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Design Of Global Optimization Algorithms For Single-Objective And Multi-Objective Optimization Problems

Posted on:2009-06-25Degree:MasterType:Thesis
Country:ChinaCandidate:Y JiangFull Text:PDF
GTID:2120360242977934Subject:Systems Engineering
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Optimization problems widely exist in science research and engineering experence. Becase their objective and constrained functions are complicated, it is difficult to get their global optimal solutions, especial for the higher dimensional optimization problems. In order to solve complex optimization problems which are difficult to be handled by the existing algorithms, this thesis presents one improved algorithm for single-objective optimization problems and another modified algorithm for multiple-objective optimization problems.For the global optimization problem with single objective, the efficient global optimization (EGO) algorithm proposed by Jones is described. In the improved algorithm, the Nelder-Mead simplex (direct search) method is used to accelerate its convergence. Take the standard cross validate residual value of the solution whose expected improvement is maximal as evaluation criterion for fitting a curve. When the maximized expected improvement approaches zero, the algorithm stops, which is chosen as the termination criterion. All of these improvemts make the theory more perfect.For the multiobjective optimization problems, the NSGA-II algorithm proposed by Deb is describled. Based on the NSGA-II algorithm, a modified algorithm is presented. In fact, the elitist solutions are taken into account in the crossover and mutation operators. The crowding distance of the ilelitist solutions is also considered when sorting, and a new termination criterion is given. Compared against the NSGA-II algorithm, the modified algorithm has the better convergence, and the obtained optimal solution set has the better uniform distribution. Finally, with the design and analysis of computer experiments (DACE) model used in the EGO algorithm, the continous pareto optimal front is fitted, and good results are gotten.The numerical simulation results show that these two improved algorithms outperform the original ones.
Keywords/Search Tags:Design and analysis of computer experiments (DACE) model, Expected Improvement, Pareto optimal front, Crowding distance
PDF Full Text Request
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