Pareto-aware strategies for faster convergence in multi-objective multi-scale search optimization

In this paper, a new multi-objective optimization algorithm in a multi-scale framework with faster convergence characteristics is presented, referred to as the Pareto-Aware DIviding RECTangles (PA-DIRECT) method. PA-DIRECT follows the Multi-scale Search Optimization (MSO) framework and considers Pareto-optimality of the sampled points in the objective space during its search. The importance of Pareto awareness is highlighted in PA-DIRECT through the use of two selection strategies for Potentially Optimal Hyper-rectangles (POHs), on the (a) approximate Pareto front and (b) dominated fronts. With the aim of performing sampling conservatively, both strategies are embedded with the concept of diversification through the use of a modified Hypervolume measure that accounts for diversity in (a) and the number of dominating points in (b). Further, a new Pareto-aware global score assignment, aligned to the notion of Pareto-awareness, is introduced. PA-DIRECT  has been benchmarked against MO-DIRECT and other state-of-the-art algorithms selected from different techniques of multi-objective optimization solvers using a bi-objective test suite on the Comparing Continuous Optimisers (COCO) platform. The study results substantiate the efficacy of PA-DIRECT in providing a high-quality approximate set, especially for multi-modal problems.