Abstract
The Vehicle Routing Problem (VRP) is a highly researched discrete optimization task. The first article dealing with this problem was published by Dantzig and Ramster in 1959 under the name Truck Dispatching Problem. Since then, several versions of VRP have been developed. The task is NP difficult, it can be solved only in the foreseeable future, relying on different heuristic algorithms. The geometrical property of the state space influences the efficiency of the optimization method. In this paper, we present an analysis of the following state space methods: adaptive, reverse adaptive and uphill-downhill walk. In our paper, the efficiency of four operators are analysed on a complex Vehicle Routing Problem. These operators are the 2-opt, Partially Matched Crossover, Cycle Crossover and Order Crossover. Based on the test results, the 2-opt and Partially Matched Crossover are superior to the other two methods.
Highlights
The Vehicle Routing Problem (VRP) is one of the best known discrete optimization tasks
During the basic VRP, the positions and demands of the customers are given in advance, and the number of vehicles and capacity limit are known in advance
We have presented the fitness state space analysis of a complex Vehicle Routing Problem
Summary
The Vehicle Routing Problem (VRP) is one of the best known discrete optimization tasks. During the basic VRP, the positions and demands of the customers are given in advance, and the number of vehicles and capacity limit are known in advance. Starting from the depot, vehicles visit customers and return to the depot. The objective of the optimization is the minimization of the distance travelled by the vehicles. The VRP was first introduced by Dantzig and Ramster [1] as Truck Dispatching Problem. Many types and constraints of the problem have emerged as the complexity of transportation tasks has begun to increase. We will introduce some types of problems.
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