PolyEDA: Combining Estimation of Distribution Algorithms and Linear Inequality Constraints

Estimation of distribution algorithms (EDAs) are population-based heuristic search methods that use probabilistic models of good solutions to guide their search. When applied to constrained optimization problems, most evolutionary algorithms use special techniques for handling invalid solutions. This paper presents PolyEDA, a new EDA approach that is able to directly consider linear inequality constraints by using Gibbs sampling. Gibbs sampling allows us to sample new individuals inside the boundaries of the polyhedral search space described using a set of linear inequality constraints by iteratively constructing a density approximation that lies entirely inside the polyhedron. Gibbs sampling prevents the creation of infeasible solutions. Thus, no additional techniques for handling infeasible solutions are needed in PolyEDA. Due to its ability to consider linear inequality constraints, PolyEDA can be used for highly constrained optimization problems, where even the generation of valid solutions is a non-trivial task. Results for different variants of a constrained Rosenbrock problem show a higher performance of PolyEDA in comparison to a standard EDA using rejection sampling.