Parallel genetic algorithm with population-based sampling approach to discrete optimization under uncertainty

Nithya Subramanian, Purdue University

Abstract

Optimization under uncertainty accounts for design variables and external parameters or factors with probabilistic distributions instead of fixed deterministic values; it enables problem formulations that might maximize or minimize an expected value while satisfying constraints using probabilities. For discrete optimization under uncertainty, a Monte Carlo Sampling (MCS) approach enables high-accuracy estimation of expectations but it also results in high computational expense. The Genetic Algorithm (GA) with a Population-Based Sampling (PBS) technique enables optimization under uncertainty with discrete variables at a lower computational expense than using Monte Carlo sampling for every fitness evaluation. Population-Based Sampling uses fewer samples in the exploratory phase of the GA and a larger number of samples when `good designs' start emerging over the generations. This sampling technique therefore reduces the computational effort spent on `poor designs' found in the initial phase of the algorithm. Parallel computation evaluates the expected value of the objective and constraints in parallel to facilitate reduced wall-clock time. A customized stopping criterion is also developed for the GA with Population-Based Sampling. The stopping criterion requires that the design with the minimum expected fitness value to have at least 99% constraint satisfaction and to have accumulated at least 10,000 samples. The average change in expected fitness values in the last ten consecutive generations is also monitored. The optimization of composite laminates using ply orientation angle as a discrete variable provides an example to demonstrate further developments of the GA with Population-Based Sampling for discrete optimization under uncertainty. The focus problem aims to reduce the expected weight of the composite laminate while treating the laminate's fiber volume fraction and externally applied loads as uncertain quantities following normal distributions. Construction of the laminate stiffness matrix implements a square fiber model with a fiber volume fraction sample. The calculations to establish the expected values of constraints and fitness values use the Classical Laminate Theory. The non-deterministic constraints enforced include the probability of satisfying the Tsai-Hill failure criterion and the maximum strain limit. The results from a deterministic optimization, optimization under uncertainty using Monte Carlo sampling and Population-Based Sampling are studied. Also, the work investigates the effectiveness of running the fitness analyses in parallel and the sampling scheme in parallel. Overall, the work conducted for this thesis demonstrated the efficacy of the GA with Population-Based Sampling for the focus problem and established improvements over previous implementations of the GA with PBS.

Degree

M.S.A.A.

Advisors

Crossley, Purdue University.

Subject Area

Aerospace engineering

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