Enhanced Monarch Butterfly Optimization Algorithm with Rank-Based Selection and Random Jump Strategy for Constrained Engineering Problems

Nature-inspired algorithms have become increasingly prevalent in engineering and mathematical optimization due to their efficacy and adaptability. Among these algorithms, the Monarch Butterfly Optimization Algorithm (MBOA) is a population-based metaheuristic, characterized by its simple implementation and the utilization of the Migration Operator (MO) and Butterfly Adjusting Rate (BAR) to guide the search path of butterflies. However, the algorithm can suffer from susceptibility to local optima traps, early convergence, and inferior performance due to a lack of random factors. To address these challenges, we propose an Enhanced Monarch Butterfly Optimization Algorithm (E-MBOA) that incorporates Ranking-based Selection (RBS) and a Random Jumping strategy. The RBS prioritizes the search direction based on individuals' ranks in the population, enhancing the search process by encouraging the exploration of feasible areas with lower objective function values. By employing the Random Jumping strategy, the process can effectively investigate the search space and avoid local optima, thus mitigating early convergence issues. The proposed model is assessed on a variety of mechanical and engineering design problems. Results are contrasted to other optimization approaches published in the literature, demonstrating that the proposed model offers faster convergence to global optima and effectively avoids local optima traps. E-MBOA's performance validates its feasibility and effectiveness as a powerful tool for resolving complex engineering optimization problems.