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Abstract
Solving Constrained Optimization Problems (COPs) has been an important research topic in the optimization, operation research, and computer science domains. Over the last few decades, evolutionary algorithms (EAs) have been widely adopted to solve such problems. However the main search operators of EAs, such as crossover and mutation, are usually the same for both unconstrained and constrained problems. In other words, the search operators are designed mainly to improve fitness value while also maintaining diversity in its population, but they do not directly act to reduce constraint violations of constrained problems. Interestingly, the so called constraint handling techniques, used with most evolutionary algorithms, are not an integral part of the evolutionary search process. Instead, the constraint violations are only considered in the ranking and selection of individuals for participation in the search process. Over the last few years, constraint consensus (CC) methods have been used to improve only infeasible solutions, by moving them to the feasible space. Although CC has shown good performance in solving non-convex COPs, still there are shortcomings.
Therefore, in this thesis, the constraint handling mechanism is incorporated within the EA search process, so that it will improve the feasibility, as well as the fitness of the individuals as the evolutionary process progresses. Firstly, as a preliminary work, the concept of traditional CC methods is combined with an EA. Here, differential evolution (DE) is considered (DE-DBmax) for improving the constraint handling process. The CC operation will be used as an additional step within the evolutionary framework. Secondly, different from the literature, a new DE mutation operator is introduced (DEbavDBmax). It incorporates a mechanism, based on CC, to directly help in reducing the constraint violations during the evolutionary search process.
Rather than using CC to move the infeasible individuals toward the feasible space, in this thesis, another novel approach is designed to use CC to improve the feasible individuals, i.e., searching from the interior of feasible region. This is done by proposing a new mutation operator (DE-FMO) that guides selected feasible individuals
to move towards the best reference solution.
A general framework is also proposed to utilize the strengths of constraint consensus to improve both feasible and infeasible solutions. This is done by proposing a new DE mutation operator (DE-IMO-FMO) that can directly help to reduce the constraint violations during an evolutionary search and also guide selected feasible individuals to move towards better solutions.
All of the above algorithms are tested on 36 well-known constrained problems with different mathematical properties. The experimental results show that DE-DBmax, DEbavDBmax, DE-FMO and DE-IMO-FMO are able to obtain better results than DE and save computational time by 42.8%, 49.5%, 39.4% and 40.0% for small dimensional problems, respectively, and by 3.3%, 12.5%, 14.2% and 16.0% for high dimensional problems, respectively. The statistical comparisons have also confirmed the benefits of the proposed methods. In comparison with the state-of-the-art algorithms, all algorithms are either competitive or better than them, especially for the higher dimensional problems.