Fitness Landscape Analysis and Edge Weighting-Based Optimization of Vehicle Routing Problems

Tamás Bányai,Anita Agárdi,László Kovács

doi:10.3390/pr8111363

Abstract

Vehicle routing problem (VRP) is a highly investigated discrete optimization problem. The first paper was published in 1959, and later, many vehicle routing problem variants appeared to simulate real logistical systems. Since vehicle routing problem is an NP-difficult task, the problem can be solved by approximation algorithms. Metaheuristics give a “good” result within an “acceptable” time. When developing a new metaheuristic algorithm, researchers usually use only their intuition and test results to verify the efficiency of the algorithm, comparing it to the efficiency of other algorithms. However, it may also be necessary to analyze the search operators of the algorithms for deeper investigation. The fitness landscape is a tool for that purpose, describing the possible states of the search space, the neighborhood operator, and the fitness function. The goal of fitness landscape analysis is to measure the complexity and efficiency of the applicable operators. The paper aims to investigate the fitness landscape of a complex vehicle routing problem. The efficiency of the following operators is investigated: 2-opt, order crossover, partially matched crossover, cycle crossover. The results show that the most efficient one is the 2-opt operator. Based on the results of fitness landscape analysis, we propose a novel traveling salesman problem genetic algorithm optimization variant where the edges are the elementary units having a fitness value. The optimal route is constructed from the edges having good fitness value. The fitness value of an edge depends on the quality of the container routes. Based on the performed comparison tests, the proposed method significantly dominates many other optimization approaches.

Highlights

Introduction and Related ResearchVehicle routing problem (VRP) is a highly investigated discrete optimization problem
Based on the results presented in that analysis: (a) the fastest algorithms are the greedy and savings method, but they provide an average tour quality; (b) the nearest neighbor and nearest insertion algorithms are dominated by the greedy and savings methods both in time and tour quality factors; (c) the best route quality can be achieved by the application on 3-opt/5-opt methods (Lin-Kernighan and Helsgaun); (d) considering both the time and tour quality, the chained Lin-Kernighan algorithm shows the best performance; (e) the evolutionary and swarm optimization methods are dominated by the k-opt methods both in time and tour quality factors; (f) the tour-merging methods applied on the chained
The structure of the fitness landscape is greatly influenced by the neighborhood operator, as the mainThe goal of fitness landscape analysis is istogreatly prove influenced the efficiency of the algorithms. operator, Four operators structure of the fitness landscape by the neighborhood as the were used in the analyses, as follows: 2-opt, cycle crossover, order crossover, partially matched main goal of fitness landscape analysis is to prove the efficiency of the algorithms

Summary

Introduction

Vehicle routing problem (VRP) is a highly investigated discrete optimization problem. Since VRP is an NP-difficult task, the problem has already been solved by several approximation algorithms such as metaheuristics. Since 1959, when the first VRP article was published [1], several publications have been published, and these publications solve different types of tasks, which may have different components, constraint factors, and objective functions. These task types, constraints, and objective function components are presented. The customers have product demands and the vehicles transport the product from the depot to the customers. The demands of the customers can be served by a single vehicle at the same time and all demands of all customers must be satisfied

Methods

Results

Conclusion