Five-Element Cycle Optimization Algorithm Based on an Integrated Mutation Operator for the Traveling Thief Problem

This paper presents a novel algorithm named Five-element Cycle Integrated Mutation Optimization (FECOIMO) for solving the Traveling Thief Problem (TTP). The algorithm introduces a five-element cycle structure that integrates various mutation operations to enhance both global exploration and local exploitation capabilities. In experiments, FECOIMO was extensively tested on 39 TTP instances of varying scales and compared with five common metaheuristic algorithms: Enhanced Simulated Annealing (ESA), Improved Grey Wolf Optimization Algorithm (IGWO), Improved Whale Optimization Algorithm (IWOA), Genetic Algorithm (GA), and Profit-Guided Coordination Heuristic (PGCH). The experimental results demonstrate that FECOIMO outperforms the other algorithms across all instances, particularly excelling in large-scale instances. The results of the Friedman test show that FECOIMO significantly outperforms other algorithms in terms of average solution, maximum solution, and solution standard deviation. Additionally, although FECOIMO has a longer execution time, its complexity is comparable to that of other algorithms, and the additional computational overhead in solving complex optimization problems translates into better solutions. Therefore, FECOIMO has proven its effectiveness and robustness in handling complex combinatorial optimization problems.