A Discrete State Transition Algorithm for Generalized Traveling Salesman Problem

TL;DR

This paper introduces a novel discrete state transition algorithm for the generalized traveling salesman problem, incorporating new local search and update mechanisms to improve search efficiency and solution quality.

Contribution

It proposes a new discrete state transition algorithm with a K-circle local search operator and a Double R-Probability update mechanism for GTSP.

Findings

DSTA outperforms existing heuristics in solution quality.

DSTA demonstrates strong adaptability across GTSP instances.

Experimental results confirm DSTA's superior search ability.

Abstract

Generalized traveling salesman problem (GTSP) is an extension of classical traveling salesman problem (TSP), which is a combinatorial optimization problem and an NP-hard problem. In this paper, an efficient discrete state transition algorithm (DSTA) for GTSP is proposed, where a new local search operator named \textit{K-circle}, directed by neighborhood information in space, has been introduced to DSTA to shrink search space and strengthen search ability. A novel robust update mechanism, restore in probability and risk in probability (Double R-Probability), is used in our work to escape from local minima. The proposed algorithm is tested on a set of GTSP instances. Compared with other heuristics, experimental results have demonstrated the effectiveness and strong adaptability of DSTA and also show that DSTA has better search ability than its competitors.