Decomposition-Based Approach for Solving Large Scale Multi-objective Problems


Decomposition is a well-established mathematical programming technique for dealing with multi-objective optimization problems (MOPs), which has been found to be efficient and effective when coupled to evolutionary algorithms, as evidenced by MOEA/D. MOEA/D decomposes a MOP into several single-objective subproblems by means of well-defined scalarizing functions. It has been shown that MOEA/D is able to generate a set of evenly distributed solutions for different multi-objective benchmark functions with a relatively low number of decision variables (usually no more than 30). In this work, we study the effect of scalability in MOEA/D and show how its efficacy decreases as the number of decision variables of the MOP increases. Also, we investigate the improvements that MOEA/D can achieve when combined with coevolutionary techniques, giving rise to a novel MOEA which decomposes the MOP both in objective and in decision variables space. This new algorithm is capable of optimizing large scale MOPs and outperforms MOEA/D and GDE3 when solving problems with a large number of decision variables (from 200 up to 1200).