Direction Estimation for Collaborative Search in MOEA/D

The decomposition-based multi-objective evolutionary algorithm (MOEA/D) is an efficient framework for solving multi-objective optimization problems. It decomposes a multi-objective optimization problem into a set of single-objective optimization subproblems and solves them collaboratively. However, most MOEA/D variants use heuristic operators to generate new solutions, which might lead to inefficient search performance. Direction estimation is a powerful derivative-free technique for tackling black-box optimization problems. By iteratively estimating valid search directions, this method can efficiently search for the optimal solution in a principled way; yet it suffers from high computational cost since it requires a number of function evaluations to approximate the true gradient. In this work, we leverage the neighborhood structure of MOEA/D and interactions among different subproblems to estimate a promising descent direction. We demonstrate that sharing and exploiting valuable information among neighboring subproblems can significantly reduce the overall computational budget for direction estimation in MOEA/D (MOEA/D-DirE). Experimental results demonstrate that the proposed MOEAD-DirE algorithm outperforms many multi-objective evolutionary algorithms on various multi-objective optimization problems.