On the use of gradient-based repair method for solving constrained multiobjective optimization problems—a comparative study

In this chapter, we study the effect of repairing infeasible solutions using the gradient information for solving constrained multiobjective problems (CMOPs) with multiobjective evolutionary algorithms (MOEAs). For this purpose, the gradient-based repair method is embedded in six classical constraint-handling techniques: constraint dominance principle, adaptive threshold penalty function (ATP), C-MOEA/D, stochastic ranking, e-constrained and improved e-constrained. The test functions used include classical problems with inequality constraints (CFs and LIRCMOPs functions) as well as six recent problems with equality constraints. The obtained results show that the gradient information coupled with a classical technique is not computationally prohibitive and can make the given classical technique much more robust. Moreover, in highly constrained problems, like those involving equality constraints, the use of the gradient for repairing solutions may not only be useful but also necessary in order to obtain a good approximation of the true Pareto front.Peer ReviewedPostprint (author's final draft