A New Steady-State MOEA/D for Sparse Optimization

Abstract

The classical algorithms based on regularization usually solve sparse optimization problems under the framework of single objective optimization, which combines the sparse term with the loss term. The majority of these algorithms suffer from the setting of regularization parameter or its estimation. To overcome this weakness, the extension of multiobjective evolutionary algorithm based on decomposition (MOEA/D) has been studied for sparse optimization. The major advantages of MOEA/D lie in two aspects: (1) free setting of regularization parameter and (2) detection of true sparsity. Due to the generational mode of MOEA/D, its efficiency for searching the knee region of the Pareto front is not very satisfactory. In this paper, we proposed a new steady-state MOEA/D with the preference to search the region of Pareto front near the true sparse solution. Within each iteration of our proposed algorithm, a local search step is performed to examine a number of solutions with similar sparsity levels in a neighborhood. Our experimental results have shown that the new MOEA/D clearly performs better than its previous version on reconstructing artificial sparse signals.