Hybrid Ant Colony Optimization with Force-Directed Layouts for Solving the Traveling Salesman Problem

Abstract

This paper presents a hybrid approach to solving the classical Traveling Salesman Problem (TSP) by combining Ant Colony Optimization (ACO) with force-directed graph layouts. Inspired by natural ant foraging behaviors, the proposed algorithm simulates pheromone-based learning and dynamically distributes nodes to enhance solution quality and visualization. Implemented within the Godot game engine using GDScript, the method demonstrates rapid convergence toward near-optimal solutions across multiple runs. Real-time visualization aids intuitive understanding of algorithm dynamics. Comparative experiments show that the hybrid model significantly improves convergence speed and path optimization over traditional ACO baselines. Potential extensions to larger, high-dimensional optimization problems are discussed.