中文摘要：

差分进化算法是一种结构简单、易用且鲁棒性强的全局搜索启发式优化算法,它可以结合约束处理技术来解决约束优化问题.机器学习在进化算法中,经常可以引导种群的进化,而且被广泛地应用于无约束的差分进化算法中,但对于约束差分进化算法却很少有应用.针对这一情况,提出了一种基于反向学习的约束差分进化算法框架.该算法框架采用基于反向学习的机器学习方法,提高约束差分进化算法的多样性和加速全局收敛速度.最后把该算法框架植入了两个著名的约束差分进化算法：（μ＋λ）-CDE和ECHT,并采用CEC 2010的18个Benchmark函数进行了实验评估,实验结果表明：与（μ＋λ）-CDE和ECHT相比,植入后的算法具有更强的全局搜索能力、更快的收敛速度和更高的收敛精度.

英文摘要：

Differential evolution is a global heuristic algorithm,which is simple,easy-to-use and robust in practice.Combining with the constraint-handling techniques,it can solve constrained optimization problems. Machine learning often guides population to evolve in the evolution computation,and is widely applied to unconstrained differential evolution algorithm. However,machine learning is rarely applied to constrained differential evolution algorithm,so this paper proposed a constrained differential evolution algorithm framework using opposition-based learning. The algorithm can improve the diversity and convergence of differential evolution. At last,the proposed algorithm framework is applied to two popular constrained differential evolution variants,that is（ μ ＋ λ）-CDE and ECHT-DE. And 18 benchmark functions presented in CEC 2010 are chosen as the test suite,experimental results showthat comparing with（ μ ＋ λ）-CDE and ECHT-DE,our algorithms are able to improve global search ability,convergence speed and accuracy in the majority of test cases.