The Boltzmann machine is one of the most popular neural network models used to cope with difficult combinatorial optimisation problems. It has been used to find near optimum solutions to such hard problems as graph partitioning and the Travelling Salesman problem. However, very little is known about the time complexity of solving combinatorial optimisation problems on Boltzmann machines. This issue is important because it will help us better understand the power of Boltzmann machines in dealing with hard problems. This paper studies the time complexity of maximum matching in a graph on Boltzmann machines. It is shown that some widely-used Boltzmann machines cannot find a maximum matching in average time polynomial in the number of nodes of the graph although there are conventional deterministic algorithms which solve the problem in polynomial time. On the other hand, this paper also shows that a simpler model of Boltzmann machines, with the "temperature" parameter fixed at some constan...

Simulated Annealing (SA) is a powerful stochastic search algorithm applicable to a wide range of problems. This paper presents some experiments of applying SA to an NP-hard problem, i.e., call routing in circuit-switched telecommunications networks. The call routing problem considered here can be described as assigning calls to paths in a network so that the number of calls blocked can be minimised. Previously, the problem has been approached by linear programming and some heuristic algorithms. However, none of these algorithms has solved the problem satisfactorily due to the nonlinear nature of the problem. Linear programming can only find a rough approximation to the actual global optimal solution. This paper applies SA to the call routing problem in circuit-switched telecommunication networks. We have carried out two sets of experiments. The first set investigates random selection of paths in SA with uniform distribution. The second set studies non-uniform probabilistic selection of...

Software Abstract — Generating test data for Object-Oriented (OO) software is a hard task. Little work has been done on the subject, and a lot of open problems still need to be investigated. In this paper we focus on container classes. They are used in almost every type of software, hence their reliability is of utmost importance. We present novel techniques to generate test data for container classes in an automatic way. A new representation with novel search operators is described and tested. A way to reduce the search space for OO software is presented. This is achieved by dynamically eliminating the functions that cannot give any further help from the search. Besides, the problem of applying the branch distances of disjunctions and conjunctions to OO software is solved. Finally, Hill Climbing, Genetic Algorithms and Memetic Algorithms are used and compared. Our empirical case study shows that our Memetic Algorithm outperforms the other algorithms. I.

The purpose of this research is to improve an optimization model of a twodimensional cutting stock problem in the steel industry. The improvements address the functionality of the model and solution times of the optimization problem. The research problem is important, since even small improvements in the cutting layouts result in large savings of raw material and energy when the amount of produced material is huge. The research methods consist of benchmarking the improved model against the current one. Although numerous

Abstract. Searching on the Internet has grown in importance over the last few years, as huge amount of information is invariably accumulated on the Web. The problem involves locating the desired information and corresponding URLs on the WWW. With billions of webpages in existence today, it is important to develop efficient means of locating the relevant webpages on a given topic. A single topic may have thousands of relevant pages of varying popularity. Top- k document retrieval systems identifies the top- k ranked webpages pertaining to a given topic. In this paper, we propose an efficient top-k document retrieval method (TkRSAGA), that works on the existing search engines using the combination of Simulated Annealing and Genetic Algorithms. The Simulated Annealing is used as an optimized search technique in locating the top-k relevant webpages, while Genetic Algorithms helps in faster convergence via parallelism. Simulations were conducted on real datasets and the results indicate that TkRSAGA outperforms the existing algorithms. 1