Directed mating using inverted PBI function for constrained multi-objective optimization

In evolutionary constrained multi-objective optimization, the directed mating utilizing useful infeasible solutions having better objective function values than feasible solutions significantly contributes to improving the search performance. This work tries to further improve the effectiveness of the directed mating by focusing on the search directions in the objective space. Since the conventional directed mating picks useful infeasible solutions based on Pareto dominance, all solutions are given the same search direction regardless of their locations in the objective space. To improve the diversity of the obtained solutions in evolutionary constrained multi-objective optimization, we propose a variant of the directed mating using the inverted PBI (IPBI) scalarizing function. The proposed IPBI-based directed mating gives unique search directions to all solutions depending on their locations in the objective space. Also, the proposed IPBI-based directed mating can control the strength of directionality for each solution´s search direction by the parameter θ. We use discrete m-objective k-knapsack problems and continuous mCDTLZ problems with 2–4 objectives and compare the search performances of TNSDM algorithm using the conventional directed mating and the proposed TNSDM-IPBI using IPBI-based directed mating. The experimental results shows that the proposed TNSDM-IPBI using the appropriate θ^∗ achieves higher search performance than the conventional TNSDM in all test problems used in this work by improving the diversity of solutions in the objective space.