Integrating decomposition methods with user preferences for solving many-objective optimization problems

This research aims to investigate methods to solve many-objective (a multi-objective problem with three or more objectives) optimization problems. To achieve this, we propose an algorithm combining user-preference and decomposition approaches. The main reasons that decomposition-based evolutionary multi-objective optimization (EMO) methods are employed in this research are: firstly, they suffer less from the selection pressure issue in comparison to dominance ranking as they rely on decomposition methods such as Weighted-sum, Tchebycheff and Penalty-based Boundary Intersection (PBI) to convert a multi-objective problem into a set of single-objective problems. Secondly, decomposition approaches employ a set of weight vectors which give us a reasonable control of solutions in the objective space. As user-preference approaches alleviate the scalability issue of many-objective problems, they are adopted in this research. User-preference methods can potentially save a considerable amount of computational resources by searching on more desired regions rather than the entire Pareto-optimal front. In this research, user-preference is defined in the form of one or more reference points or directions. The proposed algorithm outperforms R-NSGA-II which is one of popular dominance-based approaches on many-objective optimization problems. Finding a diverse set of solutions is another major challenge for EMOs. The issue of solution diversity is of greater importance when dealing with many-objective problems. In this thesis, we propose an algorithm using a mechanism to update the weight vectors according to feedback that quantifies the uniformity of the solutions in the objective space. Two existing metrics and a newly developed metric are adopted as feedback mechanisms.

These metrics allow us to assess the contribution of each solution towards improving the overall uniformity of the solution set in the objective space, and to use this information to update the weight vectors adaptively so that the overall uniformity is maintained. The overarching is to identify sparse areas in the objective space, and move the solutions from the denser to sparse areas. The newly developed metric uses the idea of electrostatic equilibrium to calculate the direction in which each solution should move in order to improve the overall uniformity. As we use decomposition methods in this research, the availability of weight vectors gives us an explicit means of controlling the uniformity of solutions in the objective space. Since existing metrics are neither sufficiently accurate nor scalable to measure the performance of user-preference based EMO algorithms, we develop a new performance metric to fill this gap. The proposed metric uses a composite front as a substitute for the Pareto-optimal front then a preferred region is defined on the composite front. Performances of the new metric are compared against a baseline which relies on knowledge of the Pareto-optimal front. One of the key advantages of the proposed metric is that it does not depend on prior knowledge of the Pareto-optimal front of a particular problem, which is most likely the case in real-world situations.