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Doctoral Dissertation Announcement
Candidate: Jumana Ali Alshawawreh
Doctor of Philosophy
Department: Electrical and Computer Engineering
Title: Multi-Scale Optimization Using a Genetic Approach
Dr. Frank Severance, Chair
Dr. Damon Miller
Dr. Liang Dong
Dr. Melinda Koelling
Date: Friday, February 11, 2011 11:00 a.m. to 1:00 p.m.
College of Engineering and Applied Sciences, Room C-136
The multi-scale algorithm is a new optimization procedure based on a genetic approach. It can be considered as a stochastic optimization method requiring only function evaluations and random search to locate the global solution to an optimization problem. The algorithm is called multi-scale because it has the ability to use a large scale in the initial stages then use a scale refinement near the optimal point. This is done by using membership functions as random generator in the mutation operation. The search direction in the case of a two variable function is the polar coordinate, where the efficiency in locating the optimal solution is validated in several examples. Then the idea of the polar coordinate is generalized for N variables functions.
Two new adaptive penalty methods were proposed to solve the constrained optimization problems. The main idea in those methods is to have balanced weighting of the both terms in the penalty objective function, the original objective function and the penalty function in order to locate a feasible optimal solution.
Several unconstrained benchmark functions with different features were used to investigate the capability of multi-scale algorithm to locate the global optimal solution. Both engineering and classical mathematical optimization benchmarks problems were used to test the performance of the proposed penalty method. These problems include the design of a welded beam, design of a pressure vessel, minimization of the weight of a tension/compression spring, minimization of the weight of a speed reducer and Himmelblau's nonlinear optimization problem.
Finally, the multi-scale algorithm was used to find the optimal power flow on power system network. The aim in optimal power flow problem is to minimize the total cost of generation power plants subject to several constraints in order to maintain the power system network stability. The optimal power flow of IEEE-26 bus power system network and IEEE-30 bus power system networks were calculated using the multi-scale algorithm.