Equality Constrained Multi-objective optimization

The Evolutionary Algorithms community have had lukewarm interest in Equality constrained Multi-objective (MO) Optimization problems so far. Recently, we proposed a Most Probable Point (MPP) based repair method for equality constraint handling, where we concentrated on single-objective optimization problems. In the present work, we focus our attention to equality constrained MO optimization. We first propose a set of equality constrained MO test problems (having upto 30 variables) and then suggest a more pragmatic clustering based method for selecting the infeasible solutions to be repaired which reduces the number of function evaluations considerably. The repair procedure is integrated with the popular Evolutionary MO optimization (EMO) procedure, the NSGA-II. The results will show that the proposed procedure reaches the feasible state faster, as compared to NSGA-II for all the test problems and hence show promise as an effective method for handling equality constraints in MO optimization.