# SOM-Guided Evolutionary Search for Solving MinMax Multiple-TSP

## TL;DR

This paper introduces a hybrid approach combining Self Organizing Maps, Evolutionary Algorithms, and Ant Colony Systems to effectively solve the MinMax Multiple-TSP, outperforming existing methods on benchmark instances.

## Contribution

It presents a novel hybrid method integrating neural networks and meta-heuristics for MinMax Multiple-TSP, demonstrating superior performance over previous approaches.

## Key findings

- Hybrid approach outperforms existing methods on TSPLIB instances.
- Neural network and meta-heuristic hybridization significantly improves solution quality.
- The method effectively addresses the MinMax formulation of multiple TSP problems.

## Abstract

Multiple-TSP, also abbreviated in the literature as mTSP, is an extension of the Traveling Salesman Problem that lies at the core of many variants of the Vehicle Routing problem of great practical importance. The current paper develops and experiments with Self Organizing Maps, Evolutionary Algorithms and Ant Colony Systems to tackle the MinMax formulation of the Single-Depot Multiple-TSP. Hybridization between the neural network approach and the two meta-heuristics shows to bring significant improvements, outperforming results reported in the literature on a set of problem instances taken from TSPLIB.