# Multi-Scale Optimization Using a Genetic Algorithm

## Date of Award

1-2011

## Degree Name

Doctor of Philosophy

## Department

Electrical and Computer Engineering

## First Advisor

Dr. Frank Severance

## Second Advisor

Dr. Damon Miller

## Third Advisor

Dr. Liang Dong

## Fourth Advisor

Dr. Melinda Koelling

## Abstract

The Multi-Scale Algorithm (MSA) 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 searches to locate an optimal solution to an optimization problem. The algorithm is called multi-scale since it has the ability to use a large scale in the initial stages then to use a scale refinement near the optimal point. This is done by using membership functions as a random generator in the mutation operation. Polar coordinate variables are used to perform the MSA for functions of two variables, where the efficiency in locating an optimal solution is validated in several examples. The concept of the polar coordinate variables is generalized for functions of *N* variables.

Two new adaptive penalty methods are proposed to solve constrained optimization problems. The main idea in those methods is to have a balanced weighting of both terms in an unconstrained objective function; i.e. 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 global optimal solutions. 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 in a power system network. The aim is to minimize the total cost of generation power plants subject to several constraints in order to maintain power system network stability. The optimal power flow of the IEEE-26 bus power system network and IEEE-30 bus power system network were successfully calculated using the Multi- Scale Algorithm.

## Access Setting

Dissertation-Open Access

## Recommended Citation

Alshawawreh, Jumana Ali, "Multi-Scale Optimization Using a Genetic Algorithm" (2011). *Dissertations*. 337.

https://scholarworks.wmich.edu/dissertations/337