# Genetic Algorithm with Optimal Recombination for the Asymmetric Travelling Salesman Problem

## TL;DR

This paper introduces a novel genetic algorithm with optimal recombination and advanced heuristics for the asymmetric travelling salesman problem, demonstrating competitive performance on benchmark instances.

## Contribution

It presents a new genetic algorithm that integrates optimal recombination, a specialized mutation operator, and heuristic-based initialization for improved asymmetric TSP solutions.

## Key findings

- Achieves competitive results on TSPLIB instances.
- Outperforms some existing memetic algorithms.
- Effectively combines heuristics with genetic operators.

## Abstract

We propose a new genetic algorithm with optimal recombination for the asymmetric instances of travelling salesman problem. The algorithm incorporates several new features that contribute to its effectiveness: (i) Optimal recombination problem is solved within crossover operator. (ii) A new mutation operator performs a random jump within 3-opt or 4-opt neighborhood. (iii) Greedy constructive heuristic of W.Zhang and 3-opt local search heuristic are used to generate the initial population. A computational experiment on TSPLIB instances shows that the proposed algorithm yields competitive results to other well-known memetic algorithms for asymmetric travelling salesman problem.