Hierarchical Convergence to Multiple Alternate Solutions: Population versus Point-based Algorithms
Ahmer Khan, Kalyanmoy Deb · Proceedings of the Genetic and Evolutionary Computation Conference Companion · 2025
Evolutionary algorithms to solve multi-modal and multi-objective optimization problems do not follow any specific order of convergence to different optimal solutions. However, there exist certain problems, in which a hierarchical discovery of multiple critical solutions is must to constitute the desired set of solutions. A recently introduced innovation path (IP) problem is one such problem. In solving such problems, point-based algorithms, which find one targeted solution in a single application, becomes relevant. In this paper, we address this important aspect of convergence behavior of an evolutionary multi-objective optimization (EMO) algorithm visa-vis a point-based algorithm. The challenges of both approaches are discussed with examples. Results on a number of problems show that despite the apparent advantage of a point-based approach for finding hierarchical solutions one by one, the proposed population-based EMO approach enables a flexible and global search for finding multiple IP solutions in a single run.