Evolutionary Algorithms for Complex Continuous Optimization Problems

Continuous optimization problems are frequently encountered in the fields of mathematics and engineering. Based on their properties, continuous optimization problems can be briefly classified into four categories: unconstrained singleobjective optimization problems (USOPs), constrained single-objective optimization problems (CSOPs), unconstrained multi-objective optimization problems (UMOPs), and constrained multi-objective optimization problems (CMOPs). Under certain conditions, these four kinds of optimization problems will have very complex characteristics, e.g., the variables of USOPs are highly correlated with each other, CSOPs and CMOPs include equality and nonlinear constraints, and the Pareto sets of UMOPs have nonlinear structures. This thesis aims at solving the above four kinds of complex continuous optimization problems based on evolutionary algorithms (EAs), which are intelligent optimization and search techniques inspired by nature. The main contributions can be summarized as follows. 1) EAs for complex continuous USOPs: We concentrate on the solution of complex continuous USOPs by making use of differential evolution (DE) which is one of the main branches of EAs. In one respect, the experiences and knowledge about DE obtained by the researchers are used to build two knowledge bases: trial vector generation strategy base and control parameter setting base. Afterward, a novel method, referred as composite DE is proposed. On the other hand, we reveal one of the major drawbacks of the existing DE, and propose a generic framework to enhance the search ability of DE based on orthogonal crossover. 2) EAs for complex continuous CSOPs: When using EAs to solve complex continuous CSOPs, one of the key points is how to handle the constraints. We clarify the essence and core problems of the methods based on multi-objective optimization techniques, which is one kind of the constraint-handling techniques. Then, three novel algorithms (i.e., CW, HCOEA, and ATMES) have been proposed. Since in CW, HCOEA, and ATMES, some parameters are problem-dependent and the performance of them is not very good when solving some complex continuous CSOPs, three improved versions (i.e., CMODE, DyHF, and (μ+λ)-CDE) have been presented for CW, HCOEA, and ATMES, respectively. Overall, the improved versions put more emphasis on exploiting the domain-specific knowledge, and integrate the constraint-handling techniques with the search algorithms effectively. The above work establishes a systematic framework for solving complex continuous CSOPs based on EAs. 3) EAs for complex continuous UMOPs: We investigate a regularity model-based multi-objective estimation of distribution algorithm (RM-MEDA) for complex continuous UMOPs. RM-MEDA is a kind of estimation of distribution algorithms and, therefore, modeling plays a critical role. In this thesis, we analyze the main drawback of modeling in RM-MEDA, and propose a novel operator to reduce the redundant clusters of the population and to build more precise model. 4) EAs for complex continuous CMOPs: According to the features of complex continuous CMOPs, we generalize the idea of the adaptive trade-off model which is proposed for CSOPs. The generalized trade-off model contains three situations. In the second situation, we balance the degree of constraint violation and each objective function adaptively, and incorporate the degree of constraint violation into each objective function. By doing this, a CMOP is converted into an UMOP without the increase of the number of objective functions. Extensive experiments have been carried out to demonstrate the performance of all the methods presented in this thesis. List of Publications