A Novel Genetic Algorithm for GTSP

Abstract

Abstract-The Generalized Travelling Salesman Problem (GTSP) is a special instance of the well-known travelling salesman problem which belongs to NP-hard class of problems. In the GTSP problem which is being addressed in this research we split the set of nodes (e.g. cities) into non-overlapping subsets; where the optimal solution is a minimum cost tour visiting exactly one node from each subset. In this paper a genetic algorithm with new and innovative way of generating initial population is presented. Concepts like cluster segmentation, partially greedy crossover, greedy insert mutation and enhanced swap mechanisms are also introduced. An initial analysis of the proposed algorithm shows enhanced results in terms of optimality and computational time as compared to existing approaches.Index Terms-Generalized travelling salesman problem, genetic algorithms, greedy insert mutation, partially greedy crossover.

Using K-means Radius Particle Swarm Optimization for the Travelling Salesman Problem

“…As shown in Figure 12, a 2-OPT heuristic can modify the tour in a way that shortens the travel cost of the tour. For example, if a tour begins in Figure 12(a), a 2-OPT randomly swap point i is 2 and k is 4, and insert the new tour (1, 2), (4,3), and (5) that results in the tour shown in Figure 12(b). The pseudo-code of the 2-OPT heuristic is given in Algorithm 3.…”

“…Several different methods have been proposed to solve this problem. The methods include genetic algorithm [3], ant colony optimization [4], particle swarm optimization (PSO) [5], and honey bees mating optimization algorithm [6]. Due to reason that the TSP is non-deterministic polynomial-time hard (NP-hard), only small instances can be solved to optimality.…”