Post Pareto-optimal pruning algorithm for multiple objective optimization using specific extended angle dominance

• We use specific bias parameter (τ) to express preference in pruning.
• MOEA/D is modified and integrated with our ASA for pruning solutions.
• Single level and two-level pruning are presented.
• Our ASA provides high-quality solutions in terms of convergence to optimality.
• Generational Distance (GD), a standard convergence metric, is used for performance evaluation.

For the last two decades, significant effort has been devoted to exploring Multi-Objective Evolutionary Algorithms (MOEAs) for solving complex practical optimization problems. MOEAs approximate a representative set of Pareto-optimal solutions and present them to the decision maker (DM). Recently, studies in this area have focused on decision-making techniques in order to help the DM to arrive at a single preferred solution. This paper presents a pruning algorithm which can be applied in the post Pareto-optimal phase to select a subset of robust Pareto-optimal solutions before presenting them to the DM. Our algorithm is called Angle based with Specific bias parameter pruning Algorithm (ASA). Our pruning method begins by calculating the angle between each pair of solutions using an arctangent function. We introduce a bias intensity parameter to calculate a threshold angle in order to identify areas with desirable solutions based on the DM׳s preference. The bias parameter can be tuned specifically for each objective. We also propose a technique to determine a region of interest using reference point to MOEA/D algorithm which leads to a modified version of MOEA/D (PR-MOEA/D). The experimental results show that our pruning algorithm provides a robust subset of Pareto-optimal solutions for our benchmark problems when evaluating solutions in terms of convergence to optimality.