A decomposition-based many-objective evolutionary algorithm updating weights when required

Multi-objective evolutionary algorithms based on decomposition (MOEA/D) usually work effectively when they have an appropriate set of weight vectors. A uniformly distributed set of unchanging weight vectors may lead to well-distributed solutions over a smooth, continuous, and well-spread Pareto front. However, fixed-value weight vectors may lead to solutions that fail, depending on the geometry of the problem. Several studies have used a predefined lapse of time to adapt weight vectors. This suggests that adaptation may not be being performed at the most appropriate moments of the evolutionary process. This paper presents the MOEA/D with updating when required (MOEA/D-UR) that uses a metric that detects improvements so as to determine when to adjust weights and a procedure for dividing the objective space in order to increase diversity. The results of experimental tests, which used real-world problems and the problem classes WFG1-WFG9, DTLZ1-DTLZ7, IDTLZ1-2, and MaOP1-6 with 3, 5, 6, 8, 10, 12, and 15 objectives, suggest that MOEA/D-UR is more effective, when compared with ten state-of-the-art algorithms.