Directly Targeting Convex Pareto Solutions
Abstract
When solving problems with multiple conflicting objectives, evolutionary multi and many-objective optimization (EMO/EMaO) algorithms attempt to find a number of diverse Pareto-optimal (PO) solutions, irrespective of whether the resulting PO front (PF) has convex, concave, or a mix of both shape. Despite this ability, finding the convex part of the PF alone can be an algorithmic challenge. Moreover, from a trade-off perspective and a easier relevance of PO solutions with objectives, decision-makers may prefer solutions from the convex parts of the PF. In such scenarios, one approach would be to first find a representative solution set on the entire PF and then select the convex part, which may not computationally effective. Here, we propose a convex-PF seeking EMO - CPF-NSGA-III - a new algorithm that directly finds only the convex PO solutions without wasting effort on other parts. Our method, extended with an dynamic algorithmic parameter update strategy, uses a linear programming technique to identify convex solutions during the search process. We test our approach on problems with two to 10 objectives, demonstrating the effectiveness of CPF-NSGA-III.
Authors: Kalyanmoy Deb, Shashank Raj
Published in: Genetic and Evolutionary Computation Conference Companion (GECCO Companion) (2026)