Some of the New Indicators in Genetic Algorithms for the Traveling Salesman Problem

Abstract

The Traveling Salesman Problem (TSP) is a classic NP-hard problem example. In this regard, the development of new methods for solving it, is an urgent task. Considering that the time complexity finding the exact solution is a factorial or exponential dependence on the input data, there are many methods for approximate solution of TSP. In this case, algorithms based on probabilistic-directed search are popular. Among these are genetic and bio-inspired algorithms. This paper presents two new indicators in genetic algorithms (GA) for analyzing the degradation degree of the population. Special software was developed for the GA analysis, which was tested on the well-known benchmark: bier 127. A number of representation issues are discussed along with genetic Edge Recombination Crossover (ERX) and Partially-mapped crossover (PMX). Test results indicate that the GA with ERX gives an advantage in the diversity of the population in front of the GA with the PMX. The obtained information is useful for further genetic algorithm parameters settings. As a result, developed indicators can be used for forward estimation of the GA prospects even before applying it to a real task. They can be also used for parameter settings of the GA.