Advanced genetic algorithm to solve MINLP problems over GPU

In this paper we propose a many-core implementation of evolutionary computation for GPGPU (General-Purpose Graphic Processing Unit) to solve non-convex Mixed Integer Non-Linear Programming (MINLP) and non-convex Non Linear Programming (NLP) problems using a stochastic algorithm. Stochastic algorithms being random in their behavior are difficult to implement over GPU like architectures. In this paper we not only succeed in implementation of a stochastic algorithm over GPU but show considerable speedups over CPU implementations. The stochastic algorithm considered for this paper is an adaptive resolution approach to genetic algorithm (arGA), developed by the authors of this paper. The technique uses the entropy measure of each variable to adjust the intensity of the genetic search around promising individuals. Performance is further improved by hybridization with adaptive resolution local search (arLS) operator. In this paper, we describe the challenges and design choices involved in parallelization of this algorithm to solve complex MINLPs over a commodity GPU using Compute Unified Device Architecture (CUDA) programming model. Results section shows several numerical tests and performance measurements obtained by running the algorithm over an nVidia Fermi GPU. We show that for difficult problems we can obtain a speedup of up to 20x with double precision and up to 42x with single precision.