A Novel Discrete Differential Evolution Algorithm for Solving the Traveling Salesman Problem

Abstract

This research introduces a novel approach, Discrete Differential Evolution (DDE), to address the Traveling Salesman Problem (TSP), a classic combinatorial optimization challenge with wide-ranging real-world applications. While initially designed for continuous optimization problems, the Differential Evolution algorithm has been adapted to suit the discrete nature of the TSP. Our approach involves several key modifications to the standard Differential Evolution algorithm. These include the creation of mutant vectors through random subtour optimization, the utilization of order crossover to generate trial vectors, and the application of a pool tournament population selection method to identify the most promising candidates. To assess the effectiveness of our proposed algorithm, we conducted comprehensive computational experiments across multiple TSP instances. Comparative analyses against other algorithms, such as the Hybrid Differential Evolution (HDE) and Discrete Particle Swarm Optimization (DPSO), consistently demonstrated that our proposed DDE outperformed the competitors on all Traveling Salesman test instances. This underscores the algorithm's superior performance, as evidenced by its consistently superior results in both the best and the mean solution quality, along with lower Relative Error (RE) values, signifying its proficiency in identifying routes closer to the optimum.