Statistical measures of a fitness landscape for the vehicle routing problem

2008 ◽  
Author(s):  
Zbigniew J. Czech
Keyword(s):  
Vehicle Routing ◽  
Vehicle Routing Problem ◽  
Fitness Landscape ◽  
Routing Problem ◽  
Statistical Measures

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

Processes ◽  
2020 ◽  
Vol 8 (11) ◽  
pp. 1363
Author(s):  
László Kovács ◽  
Anita Agárdi ◽  
Tamás Bányai
Keyword(s):  
Vehicle Routing ◽  
Vehicle Routing Problem ◽  
Fitness Landscape ◽  
Fitness Function ◽  
Search Space ◽  
Landscape Analysis ◽  
Discrete Optimization Problem ◽  
Routing Problem ◽  
Fitness Landscape Analysis ◽  
Fitness Value

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.

scholarly journals An Attraction Map Framework of a Complex Multi-Echelon Vehicle Routing Problem with Random Walk Analysis

2021 ◽  
Vol 11 (5) ◽  
pp. 2100
Author(s):  
Anita Agárdi ◽  
László Kovács ◽  
Tamás Bányai
Keyword(s):  
Random Walk ◽  
Vehicle Routing ◽  
Vehicle Routing Problem ◽  
Optimization Problem ◽  
Fitness Landscape ◽  
Basin Of Attraction ◽  
Discrete Optimization Problem ◽  
Routing Problem ◽  
The Basin Of Attraction ◽  
Random Walk Analysis

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.

Sign in / Sign up

Export Citation Format

Share Document