User-preference based evolutionary algorithms for many-objective optimisation

Evolutionary Algorithms (EA) have enjoyed great success in finding solutions for multi-objective problems that have two or three-objectives in the past decade. The majority of these Evolutionary Multi-objective Optimisation (EMO) algorithms explored the decision-space using the selection pressure governed methods that are based on dominance relation. Although these algorithms are effective locating solutions for multi-objective problems, they have not been very successful for problem instances having more than three objectives, usually named as many-objective problems. The main reason behind this shortcoming is the fact that the dominance comparison becomes ineffective as the number of objectives increases.<br><br>In this thesis, we incorporate some user-preference methods into EMO algorithms to enhance their ability to handle many-objective problems. To this end, we introduce a distance metric derived from user-preference schemes such as the reference point method and light beam search found in multi-criteria decision making. This distance metric is used to guide the EMO algorithm to locate solutions within certain areas of the objective-space known as preferred regions. In our distance metric approach, the decision maker is allowed to specify the amount of spread of solutions along the solution front as well. We name this distance metric based EMO algorithm as d-EMO, which is a generalised framework that can be constructed using any EA. This distance metric approach is computationally less expensive as it does not rely on dominance ranking methods, but very effective in solving many-objective problems.<br><br>One key issue that remains to be resolved is that there are no suitable metrics for comparing the performance of these user-preference EMO algorithms. Therefore, we introduce a variation of the normalised Hyper-Volume (HV) metric suitable for comparing user-preference EMO algorithms. The key feature in our HV calculation process is to consider only the solutions within each preferred region. This methodology favours user-preference EMO algorithms that have converged closely to the Pareto front within a preferred region. <br><br>We have identified two real-world engineering design problems in optimising aerofoil and lens designs, and formulated them as many-objective problems. The optimisation process of these many-objective problems is computationally expensive. Hence, we use a reference point PSO algorithm named MDEPSO to locate solutions effectively in fewer function evaluations. This PSO algorithm is less prone to getting stuck in local optimal fronts and still retains its fast convergence ability. In MDEPSO, this feature is achieved by generating leader particles using a differential evolution rule rather than picking particles directly from the population or an external archive. The main feature of the optimisation process of these aerofoil and lens design problems is the derivation of reference points based on existing designs. We illustrate how these existing designs can be used to either obtain better or new design solutions that correspond to various requirements. This process of deriving reference points based on existing design models, and integrating them into a user-preference EMO framework is a novel approach in the optimisation process of such computationally expensive engineering design problems.