Adaptive geometric angle-based algorithm with independent objective biasing for pruning Pareto-optimal solutions

Real-life problems are multi-objective in nature. Prioritizing one objective could suddenly deteriorate other objectives. Furthermore, there is no existence of single best trade-off solution in multi-objective frameworks with many competing objectives. As a decision maker´s (DM) opinion is concerned, allowing the DM decides his/her prefer objective is one of the interesting research directions in multi-criteria decision making (MCDM) community. In this paper, we propose an algorithm to help the decision maker (DM) choosing the final best solution based on his/her prefer objective. The main contribution of our algorithm is filter out undesired solutions and provides more robust trade-off set of optimal solutions to the DM. Our algorithm is called an adaptive angle based pruning algorithm with independent bias intensity tuning (ADA-τ). Our pruning method begins by calculating the angle between a pair of solutions by using a simple geometric function that is an inverse tangent function. The bias intensity parameter of each objective is introduced as a minimum threshold angle in order to approximate the portions of desirable solutions based on DM´s prefer objective. We consider several benchmark problems including two and three-objective problems. We approximate Pareto-set of each problem using a simple version of MOEA/D algorithm, and then the pruning algorithm is applied. The experimental result has shown that our pruning algorithm provides a robust sub-set of Pareto-optimal solutions for each benchmark problem. The pruned Pareto-optimal solutions distributed and covered multiple regions instead of a single region of Pareto front when the equal biasing is applied. In addition, it is clearly shown that the pruned Pareto-optimal solutions are located at knee regions of the Pareto front with appropriate bias allocation.