Optimization of Multiple Traveling Salesmen Problem by a Novel Representation Based Genetic Algorithm

Abstract

The Vehicle Routing Problem (VRP) is a complex combinatorial optimization problem that can be described as follows: given a fleet of vehicles with uniform capacity, a common depot, and several costumer demands; find the set of routes with overall minimum route cost which service all the demands. The multiple traveling salesman problem (mTSP) is a generalization of the well-known traveling salesman problem (TSP), where more than one salesman is allowed to be used in the solution. It is well-known that mTSP-based algorithms can also be utilized in several VRPs by incorporating some additional site constraints. The aim of this chapter is to review how genetic algorithms can be applied to solve these problems and to propose a novel, interpretable representation based algorithm.The elaborated heuristic algorithm is demonstrated by examples considering different round tour types determination of further tasks for optimal operation of the distribution system for instance the modification of the vehicle capacity, and the effects of change of cost elements and data structure.

Cooperative multi-task assignment for heterogonous UAVs

“…In multiplechromosome structure GA (MSGA), classical genetic operators such as crossover and mutation operators need to be modified. Such modification has been suggested for solving Multiple Traveling Salesmen Problem (mTSP) [1].…”

“…Novel Chromosome Structure: The modification of [1] is not sufficient for cooperative multi task assignment problem as it cannot be reduced to mTSP 2 . To be able to apply MSGA to UAV domain, we further modified the chromosome structure.…”

“…Some agents may be left unused if they are not needed like agent a6. Genetic Operators: We adopt the GA operators of [1] and introduce two novel ones which we describe in the next section. The in-route and cross-route mutations we employ are adopted from [1] with small modifications to work with our novel chromosome structure.…”

Localising and quantifying damage by means of a multi-chromosome genetic algorithm

“…Baine [15] used four chromosomes to represent the input and output fuzzy sets of a proportional-plus-derivative fuzzy logic controller. Király and Abonyi [16] codified the possible solutions to the multiple travelling salesmen problem by assigning one chromosome for each salesman in the solution.…”

Two phase heuristic algorithm for the multiple-travelling salesman problem

“…Clearly, TSP is a special case of MTSP for m = 1. Heuristic approaches can be utilised to solve MTSP Kiraly and Abonyi (2011), such as the ant colony optimisation algorithm (ACO) Singh and Mehta (2014), particle swarm optimisation algorithm (PSO) Yan et al (2012), and the genetic algorithm (GA) Avin et al (2012), to name but a few. However, there are a variety of aspects, which require further improvements.…”