Extreme Learning Surrogate Models in Multi-objective Optimization based on Decomposition

• The problem of solving expensive MOPs with small evaluation budgets is treated.
• The paper investigates the use of ELM as a surrogate model in MOEAs.
• A procedure is used to automatically select ELM parameters.
• The scalability of surrogates concerning the total of decision variables and number of objectives is evaluated.
• Experimental results show the good performance of ELMOEA/D in different problems.

This paper proposes ELMOEA/D, a surrogate-assisted MOEA, for solving costly multi-objective problems in small evaluation budgets. The proposed approach encompasses a state-of-the-art MOEA based on decomposition and Differential Evolution (MOEA/D-DE) assisted by Extreme Learning Machines (ELMs). ELMOEA/D is tested in instances from three well-known benchmarks (ZDT, DTLZ and WFG) with 5–60 decision variables, 2 and 5 objectives. The ELMOEA/D׳s performance is also analyzed on a real problem (Airfoil Shape Optimization). The impact of some ELMs parameters and an automatic model selection mechanism is investigated. The results obtained by ELMOEA/D are compared with those of two state-of-the-art surrogate approaches (MOEA/D-RBF and ParEGO) and a non-surrogate-based MOEA (MOEA/D). The ELMOEA/D variants are among the best results for most benchmark instances and for the real problem.