中文摘要：

工程实践中存在大量约束多目标优化问题（Constrained multi-objective optimization problems,CMOPs）,多目标进化算法是求解这类问题的一类有效方法.引入扇形采样技术,将二次变异双种群差分进化算法和约束处理方法相结合,设计求解CMOPs的进化算法——基于扇形采样的约束多目标差分进化算法（Sector-sampling-based constrained multi-objective differential evolution algorithm,SS-CMODE）.扇形采样可避免耗时的非劣操作,且能保证Pareto最优解集的良好逼近性和多样性.通过3个典型CMOPs的对比测试,表明SS-CMODE的解集均匀性和计算效率明显优于对比算法.以J23-80机械压力机使用的双曲柄串联机构多目标优化为例,研究新算法求解工程问题的有效性.以锻冲工作阶段平均速度波动最小和力传动性能最优为目标,建立机构的约束多目标优化模型,再应用SS-CMODE求解该问题.结果表明,该算法能求出多组满足约束条件的Pareto 最优解,且解集均匀性良好.

英文摘要：

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.