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Evolutionary Algorithms For Several Kinds Of Dynamic And Static Optimization Problems

Posted on:2009-07-03Degree:DoctorType:Dissertation
Country:ChinaCandidate:C A LiuFull Text:PDF
GTID:1118360272465579Subject:Applied Mathematics
Abstract/Summary:PDF Full Text Request
Because of its intelligence, wide applicability, robustness, global search ability and parallelism, evolutionary algorithm provides a new tool for complex optimization problems and has been widely used in many static optimization fields. In recent years, using evolutionary algorithm to solve dynamic optimization problems has become a new research field. In this dissertation, studies are mainly focused on several kinds of complex dynamic and static optimization problems, and new evolutionary algorithms are proposed for these problems. The main contributions of this thesis can be summarized as follows:1. When the objective functions of dynamic unconstrained multi-objective optimization problems (DUMOP) are continuously changing with time, a static optimization model and a new evolutionary algorithm for DUMOP are proposed. Firstly, the time variable period of DUMOP is divided into several equal subperiods. In each subperiod, the DUMOP is seen as a static multi-objective optimization problem (SMOP) by taking the time parameter fixed. Second, to decrease the amount of computation and efficiently solve the SMOP, each SMOP is transformed into a two-objective optimization problem. Thus, the original DUMOP is approximately transformed into several two-objective optimization problems. The theoretic analysis and the simulation results show that the proposed algorithm is effective and can find high quality solution set in varying-environment in terms of convergence, diversity, and the distribution of the obtained Pareto optimal solutions.2. A dynamic bi-objective optimization model for dynamic constrained multiobjective optimization problems with any number of objective functions is given, and a new evolutionary algorithm for it is proposed. The simulation results indicate that the proposed algorithm is effective for solving dynamic constrained multi-objective optimization problems.3. A dynamic multiobjective optimization evolutionary algorithm based on core estimation of distribution is presented. When a change in the environment is detected, the method uses the collected information from the previous search to predict the location of individuals in the next environment and an initial population in the new environment is generated. The simulation results show that the proposed algorithm can effectively track and quickly obtain the Pareto optimal solutions with smaller amount of computation.4. For a special class of dynamic multiobjective optimization problems, in which the time variable is defined on discrete space and the dimension of independent variable changes with the time, a new dynamic multiobjective optimization PSO algorithm is proposed.5. For static constrained multi-objective optimization problems, a new evolutionary algorithm is proposed. The Pareto summation rank value and the scalar constraint violation of the individual are firstly defined. Then, based on these two definitions, a new fitness function and a preference selection operator are presented with following properties: when individuals are evaluated or ranked, it is unnecessary to care about the feasibility of the individuals. It is a penalty-parameterless constraint-handling approach. Furthermore, the convergence of the proposed algorithm is proved, and the computer simulations are made and the results demonstrate the effectiveness of the proposed algorithm.6. A new method for dynamic nonlinear constrained optimization problems (DNCOP) is presented. First, inspired from the idea of multiobjective optimization, the constraints of DNCOP are transformed into one of the objective functions and thus DNCOP is transformed into unconstrained dynamic multiobjective optimization problems. For the transformed problem, a new convergent multiobjective evolutionary algorithm is proposed. The simulation results indicate that the proposed algorithm can effectively track and obtain the optimal solutions or approximately optimal solutions of DNCOP.
Keywords/Search Tags:Dynamic optimization, Multiobjective optimization, Constrained optimization, Evolutionary algorithm, Environment varying, Pareto optimal solution, Global convergence, Uniform distribution
PDF Full Text Request
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