EFFICIENT IMPLEMENTATION OF BRANCH-AND-BOUND METHOD ON DESKTOP GRIDS

The Berkeley Open Infrastructure for Network Computing (BOINC) is an opensource middleware system for volunteer and desktop grid computing. In this paper we propose BNBTEST, a BOINC version of distributed branch and bound method. The crucial issues of distributed branch-and-bound method are traversing the search tree and loading balance. We developed subtaskspackaging method and three dierent subtasks' distribution strategies to solve these

Implementation and verification of global optimization benchmark problems

The paper considers the implementation and verification of a test suite containing 150 benchmarks for global deterministic box-constrained optimization. A C++ library for describing standard mathematical expressions was developed for this purpose. The library automate the process of generating the value of a function and its’ gradient at a given point and the interval estimates of a function and its’ gradient on a given box using a single description. Based on this functionality, we have developed a collection of tests for an automatic verification of the proposed benchmarks. The verification has shown that literary sources contain mistakes in the benchmarks description. The library and the test suite are available for download and can be used freely

Using necessary optimality conditions for acceleration of the nonuniform covering optimization method

Paper deals with the non-uniform covering method that is aimed at deterministic global optimization. This method finds a feasible solution to the optimization problem numerically and proves that the obtained solution differs from the optimal by no more than a given accuracy. Numerical proof consists of constructing a set of covering sets - the coverage. The number of elements in the coverage can be very large and even exceed the total amount of available computer resources. Basic method of coverage construction is the comparison of upper and lower bounds on the value of the objective function. In this work we propose to use necessary optimality conditions of first and second order for reducing the search for boxconstrained problems. We provide the algorithm description and prove its correctness. The efficiency of the proposed approach is studied on test problems

Optimality and Complexity Analysis of a Branch-and-Bound Method in Solving Some Instances of the Subset Sum Problem

In this paper we study the question of parallelization of a variant of Branch-and-Bound method for solving of the subset sum problem which is a special case of the Boolean knapsack problem. The following natural approach to the solution of this question is considered. At the first stage one of the processors (control processor) performs some number of algorithm steps of solving a given problem with generating some number of subproblems of the problem. In the second stage the generated subproblems are sent to other processors for solving (one subproblem per processor). Processors solve completely the received subproblems and return their solutions to the control processor which chooses the optimal solution of the initial problem from these solutions. For this approach we define formally a model of parallel computing (frontal parallelization scheme) and the notion of complexity of the frontal scheme. We study the asymptotic behavior of the complexity of the frontal scheme for two special cases of the subset sum problem

Automatic Convexity Deduction for Efficient Function’s Range Bounding

Reliable bounding of a function’s range is essential for deterministic global optimization, approximation, locating roots of nonlinear equations, and several other computational mathematics areas. Despite years of extensive research in this direction, there is still room for improvement. The traditional and compelling approach to this problem is interval analysis. We show that accounting convexity/concavity can significantly tighten the bounds computed by interval analysis. To make our approach applicable to a broad range of functions, we also develop the techniques for handling nondifferentiable composite functions. Traditional ways to ensure the convexity fail in such cases. Experimental evaluation showed the remarkable potential of the proposed methods

Automatic Convexity Deduction for Efficient Function’s Range Bounding

Reliable bounding of a function’s range is essential for deterministic global optimization, approximation, locating roots of nonlinear equations, and several other computational mathematics areas. Despite years of extensive research in this direction, there is still room for improvement. The traditional and compelling approach to this problem is interval analysis. We show that accounting convexity/concavity can significantly tighten the bounds computed by interval analysis. To make our approach applicable to a broad range of functions, we also develop the techniques for handling nondifferentiable composite functions. Traditional ways to ensure the convexity fail in such cases. Experimental evaluation showed the remarkable potential of the proposed methods

EFFECTIVE REALIZATION OF EXACT ALGORITHMS FOR SOLVING DISCRETE OPTIMIZATION PROBLEMS ON GRAPHIC ACCELERATORS

Most of the problems of discrete optimization belong to the class of NP-complete problems. This means that algorithms that can find their exact solution, in general, can work with exponential complexity relative to the length of the input data. Thanks to progress, today there are technologies that have not yet been widely used to implement applied optimization methods. Among these technologies is GP GPU (General Purposed Graphical Processing Unit). The application of this technology to well-known algorithms can help to achieve greater efficiency. The purpose of this paper is to investigate the possibilities of using parallel computations on video cards to solve discrete optimization problems. The problem of a one-dimensional Boolean knapsack was chosen as the target problem. To solve the problem, methods for obtaining an exact solution are considered - the full search algorithm, which is the starting point in the study, and the "branches and boundaries" method, which allows to reduce the search by eliminating obviously inappropriate solutions. The algorithms considered are estimated in terms of the number of operations and execution time, implemented in a single-threaded configuration of the central processor, and then parallelized on a video card. Based on the results of these methods, a combined algorithm was created that combines both algorithms to achieve greater efficiency. For parallelizing the calculations on the graphics card, the CUDA technology is chosen. Algorithms are implemented in C. After the implementation of the algorithms, testing was carried out on various data sets and different configurations of the target platform. The results of experimental studies are presented, the acceleration of work is investigated with the use of parallel computations and a comparative analysis of the efficiency of the algorithms is carried out

Using BOINC desktop grid to solve large scale SAT problems

Tyt. z nagłówka.Bibliogr. s. 32-33.Many practically important combinatorial problems can be efficiently reduced to a problem of Boolean satisfiability (SAT). Therefore, the implementation of distributed algorithms for solving SAT problems is of great importance. In this article we describe a technology for organizing desktop grid, which is meant for solving SAT problems. This technology was implemented in the form of a volunteer computing project SAT@home based on a popular BOINC platform.Dostępny również w formie drukowanej.KEYWORDS: desktop grid, Boolean satisfiability problem (SAT), SAT, volunteer computing, BOINC