Jan H. M. Korst

Simulated annealing and Boltzmann machines: a stochastic approach to combinatorial optimization and neural computing

SIMULATED ANNEALING. Combinatorial Optimization. Simulated Annealing. Asymptotic Convergence. Finite-Time Approximation. Simulated Annealing in Practice. Parallel Simulated Annealing Algorithms. BOLTZMANN MACHINES. Neural Computing. Boltzmann Machines. Combinatorial Optimization and Boltzmann Machines. Classification and Boltzmann Machines. Learning and Boltzmann Machines. Appendix. Bibliography. Indices.

A quantitative analysis of the simulated annealing algorithm: A case study for the traveling salesman problem

A quantitative study is presented of the typical behavior of the simulated annealing algorithm based on a cooling schedule presented previously by the authors. The study is based on the analysis of numerical results obtained by systematically applying the algorithm to a 100-city traveling salesman problem. The expectation and the variance of the cost are analyzed as a function of the control parameter of the cooling schedule. A semiempirical average-case performance analysis is presented from which estimates are obtained on the expectation of the average final result obtained by the simulated annealing algorithm as a function of the distance parameter, which determines the decrement of the control parameter.

Boltzmann machines for travelling salesman problems

Boltzmann machines are proposed as a massively parallel alternative to the (sequential) simulated annealing algorithm. Our approach is tailored to the travelling salesman problem, but it can also be applied to a more general class of combinatorial optimization problems. For two distinct 0–1 programming formulations of the travelling salesman problem (as a linear and as a quadratic assignment problem) it is shown that near-optimal solutions can be obtained by mapping the corresponding 0–1 variables onto the logic computing elements of a Boltzmann machine, and by transforming the cost functions corresponding to the 0–1 programming formulations into the consensus function associated with the Boltzmann machine. Results of computer simulations are presented for two problem instances, i.e. with 10 cities and 30 cities, respectively.

Algorithm 864: General and robot-packable variants of the three-dimensional bin packing problem

We consider the problem of orthogonally packing a given set of rectangular-shaped boxes into the minimum number of three-dimensional rectangular bins. The problem is NP-hard in the strong sense and extremely difficult to solve in practice. We characterize relevant subclasses of packing and present an algorithm which is able to solve moderately large instances to optimality. Extensive computational experiments compare the algorithm for the three-dimensional bin packing when solving general orthogonal packings and when restricted to robot packings.

Combinatorial optimization on a Boltzmann machine

We discuss the problem of solving (approximately) combinatorial optimization problems on a Boltzmann machine. It is shown for a number of combinatorial optimization problems how they can be mapped directly onto a Boltzmann machine by choosing appropriate connection patterns and connection strengths. In this way maximizing the consensus in the Boltzmann machine is equivalent to finding an optimal solution of the corresponding optimization problem. The approach is illustrated by numerical results obtained by applying the model of Boltzmann machines to randomly generated instances of the independent set, the max cut, and the graph coloring problem. For these instances the Boltzmann machine finds near-optimal solutions whose quality is comparable to that obtained with sequential simulated annealing algorithms. The advantage of the Boltzmann machine is the potential for carrying out operations in parallel. For the problems we have been investigating, this results in a considerable speedup over the sequential simulated annealing algorithms.

Boltzmann Machines and their Applications

In this paper we present a formal model of the Boltzmann machine and a discussion of two different applications of the model, viz. (i) solving combinatorial optimization problems and (ii) carrying out learning tasks. Numerical results of computer simulations are presented to demonstrate the characteristic features of the Boltzmann machine.

Random duplicated assignment: an alternative to striping in video servers

An approach is presented for storing video data in large disk arrays. Video data is stored by assigning a number of copies of each data block to different, randomly chosen disks, where the number of copies may depend on the popularity of the corresponding video data. The approach offers an interesting alternative to the well-known striping techniques. Its use results in smaller response times and lower disk and RAM costs if many continuous variablerate data streams have to be sustained simultaneously. It also offers some practical advantages relating to reliability and extendability. Based on this storage approach, three retrieval algorithms are presented that determine, for a given batch of data blocks, from which disk each of the data blocks should be retrieved. The performance of these algorithms is evaluated from an average-case as well as a worst-case perspective. key words: video serve< striping, disk array, RAID, multimedia, variable rate

Erratum to The Three-Dimensional Bin Packing Problem: Robot-Packable and Orthogonal Variants of Packing Problems

In the three-dimensional bin packing problem the task is to orthogonally pack a given set of rectangular items into a minimum number of three-dimensional rectangular bins. We give a characterization of the algorithm proposed by Martello et al. (2000) for the exact solution of the problem, showing that not all orthogonal packings can be generated by the proposed algorithm. The packings, however, have the property of being robot packings, which is relevant in practical settings. References to the modified algorithm, which solves the orthogonal as well as robot packable three-dimensional problem, are given.

Scheduling Periodic Tasks

We consider the problem of nonpreemptively scheduling periodic tasks on a minimum number of processors, assuming that the tasks have to be executed strictly periodically. We show that the problem is NP-complete in the strong sense, even in the case of a single processor, but that it is solvable in polynomial time if the periods and execution times are divisible. The latter condition generalizes the situation in which all periods and execution times are powers of 2. We also propose an approximation algorithm, which is based on successively assigning tasks to processors according to some priority rule.

Efficiency improvements for force-directed scheduling

Force-directed scheduling is a technique which schedules operations under time constraints in order to achieve schedules with a minimum number of resources. The worst case time complexity of the algorithm is cubic in the number of operations. This is due to the computation of the changes in the distribution functions needed for the force calculations. An incremental way to compute the changes in the distribution functions, based on gradual time-frame reduction, is presented. This reduces the time complexity of the algorithm to quadratic in the number of operations, without any loss in effectiveness or generality of the algorithm. Implementations show a substantial CPU-time reduction of force-directed scheduling, which is illustrated by means of some industrially relevant examples.<<ETX>>