# Construction and reduction of the Pareto set in asymmetric travelling salesman problem with two criteria

## TL;DR

This paper applies an axiomatic Pareto set reduction approach to the bicriteria asymmetric TSP, introducing a genetic algorithm for approximation and demonstrating significant Pareto set reduction under various conditions.

## Contribution

It introduces a novel application of Pareto set reduction to the bi-ATSP and develops a new genetic algorithm for Pareto set approximation.

## Key findings

- Pareto set reduction varies with different 'quanta of information'
- Genetic algorithm effectively approximates the Pareto set
- Experimental results show significant reduction in Pareto set size

## Abstract

We consider the bicriteria asymmetric travelling 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. For the first time 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 or from TSPLIB problems.