ELMOEA/D-DE: Extreme Learning Surrogate Models in Multi-objective Optimization Based on Decomposition and Differential Evolution

Despite the success of Evolutionary Algorithms in solving complex problems, they may require many function evaluations. This becomes an issue when dealing with costly problems. Surrogate models may overcome this difficulty, though their use in problems with medium to large dimensionality is underexplored in the literature. Problems with multiple conflicting objectives can be formulated as Multi-objective Optimization Problems (MOPs). MOPs have received a great attention lately, mainly with Multi-objective Evolutionary Algorithms (MOEAs). This paper proposes ELMOEA/D-DE, a surrogate-assisted MOEA, for solving expensive MOPs in small evaluation budgets. ELMOEA/D-DE encompasses a state-of-the-art MOEA based on decomposition, Differential Evolution (DE) operators and Extreme Learning Machines. This paper tests three variants of ELMOEA/D-DE, using different DE operators, for solving five known benchmark MOPs with 10 to 60 decision variables. All variants achieve good results in terms of hyper volume metric and the best variant with operator DE/rand/1/bin is compared with two state-of-the-art approaches (MOEA/D-RBF and a non-surrogate-based MOEA), achieving the best results in all but one problems instances.