Novel Algorithms for Quadratic Programming by Using Hypergraph Representations

In this paper novel algorithms are introduced for solving NP hard discrete quadratic optimization problems commonly referred to as unconstrained binary quadratic programming. The proposed methods are based on hypergraph representation and recursive reduction of the dimension of the search space. In this way, efficient and fast search can be carried out and high quality suboptimal solutions can be obtained in real-time. The new algorithms can directly be applied to the quadratic problems of present day communication technologies, such as multiuser detection and scheduling providing fast optimization and increasing the performance. In the case of multiuser detection, the achieved bit error rate can approximate the Bayesian optimum and in the case of scheduling better Weighted Tardiness can be achieved by running the proposed algorithms. The methods are also tested on large scale quadratic problems selected from ORLIB and the solutions are compared to the ones obtained by traditional algorithms, such as Devour digest tidy-up, Hopfield neural network, local search, Taboo search and semi definite relaxing. As the corresponding performance analysis reveals the proposed methods can perform better than the traditional ones with similar complexity.