Global design optimization using stochastic methods and parallel processing

Mir Mohamed Atiqullah, Purdue University

Abstract

Optimization is an important step in the mechanical design process. With the ever increasing demand for solving larger and more complex multimodal design optimization problems, there is a need for robust algorithms to find the global optimum. In this work two novel design optimization methods have been considered, Simulated Annealing (SA) and Genetic Algorithm (GA). Both of these methods work in discrete steps and are capable of locating the global optimum. Simulated annealing works along the concept of annealing of solids to minimize its internal energy. From a current solution, SA randomly generates new solutions and accepts those with a probability according to some Metropolis criteria. An algorithmic development called 'Shakeup' has been proposed to help SA jump out of any local optimum. A Feasibility Improvement Scheme (FIS) is introduced which automatically steers the SA around the constraints to locate the global optimum without the need for any penalty formulation. Several design examples are solved using FIS to demonstrate its effectiveness without a penalty formulation. A simple adaptive cooling schedule for SA is proposed which is easily implemented and manipulated for best results. The proposed Parametric Schedule fared equal to or better than many known schedules. Genetic Algorithms (GA) work with a population of designs. A simple genetic algorithm has been implemented with an improved generation mechanism and an effective population scaling method. The utility of GA is demonstrated by solving several multimodal design problems. With the recent development of parallel processing systems, parallel implementation of theses algorithms is investigated. SA is implemented at the higher level where variables are allocated to the processors for annealing. The parallel GA is implemented at the lower level. Despite simplicity of the implementations, both the SA and the GA performed robustly and showed speedup on an MIMD parallel processing system. The current work has opened leads to further research in several areas such as development of efficient cooling schedules for SA and non-discretized GA. With the continued development of larger parallel processor systems, both the SA and GA hold much promise for mechanical design automation through robust global design optimization.

Degree

Ph.D.

Advisors

Rao, Purdue University.

Subject Area

Mechanical engineering

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