中文摘要：

高维目标优化是目前多目标优化领域的研究热点和难点．提出一种占优机制，即双极偏好占优用于处理高维目标优化问题．该占优机制同时考虑决策者的正偏好和负偏好信息，在非支配解之间建立了更加严格的占优关系，能够有效减少种群中非支配解的比例，引导算法向靠近正偏好同时远离负偏好的Pareto最优区域收敛．为检验该方法的有效性，将双极偏好占优融入NSGA—II中，形成算法2p-NSGA．II，并在2到15目标标准测试函数上进行测试．得到了艮好的实验结果．同时，将所提出的占优机制与目前该领域的两种占优机制g占优和r占优进行性能对比。实验结果表明，2p—NSGA-II算法无论是在求解精度还是运行效率上，整体上均优于g-NSGA．II和r-NSGA—II．

英文摘要：

Many-Objective optimization is a difficulty for classical multi-objective evolutionary algorithm and has gained great attention during the past few years. In this paper, a dominance relation named bipolar preferences dominance is proposed for addressing many-objective problem. The proposed dominance relation considers the decision maker＇s positive preference and negative preference simultaneously and creates a strict dominance relation among the non-dominated solutions, which has ability to reduce the proportion of non-dominated solutions in population and lead the race to the Pareto optimal area, which is close to the positive preference and far away from negative preference. To demonstrate its effectiveness, the proposed approach was integrated into NSGA-II to be a new algorithm denoted by 2p-NSGA-II and tested on a benchmark of two to fifteen-objective test problems. Good results were obtained. The proposed dominance relation was also compared to g-dominance and r-dominance which was the most recently proposed dominance relation, the results of comparative experiment showed 2p-NSGA-II was superior to g-NSGA-II and r-NSGA-II on a whole, no matter the accuracy of obtained solutions or the efficiency of algorithm.