Probabilistic multistart with path relinking for solving the unconstrained binary quadratic problem

Abstract

The unconstrained binary quadratic problem (UBQP) has been shown to be an excellent framework from which to solve many types of problems, both constrained and unconstrained. In this paper we investigate a solution technique for UBQP that is based on perturbing a solution by drawing from the distribution of variables' estimated effect as determined via an unbiased design of experiments (DOE) sampling of the solution space. Solution perturbation is followed by a steepest ascent local search with path relinking. A simple implementation on benchmark problems compares well in time and solution quality with published results on benchmark problems of size up to 7,000 variables. A new set of larger problems having up to 15,000 variables and with non-uniform magnitude distributions of the elements in Q are also investigated and provide evidence that magnitude distributions of Q values affect problem difficulty. These large difficult problem instances required a more sophisticated path relinking approach as well as dynamic adjustments to perturbation sampling.