Multi-objective Evolutionary Algorithms for Single-objective Constrained Optimisation

Abstract

In the real world there are a large number of optimization problems, especially in scientific research and engineering practice, which often have constraints and sometimes more than one objective. Due to the different characteristics of the problems themselves, traditional methods in operations research are no longer able to solve them independently. Evolutionary algorithms (EAs), as a global optimization method based on group search, are well suited for solving constrained optimization problems and multi-objective optimization problems. Therefore, evolutionary optimization has received increasing attention from researchers. The aim of this thesis is to design efficient multi-objective evolutionary algorithms (MOEAs) and strategies for constrained single-objective optimization problems (CSOPs) through in-depth exploration, and to conduct corresponding theoretical and experimental analysis. Specifically, the main research work of this thesis includes the following aspects. Firstly, we consider a many-objective method for solving CSOPs. The method keeps the standard objectives: the original objective function and the sum of the degrees of constraint violation. Besides them, more objectives are added into the method. One objective is based on the feasible rule. The others come from the penalty function method. Then a multiobjective differential evolution algorithm is applied to solving multi-objective optimization problems with two, three and four objectives. An experimental study on thirteen benchmark functions from IEEE CEC2006 Competition is conducted. Experimental results confirm our expectation that adding more objectives could be useful and the solution quality is improved. Secondly, we construct a new multi-objective evolutionary framework for solving CSOPs, which works by converting a CSOP into a problem with helper and equivalent objectives (HECO). An equivalent objective means that its optimal solution set is the same as that to the constrained problem but a helper objective does not. Then this multi-objective optimization problem is decomposed into a group of sub-problems using the weighted sum approach. Weights are dynamically adjusted so that each subproblem eventually tends to a problem with an equivalent objective. We theoretically analyze the computation time of the helper and equivalent objective method on a hard problem called “wide gap”. In a “wide gap” problem, an algorithm needs exponential time to cross between two fitness levels (a wide gap). We prove that using helper and equivalent objectives can shorten the time of crossing the “wide gap”. A series of derivative algorithms are then designed based on HECO, such as HECO-DE, HECO-DEtch and HECO-DEm. Extensive experimental studies show these algorithms perform much better in solving benchmark problems in IEEE CEC2017/2018 Competition, and IEEE CEC2006 Competition than other state-of-the-art EAs. Finally, apart from constraint handling techniques, we also contribute to new search operators which lead to further improvement our EAs for solving CSOPs. Two methods of studying valleys on a fitness landscape. Afterwards, the principle component analysis (PCA) could be used to characterize fitness landscapes. Based on this finding, a new search operator, called PCA-projection, is proposed. In order to verify the effectiveness of PCA-projection, we design two algorithms enhanced with PCA-projection for solving CSOPs. Experiment results indicate that the new search operator based on PCA-projection works very well

Date of Award	2021
Original language	English
Awarding Institution	Aberystwyth University
Supervisor	Jun He (Supervisor) & Changjing Shang (Supervisor)