Multi-Objective Five-Element Cycle Optimization Algorithm Based on Multi-Strategy Fusion for the Bi-Objective Traveling Thief Problem

In this paper, we propose a Multi-objective Five-element Cycle Optimization algorithm based on Multi-strategy fusion (MOFECO-MS) to address the Bi-objective Traveling Thief Problem (BITTP), an extension of the Traveling Thief Problem that incorporates two conflicting objectives. The novelty of our approach lies in a unique individual selection strategy coupled with an innovative element update mechanism rooted in the Five-element Cycle Model. To balance global exploration and local exploitation, the algorithm categorizes the population into distinct groups and applies crossover operations both within and between these groups, while also employing a mutation operator for local searches on the best individuals. This coordinated approach optimizes parameter settings and enhances the search capabilities of the algorithm. Extensive experiments were conducted on nine BITTP instances, comparing MOFECO-MS against eight state-of-the-art multi-objective optimization algorithms. The results show that MOFECO-MS excels in both Hypervolume (HV) and Spread (SP) indicators, while also maintaining a high level of Pure Diversity (PD). Overall, MOFECO-MS outperformed the other algorithms in most instances, demonstrating its superiority and robustness in solving complex multi-objective optimization problems.