New approach to solve unconstrained binary quadratic problem

Abstract

This paper addresses the unconstrained binary quadratic problem (UQP). This problem consists in minimizing a quadratic function a binary variables (0-1 variables). Accordingly, in this work, a hybrid algorithm called (HA), based on simulated annealing algorithm with some combination procedures, have been proposed and a branch and bound procedure, based on this algorithm (HA) and semi definite programing problem (SDP), has been applied. The purpose of this approach is to facilitate the resolution of the initial problem and reduce its dimension by using some fixing criteria in a repeat loop. Numerical results are presented to consolidate the demonstrated theoretical results and prove effectiveness and performance in speed and quality of our new approach.