Pareto强度值实数编码多目标贝叶斯优化算法

An Effective and Satisfactory PSRCMBOA(Pareto Strength Real-Coded Multi-objective Bayesian Optimization Algorithm)

提出了一种采用基于决策树的贝叶斯网络表示各变量之间条件相关性的分布估计算法：Pareto强度值实数编码多目标贝叶斯优化算法（PSRCMBOA）。通过构建这样的网络模型,继而对模型进行抽样以产生新个体。再对生成的新个体进行变异操作,以增加种群的多样性,提高算法的搜索能力。这种生成新个体的方法结合基于强度值的适应度计算方式以及截断选择机制,可以获得很好地逼近多目标问题的Pareto前沿,且分布均匀的非劣解集。对于约束多目标优化问题,算法采用带约束支配关系判别个体的优劣。文中用3个较难的测试问题验证该算法的性能,并将其应用于Clipper飞船返回舱的气动布局多目标优化设计。PSRCMBOA对3个测试问题找到了很贴近Pareto前沿的非劣解集。对于Clipper飞船返回舱,算法获得了分布较宽且均匀的非劣解集。分析发现,为获得高升阻比,返回舱球头半径应选择在0.155-0.165 m之间、前锥半锥角应选择在20°左右、头锥底到返回舱底部的距离可选择在3.6-4.4 m之间、柱段长可在1.2-1.5 m之间。优化结果表明,该算法能够获得高质量的非劣解集,是一种有效的多目标优化算法,能够用于对复杂的工程问题进行优化设计。

Aim. Existing multi-objective Bayesian optimization algorithms are satisfactory for discrete variables but become, in our opinion, unsatisfactory for continuous variables. We now present PSRCMBOA that is, we believe, not only satisfactory for continuous variables but also effective in the sense that it is relatively fast. In the full paper, we explain our PSRCMBOA in detail. In this abstract, we just add some pertinent remarks to listing the two topics of explanation. The first topic is the decision-tree-based Bayesian network. In the first topic, we explain how to use Bayesian network as probabilistic models to encode conditional dependencies among variables. The second topic is the PSRCMBOA. In the second topic, we explain that： （1） by building and sampling the probabilistic models, the algorithm reproduces the genetic information of the next generation; （2） combining such a reproduction mechanism with the Pareto-strength fitness evaluation and truncated selection techniques, the PSRCMBOA can approximate the probability density of solutions lying on the Pareto front; （3） in PSRCMBOA, a polynomial mutation operator is incorporated in order to enhance exploration and maintain diversities in the populations; and （4） the constrained-dominance is applied to solving constrained multi-objective optimization problems effectively. Finally, we give several numerical simulation examples. First, we evaluate the performance of PSRCMBOA with three difficult test problems. Non-dominated solution sets close to the Pareto front of the three test problems are successfully obtained by the PSRCMBOA. Then we apply it to optimizing aerodynamic configuration of Clipper reentry capsule. For Clipper reentry capsule, a broad and evenly spread non-dominated solution set is successfully obtained. Furthermore, the analysis of the non-dominated solution set shows that, in order to reach a high L/D, the sphere radius of the reentry capsule should be within 0. 155-0. 165 m, the fore half-cone angle about 20 degrees, the distance from the fore cone to bottom of the reentry capsule within 3.6-4.4 m, and the length of pole 1.2-1.5 m. These results indicate preliminarily that the PSRCMBOA is effective and satisfactory for multi-objective optimization.