Accelerated particle swarm optimization with explicit consideration of model constraints

Abstract

Population based metaheuristic can benefit from explicit parallelization in order to address complex numerical optimization problems. Typical realistic problems usually involve non-linear functions and many constraints, making the identification of global optimal solutions mathematically challenging and computationally expensive. In this work, a GPU based parallelized version of the Particle Swarm Optimization technique is proposed. The main contribution is the explicit consideration of equality and inequality constraints of general type, rather than addressing only box constrained models as typically done in acceleration studies of optimization algorithms. The implementation is tested on a set of optimization problems that serve as benchmark. Speedups averaging 299x were obtained with a single GPU on a standard PC using the PyCUDA technology. Satisfactory feasibility and optimality rates are also achieved, although a standard parameterization was adopted for all the experiments. Additional results are reported on a small set of difficult problems involving bilinear non-linearities.