The Basic Algorithm for Zero-One Unconstrained Quadratic Programming Problem with k-diagonal Matrix

Abstract

In real life, many problems can be expressed as zero-one quadratic programming problems. Therefore, it is of great significance to study how to solve the zero-one quadratic programming problem. In this paper, zero-one unconstrained quadratic programming problem with a special form is researched. We call it the k-diagonal matrix zero-one unconstrained quadratic programming problem. For this kind of special problem, targeted algorithm which is obtained by observing the characteristics of Q matrix is proposed. This paper shows the feasibility of the algorithm through derivation. And through practical examples, the algorithm is easy to be understood. In the experiments, the dimension of the problem and the value of k are changed so as to study the relationship between the speed of the algorithm and them. We can see that this algorithm is suitable for high dimensional problems and have considerable computational power.