Tractable Global Optimization Algorithms for Small Boolean Quadratic Programming Problems without Multiplications and Floating-Point Operations

Abstract

We introduce tractable global optimization algorithms for small boolean quadratic programming problems using reflected Gray coding technique. In the algorithms, the space complexity is limited to O(n²). Furthermore, we can implement them without multiplications or floating point operations when the instances are integers. Numerical experiments revealed that the proposed algorithms run as fast as interior point algorithms for solving convex relaxation problems of the original QPs.