Abstract
The paper aims to investigate the basin of attraction map of a complex Vehicle Routing Problem with random walk analysis. The Vehicle Routing Problem (VRP) is a common discrete optimization problem in field of logistics. In the case of the base VRP, the positions of one single depot and many customers (which have product demands) are given. The vehicles and their capacity limits are also fixed in the system and the objective function is the minimization of the length of the route. In the literature, many approaches have appeared to simulate the transportation demands. Most of the approaches are using some kind of metaheuristics. Solving the problems with metaheuristics requires exploring the fitness landscape of the optimization problem. The fitness landscape analysis consists of the investigation of the following elements: the set of the possible states, the fitness function and the neighborhood relationship. We use also metaheuristics are used to perform neighborhood discovery depending on the neighborhood interpretation. In this article, the following neighborhood operators are used for the basin of attraction map: 2-opt, Order Crossover (OX), Partially Matched Crossover (PMX), Cycle Crossover (CX). Based on our test results, the 2-opt and Partially Matched Crossover operators are more efficient than the Order Crossover and Cycle Crossovers.
Highlights
One of the most important tasks of logistics is the cost-effective delivery of the right goods, to the right place in the right time considering any other constraints. These problem domains belong to the area of the Vehicle Routing Problem (VRP), which has developed in several versions since its first version [1] in 1959
The set of possible states depends on the problem instance and the used operators
Two investigation methods were used in the random walk analysis
Summary
Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. One of the most important tasks of logistics is the cost-effective delivery of the right goods, to the right place in the right time considering any other constraints These problem domains belong to the area of the Vehicle Routing Problem (VRP), which has developed in several versions since its first version [1] in 1959. The number of vehicles and their capacity constraints is given in advance The vehicles start their routes form the depot, they visit some customers, and return to the depot. Vehicle Routing Problem [11], the minimization of the waiting times for the customers is the objective function.
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