Sector-sampling-based Constrained Multi-objective Differential Evolution and Its Engineering Application

Abstract

There exist many constrained multi-objective optimization problems(CMOPs) in engineering practical fields, and multi-objective evolutionary algorithms are a class of available approaches to these problems. An evolutionary algorithm is suggested for solving CMOPs, called sector-sampling-based constrained multi-objective differential evolution algorithm(SS-CMODE), which borrows the sector sampling technique, and combines the bi-subgroup differential evolution algorithm with second mutation operators and the constraint handling approach. The sector sampling technique can avoid the expensive non-dominated sorting and assure both diversity and convergence of Pareto-optimal solutions. The proposed SS-CMODE algorithm is tested against three benchmarks CMOPs and the results are compared extensively with ones obtained by the contrasted algorithm to show that the former outperforms the latter in the distribution uniformity of solutions and the computational efficiency. A multi-objective optimization problem for the series-double-crank linkage of J23-80 type mechanical press is employed as a study case to demonstrate the efficiency of the novel algorithm to solve engineering application problems. This work firstly constructs a constrained multi-objective optimization model for the linkage which takes the minimizing average velocity fluctuation and the optimizing force transmission performance for stamping-punch working stroke as design objectives. Consequently, the SS-CMODE algorithm is utilized to solve this problem. A real case study is implemented to indicate that the model and the algorithm is able to find a set of alternative solutions which are satisfied with the constraint functions and have well uniformity.