$$\delta$$ δ MOEA/D-AWACD: Improving Constant-Distance-Based MOEA/D-AWA Using a Step Function Parameter Control Mechanism

Multi-objective evolutionary algorithm based on decomposition (MOEA/D) divides a multi-objective optimization problem into several subproblems using scalarization technique. These subproblems are assigned with evenly spaced weight vectors, and they are collaboratively solved using the concept of information sharing within their own neighborhood. One of the recent algorithms, i.e., constant-distance-based neighbors for MOEA/D with dynamic weight vector adjustment (MOEA/D-AWACD), integrates the concept of constant-distance neighborhood and dynamic weight vector design. This combination creates a flexible neighborhood that can adapt to the weight vectors changes. However, MOEA/D-AWACD’s performance is dependent on a constant-distance parameter $$\delta$$ δ that adjusts the neighborhood size. To obtain an appropriate value of parameter $$\delta$$ δ , multiple and separate algorithm executions are required. Thus, in this paper, $$\delta$$ δ MOEA/D-AWACD is proposed. It employs a step-function parameter control mechanism to systematically control the parameter $$\delta$$ δ within a single algorithm execution. In a comparison study which uses ZDT, UF, and DTLZ test problems as the testbed, the proposed $$\delta$$ δ MOEA/D-AWACD is able to significantly outperform MOEA/D, MOEA/D-AWA, MOEA/D-AWACD, and non-dominated sorting genetic algorithm II (NSGA-II) in both hypervolume (HV) and inverted generational distance (IGD) metrics.