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Abstract
Optimization techniques are used extensively to solve many real-world decision making problems which have different characteristics and mathematical properties that make the process of finding their optimal solutions difficult. Evolutionary computation is one of the fastest growing areas that has been extremely successful when used to solve both unconstrained and constrained optimization problems with a wide variety of properties.
In this thesis, using Evolutionary Algorithms (EAs) to solve optimization problems, whereby a search space is usually defined by the variables bounds, is considered. However, in a constrained problem, the feasible space, which is bounded by the constraint functions, may represent a relatively small portion of the search space. Existing EAs, using an analogy of black-box optimization, ignore specific information about the functions and search space even though details of their mathematical functions and properties are known. The objective of this research was to study the properties of the functions and search space to derive information that would be useful for designing effective and efficient EAs for solving optimization problems.
The specific interests of this study are in analyzing the landscape and identifying the most attractive region for an effective search. Although Fitness Landscape Analysis (FLA) measures are helpful for judging a problems complexity, they have rarely been used in the design of an EA. In most constrained problems, the optimal solution lies on the boundary of the feasible space. As this simple information may help to concentrate the search process in certain regions instead of the entire search space, this thesis proposes new EAs that use information from the function/problem landscape and search space for constrained problems to enhance the performances of algorithms for solving continuous optimization problems.
Firstly, a FLA-based Differential Evolution (DE) algorithm for solving unconstrained optimization problems is developed. Secondly, an algorithm for solving constrained problems, in which the landscape information from both the objective and constraint functions is considered, is proposed. Thirdly, a new technique for identifying the active constraints is developed and then a reduced search space around the active constraints determined, a concept applied with evolutionary algorithms. Finally, the information from the FLA and mechanism for reducing the search space are used to design an algorithm that incorporates multiple population-based algorithms in a single algorithmic structure.
All four versions of the developed algorithm are tested by solving standard benchmark problems and their results compared with those obtained from several state-of-the-art algorithms. In all cases, they achieve significant improvements, with the first, second, third and fourth obtaining respective savings in computational time and fitness evaluations of 15.1% and 15.7%, 69.0% and 33.0%, 36.69% and 11.88% and 22.01% and 20.73%, respectively.