Cooperative Co-evolutionary Metaheuristics for Solving Large-Scale TSP Art Project

As the amount and scale of cities in Traveling Salesman Problem (TSP) rise, the algorithmic complexity is exponentially increasing. The difficulty is how to design a suitable algorithm to solve large-scale TSPs. A Cooperative Co-evolutionary Ant Colony Optimization algorithm (CC-ACO) is proposed in this paper based on the concept of divide and conquer. The Iterative Self-Organizing Data Analysis (ISODATA) clustering algorithm tackles the problem by dividing it into a set of smaller and simpler sub-components and the ACO algorithms are designed for optimizing them separately. Numerical tests are then conducted to investigate algorithms, analyze results, and compare performances. The simulation findings show a significant efficiency of the suggested algorithm on the TSPLIB data set. Finally, we extend the large-scale TSP problem to the field of art and use the presented algorithm to optimize the path of discrete pixels in the picture, showing the artistic painting of the TSP art project.

I. Introduction

The Travelling Salesman Problem [1], TSP for short, is a classic NP-hard problem in combinatorial optimization, significant in the field of operations research and theoretical computer science. The problem, first formulated in 1930, is essentially concentrated on optimization. In this context, the steady goal of researchers and practitioners is to seek a cheaper, shorter, or quicker solution.