Many-Objective Evolutionary Algorithms: Objective Reduction, Decomposition and Multi-Modality

Abstract

Evolutionary Algorithms (EAs) for Many-Objective Optimization (MaOO) problems are challenging in nature due to the requirement of large population size, difficulty in maintaining the selection pressure towards global optima and inability of accurate visualization of high-dimensional Pareto-optimal Set (in decision space) and Pareto-Front (in objective space). The quality of the estimated set of Pareto-optimal solutions, resulting from the EAs for MaOO problems, is assessed in terms of proximity to the true surface (convergence) and uniformity and coverage of the estimated set over the true surface (diversity). With more number of objectives, the challenges become more profound. Thus, better strategies have to be devised to formulate novel evolutionary frameworks for ensuring good performance across a wide range of problem characteristics.

In this thesis, the first work adopts the strategy of objective reduction to present the framework of DECOR, which handles MaOO problems through correlation-based clustering by eliminating the less conflicting objectives. While DECOR demonstrates an enhanced convergence, it reveals the necessity of better solution diversity for resembling the true surface. In the second work, ESOEA is presented, which decomposes the objective space for the collaborative optimization of multiple sub-populations. It also adaptively feedbacks the sub-population size to redistribute the solutions for the effective exploration of difficult regions in the fitness landscape. While ESOEA demonstrates enormous improvement in performance over a variety of MaOO problems, lack of theoretical foundations hinders the analysis of its properties. In the third work, the neighborhood property arising out of sub-space formation (in objective space) is recognized and used to present the framework of NAEMO. It not only demonstrates improved performance but also guarantees monotonically improving diversity, theoretically. While such reference vector assisted decomposition-based approaches are useful for good performance in the objective space, it innately neglects the solution distribution in the decision space. This behavior is disadvantageous for multi-modal problems (multiple alternative subsets within the Pareto-optimal Set independently mapping to the entire Pareto-Front). Hence, in the fourth work, the decomposition in objective space is amalgamated with graph Laplacian based clustering in the decision space to present the framework of LORD. Finally, to establish the efficacy on a real-world problem, NAEMO and LORD are customized to address the multi-modal many-objective building energy management problem. Moreover, four decision-making strategies are presented to select one of the Pareto-optimal solutions as the most relevant solution for implementation.