Extending Boundary Updating Approach for Constrained Multi-objective Optimization Problems

To date, several algorithms have been proposed to deal with constrained optimization problems, particularly multi-objective optimization problems (MOOPs), in real-world engineering. This work extends the 2020 study by Gandomi & Deb on boundary updating (BU) for the MOOPs. The proposed method is an implicit constraint handling technique (CHT) that aims to cut the infeasible search space, so the optimization algorithm focuses on feasible regions. Furthermore, the proposed method is coupled with an explicit CHT, namely, feasibility rules and then the search operator (here NSGA-II) is applied to the optimization problem. To illustrate the applicability of the proposed approach for MOOPs, a numerical example is presented in detail. Additionally, an evaluation of the BU method was conducted by comparing its performance to an approach without the BU method while the feasibility rules (as an explicit CHT) work alone. The results show that the proposed method can significantly boost the solutions of constrained multi-objective optimization.