Constrained Probabilistic Pareto Dominance for Expensive Constrained Multiobjective Optimization Problems
提出一种无参数的约束处理技术CPPD，通过概率计算平衡可行解与不可行解，并开发了基于Kriging模型的进化算法PEA和PEA+，用于解决昂贵约束多目标优化问题。
This paper proposes a new parameterless constraint-handling technique, named constrained probabilistic Pareto dominance (CPPD), for expensive constrained multiobjective optimization problems (CMOPs). In CPPD, when comparing two solutions, in terms of each original objective, we design a new objective for each solution, which is the negative product of two probabilities calculated based on the predicted fitness mean values and the uncertainty information provided by Kriging models: 1) the probability that this solution satisfies all constraints, denoted as PoF, and 2) the probability that this solution is better than the other on the original objective, denoted as PoB. It is evident that for each solution, PoF and PoB indicate its feasibility and its optimality on the corresponding original objective, respectively. Then, Pareto dominance based on new objectives is executed. As a result, both competitive feasible solutions and promising infeasible solutions with good diversity can be preserved by CPPD. These two kinds of solutions can help the population to exploit the located feasible parts and to explore new feasible parts, respectively. Further, based on CPPD, we develop a Pareto-based Kriging-assisted constrained multiobjective evolutionary algorithm (called PEA) to deal with expensive CMOPs with two or three objectives. Finally, PEA is generalized to solve expensive constrained many-objective optimization problems, named PEA+. The effectiveness of CPPD, PEA, and PEA+ is verified by comprehensive experiments.