Approach to Discrete Optimization Under Uncertainty: The Population-Based Sampling Genetic Algorithm

This paper presents the population-based sampling genetic algorithm, which allows for discrete design optimization under uncertainty. The population-based sampling approach uses the genetic algorithm population to provide samples for the probabilistic evaluation of aggregate uncertain constraint or objective functions. In population-based sampling, large numbers of samples are accumulated to evaluate the fitness values of "good" designs during the genetic algorithm run, whereas the computational cost spent on designs with "poor" fitness is minimal. Using Monte Carlo sampling with a genetic algorithm for optimization under uncertainty is a currently accepted approach; however, this approach incurs a large computational cost. In this paper, the genetic algorithm with population-based sampling generates solutions to a discrete optimization problem under uncertainty associated with a commercial satellite design that was solved in previous work via a genetic algorithm with Monte Carlo sampling. The genetic algorithm with population-based sampling and genetic algorithm with Monte Carlo sampling approaches are compared in terms of efficiency (computational cost) and effectiveness (solution quality). The comparison also examines the scalability of the algorithms' performance when solving three additional problem sizes. Furthermore, two population-based sampling variants are introduced, namely, the variable population-based sampling approach, which combines the concepts of population-based sampling and Monte Carlo sampling, and the generalized population-based sampling approach, which removes the restriction in population-based sampling that the uncertain parameters associated with the design variables all have Gaussian probability distributions.