Smallest position value approach

Abstract

In a traveling salesman problem, if the set of nodes is divided into clusters for a single node from each cluster to be visited, then the problem is known as the generalized traveling salesman problem (GTSP). Such problem aims to find a tour with minimum cost passing through only a single node from each cluster. In attempt to show how a continuous optimization algorithm can be used to solve a discrete/combinatorial optimization problem, this chapter presents a standard continuous differential evolution algorithm along with a smallest position value (SPV) rule and a unique solution representation to solve the GTSP. The performance of the differential evolution algorithm is tested on a set of benchmark instances with symmetric distances ranging from 51 (11) to 442 (89) nodes (clusters) from the literature. Computational results are presented and compared to a random key genetic algorithm (RKGA) from the literature.