Abstract
Multi-objective optimization (MOO) aims to address problems with multiple and conflicting objectives, where a single solution typically cannot optimize all objectives simultaneously. The concept of multi-objective optimization has garnered growing attention in real-world scenarios, extending beyond its applications in traditional manufacturing and engineering fields to being integrated into modern artificial intelligence techniques.Recent years have witnessed the remarkable success of evolutionary multi-objective optimization (EMO) algorithms in solving multi-objective problems (MOPs). Generally, EMO algorithms are referred to population-based MOO algorithms, where a population of solutions is maintaned to evolve towards the Pareto set. As evolutionary algorithms inspired by biological evolution, EMO algorithms involve elitist solution selection during their whole evolutionary process. The basic concept of elitist solution selection is to select promising or high-quality solutions for subsequent evolution of generations. This thesis aims to investigate and develop elitist solution selection techniques in different stages of evolutionary multi-objective algorithms.
In the initial stage of EMO algorithms, an initial population is required to be generated, which can be viewed as the elitist solution selection from the entire feasible decision variables space. Intuitively, a good initial population can significantly improve the performance of EMO algorithms. We propose and investigate the effects of different initialization methods on the performance of EMO algorithms, including diversity promotion strategies, subset selection strategies, and heuristic solution inclusion strategies. For combinatorial multi-objective problems, we propose to include a few heuristic solutions in the initial population to improve the performance of the original EMO algorithms. Furthermore, we propose a novel heuristic initialization and knowledge-based mutation method for large-scale multi-objective 0-1 Knapsack problems. Extensive experimental results clearly demonstrate the effectiveness of the proposed initialization methods, i.e., selecting elitist solutions as the initial population that benefits the performance of EMO algorithms.
During the intermediate stage of EMO algorithms, the environmental selection operator involves elitist solution selection at each generation, where the solution subset that best satisfies a specific criterion is selected as the offspring in the next generation. In this part, we focus on subset selection based on hypervolume, i.e., we select a subset that maximizes the hypervolume indicator as the next generation. More specifically, to efficiently solve hypervolume subset selection (HSS) problems while maintaining a good solution quality, we propose a fast and scalable hypervolume subset selection method for many-objective optimization based on the determinantal point process (DPP), named DPP-HSS, which is fully free of hypervolume contribution calculation. We also propose a novel learning-to-rank based framework, named LTR-HSS, for solving challenging HSS problems with a large number of objectives.
In the final stage of the evolution of EMO algorithms, a post-processing stage is usually needed to select a small number of solutions for the decision-maker (DM). In this part, we consider two scenarios. First, we assume that a large number of candidate solutions are obtained, where a subset with the largest hypervolume value is needed to present to the DM. We propose a framework called HSS/D for high-speed solving of hypervolume subset selection. This framework takes a decomposition view of HVC calculation, completely eliminating the need for HVC or approximate HVC calculation. In another scenario, we assume that the DM wants to choose a single preferred solution from a large number of candidate solutions using only a small number of pair-wise comparisons and his perferences over objectives is unknown in advance. To finish this elitist solution selection task, we propose an interactive final solution selection (IFSS) method for multi-objective optimization. The proposed IFSS method aims to provide a good final solution through several interactions with the DM. Extensive experiments are conducted on various test problems to demonstrate the effectiveness of the proposed IFSS method.
| Date of Award | 15 Sept 2025 |
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| Original language | English |
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| Supervisor | Qingfu ZHANG (Supervisor) & Hisao Ishibuchi (External Supervisor) |