Constraint Handling Methods For Evolutionary Optimization Algorithm And Their Application

Constrained optimization problems are frequently encountered in the fields ofnatural science and engineering application, therefore the study on these problems hastheoretical significance and practical value. These problems usually includemulti-model objective functions, equality and non-linear constraints, disjointedfeasible regions and other characteristics, so solving these problems becomes verydifficult. Evolutionary Algorithms (EAs) are intelligent search and optimizationmethods inspired by nature. Due to their good adaptability and huge developmentprospect, evolutionary algorithm receives wide attention from researchers, beingapplied in various fields.EAs are unconstrained optimization methods in nature. When EAs are used tosolve the constrained optimization problems, some extra constraint handling methodsare needed to transform the constrained optimization problems to the unconstrainedones. The constraint handling methods have a large effect on the result of theconstrained optimization problems.This thesis mainly studies the constraint handling methods for evolutionaryoptimization algorithms used to solve the constrained optimization problems. Themain contribution of this thesis can be summarized as follows:1. This thesis proposes the concept of minimum penalty coefficient, using theminimum penalty coefficient to determine a suitable coefficient for the penaltyfunction method. Some theorems and corollary on the minimum penalty coefficientare established and a Minimum Penalty (MP) algorithm is devised by combining theminimum penalty theorem and a differential evolution. The new algorithm isextensively evaluated with some standard test function in the domain of constrainedevolutionary optimization and the results are compared with other constrainedevolutionary algorithms, indicating that the new algorithm is quite effective. Finally,the application of the new algorithm on the5engineering design problems furtherdemonstrates the effectiveness of the new algorithm.2. This thesis proposes the concept of biased dominance (or b-dominance), usingthe biased dominance to handle the constraints. Combining the biased dominance and a differential evolution, a Biased Multiobjective Optimization (BMO) algorithm isproposed. The new algorithm is extensively evaluated and discussed, comparing withother constrained evolutionary algorithms. The results show that the new algorithm isa quite effective algorithm. The engineering application further indicates theeffectiveness of the new algorithm.