Constrained multi-objective optimization evolutionary algorithm for real-world continuous mechanical design problems

During the past two decades, evolutionary algorithms have seen great achievements in solving complex optimization problems owing to the advantages brought by their properties, especially constrained multi-objective optimization problems (CMOPs) with multiple conflicting objective functions and constraints which widely exist in industry, scientific research, and daily life. Among the real-world CMOPs, mechanical design problems (MDPs) from the industry widely exist and are important, while unfortunately, most constrained multi-objective evolutionary algorithms (CMOEAs), developed based on benchmark CMOPs, neglect the specific features and challenges of MDPs and thus cannot solve them well to provide the practitioners promising Pareto optimal solutions for decision making. To overcome this limitation, this paper analyzes the features and challenges of MDPs, including badly scaled objective space, decision space properties, and decision variable linkages. Then, we propose a new CMOEA named CMORWMDP. First, instead of the homogeneous operator in existing CMOEAs, a heterogeneous operator strategy is adopted to use the operator of Genetic Algorithm to enhance the convergence and the operator of Differential Evolution to tackle variable linkages. In addition, an improved fitness function that considers normalization is designed for environmental and mating selections. The proposed algorithm is simple, parameter-free, and easy to implement. Experiments on 21 real-world MDPs show its superiority compared to 20 state-of-the-art CMOEAs under the Friedman test and Wilcoxon test on different metrics, demonstrating the effectiveness of the heterogeneous operator and normalization-based fitness for selections for real-world MDPs. Moreover, the effectiveness of the proposed algorithm in solving other real-world CMOPs is also verified, revealing that our methods are very promising in tackling real-world problems.