DISCRETE DESIGN OPTIMIZATION UNDER UNCERTAINTY: A GENERALIZED POPULATION-BASED SAMPLING GENETIC ALGORITHM

This paper presents the Generalized PopulationBased Sampling (GPBS) approach, which is a generalized version of the Population-Based Sampling (PBS) approach that was developed by the authors of this paper in earlier work. PBS is a Genetic Algorithm (GA) based approach that allows for discrete design optimization under uncertainty and requires a computational cost that is two orders of magnitude lower than the state-of-the-art method that couples the GA with Monte Carlo Sampling (MCS). The PBS approach uses the population-based search of the GA to provide samples that are used in the statistical evaluation of aggregate, uncertain fitness functions. In PBS, while large numbers of samples are accumulated to evaluate the fitness values of “good” designs, the computational cost spent on designs with “poor” fitness is minimal. The main assumption in PBS is that the uncertain parameters associated with the design variables all have Gaussian probability distributions; hence, the probability distributions of aggregate fitness functions are assumed to be Gaussian themselves. This valid assumption is used to impose constraints on estimated probabilities of success of expected values of aggregate fitness functions even when the number of samples accumulated is small, which is usually the case at the beginning of the optimization run. The suggested GPBS approach generalizes the PBS approach by allowing design variables’ uncertain parameters with non-Gaussian probability distributions and by eliminating the normality assumption on the probability distributions of aggregate fitness functions. The GPBS approach combines the concepts of MCS and PBS and imposes constraints on calculated, rather than estimated, probabilities of success of expected values of aggregate fitness functions. In this paper, the probabilistic approaches described above are implemented for reliability-based design of a communication satellite with uncertain component failure rates. NOMENCLATURE c penalty multiplier ( ) E expected value f fitness function g inequality constraint function G uncertain inequality constraint function samples N number of samples ( ) P probability of payload R total payload reliability spacecraft R total spacecraft reliability m std measured standard deviation of aggregate probabilistic function