目标约束融合的约束多目标免疫算法及性能评价准则

A constrained multi-objective immune algorithm based on objective and constraint fusion and performance evaluation metric

免疫算法求解约束多目标优化问题时,如何设计抗体的亲和力,以及如何保持或提高种群的多样性为算法设计的关键.本文基于免疫系统的固有免疫和自适应免疫交互运行模式,提出目标约束融合的并行约束多目标免疫算法(parallel constrained multiobjective immune algorithm,PCMIOA).利用支配度和浓度设计抗体的亲和力,提出了目标约束融合的评价方法,增强了算法的收敛性.借助基因重组中DNA片段的转移机制,设计一种转移(transformation)算子,提高了种群的多样性.针对已有性能评价准则存在的不足给出一种改进的支配范围评价准则.数值实验选用12个约束二目标和4个非约束三目标测试函数验证PCMIOA的优化性能,并将其与3种著名的约束多目标算法和5种非约束多目标算法进行比较.结果表明:PCMIOA具有较强的优化性能.与其他算法相比,PCMIOA所获的Pareto最优前沿能较好的逼近真实Pareto最优前沿,且分布较均匀.

How to design the affinity of an antibody and to maintain or improve the population diversity has always been a key problem, when an immune algorithm is applied to solve constrained multi-objective optimization problems （CMOPs）. To solve this problem, we propose a parallel constrained multi-objective immune algorithm （PCMIOA） by merging objectives and constraints, based on the interactive operation of innate immune and adaptive immune in the immune system. In this algorithm, we define the affinity of an antibody by using the domination degree and density, and develop an evaluation approach for assembled objectives and constraints, which accelerates the convergence of PCMIOA. In addition, a transformation mechanism that occurs in the recombination process of DNA segment is presented to improve the population diversity. An improved domination scope metric is developed in order to overcome the disadvantages of the existing ones. PCMIOA is applied to solve a set of twelve two-objective CMOPs and four unconstrained three-objective test problems. The experimental results indicate that PCMIOA is able to achieve a superior performance. The Pareto-optimal front obtained by PCMIOA very well approximates the true Pareto-optimal front and exhibits a well-spread when compared to three modern constrained multi-objective algorithms and five unconstrained multi-objective algorithms.