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

Abstract

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