基于网络响应面的多目标优化方法

为提高多目标优化算法的收敛性以及Pareto解的分布均匀性,构建了基于网络响应面的多目标优化方法.将前馈（BP）网络以及自适应共振（ART）网络的优点相结合,充分利用各子目标每1次独立优化时获得的最优解,并将其作非占优判断后作为初始样本自适应地构建网络响应面,从而提高了Pareto解的收敛性以及多样性指标.对网络获得的每个新类进行各子目标值计算,同时对该子目标值做相似度计算,进一步剔除相似度高的样本,从而提高了Pareto解的分布性指标.通过常用的多目标优化测试函数验证该方法,并与改进的非支配排序遗传算法（NSGA-Ⅱ）以及随机权和算法作对比,结果表明该方法能明显改善多目标优化方法的各性能指标.

Multi-objective optimization method based on network response surface

In order to improve the solving performance of multi-objective optimization method,a multi-objective optimization method of matched response surface based on neural network was proposed.By combining the advantages of the back-propagation(BP) network with the adaptive resonance theory(ART) network and making full use of the optimal solution obtained in the independent sub-objective optimization process which was non-dominantly judged and used as the initial sample to determine the adaptive response surface construction of the network,the proposed method enhancesd convergence and diversity index for Pareto solutions.The sub-objective values were calculated for the new class which the network obtains,and the distributed computing of sub-objective values was carried out to further exclude similar samples(i.e.,Pareto solution),thereby enhancing the distribution index for Pareto solutions.Comparison studies of this method with the improved no-dominated sorting genetic algorithm(NSGA-Ⅱ) and random weight-sum method on some commonly used benchmark problem instances indicate that the multi-objective optimization method based on network to match response surface can improve the comprehensive performance of multi-objective optimization.