TWO-LEVEL GRAPH PARTITIONING ALGORITHM

Abstract

The paper discusses one of the important clasess of discrete optimization problems, combinatorial and logical problems on graphs. These problems belong to the class of NP-hard and NPdifficult optimization problems. The paper describes the partitioning optimization problem and the problem statement. To effectively solve this problem, the authors propose a new “search-evolution” strategy. On the basis of this strategy, a new search architecture based on a multi-level approach has been proposed. The principal difference of the proposed approach is the division of the search into two stages and the use of different methods at each stage. At the first stage, cluster selection is proposed. At the second stage, a genetic algorithm was proposed as an optimization method, which allows for efficient rearrangement of the constructed clusters. Based on the proposed architecture, a two-level algorithm has been developed that allows parallelizing the search process and obtaining sets of optimal and quasi-optimal solutions in a time comparable to iterative algorithms. The developed algorithm has been implemented in the C # programming language. Two types of computational experiments have been conducted on benchmarks. This is a division of the graph into 4 and 8 parts.The results of the research show that the developed approach allows you to get more effective solutions, because obtained results are on average 5 % better than the partitions obtained using the wellknown HMetis PGA Complex algorithms, which indicates the effectiveness of the proposed approach. Time complexity lies within – O(n log n) - O(n²).