Reduction of the Pareto Set in Bicriteria Asymmetric Traveling Salesman Problem

TL;DR

This paper applies an axiomatic Pareto set reduction method to the bicriteria asymmetric traveling salesman problem, demonstrating how specific information can significantly reduce the solution set in complex instances.

Contribution

It introduces a novel approach combining Pareto set reduction with a multi-objective genetic algorithm for bi-ATSP.

Findings

Pareto set can be effectively reduced using 'quanta of information'

The reduction degree varies with different problem structures

The method improves solution efficiency in complex bi-ATSP instances

Abstract

We consider the bicriteria asymmetric traveling salesman problem (bi-ATSP). Optimal solution to a multicriteria problem is usually supposed to be the Pareto set, which is rather wide in real-world problems. We apply to the bi-ATSP the axiomatic approach of the Pareto set reduction proposed by V. Noghin. We identify series of "quanta of information" that guarantee the reduction of the Pareto set for particular cases of the bi-ATSP. An approximation of the Pareto set to the bi-ATSP is constructed by a new multi-objective genetic algorithm. The experimental evaluation carried out in this paper shows the degree of reduction of the Pareto set approximation for various "quanta of information" and various structures of the bi-ATSP instances generated randomly.