双种群遗传算法在求解车辆路径问题上所存在的不足.通过仿真实验,将改进的双种群遗传算法与其它几种遗传算法进行比较,改进的双种群遗传算法比其它几种遗传算法显著提高了优化效果.实验结果表明,该算法可以有效求得该问题的优化解,是解决车辆路径问题的好方法.