META-HEURISTIC ALGORITHMS FOR MINIMIZING THE NUMBER OF CROSSING OF COMPLETE GRAPHS AND COMPLETE BIPARTITE GRAPHS

The minimum crossing number problem is among the oldest and most fundamental problems arising in the area of automatic graph drawing. In this paper, eight population-based meta-heuristic algorithms are utilized to tackle the minimum crossing number problem for two special types of graphs, namely complete graphs and complete bipartite graphs. A 2-page book drawing representation is employed for embedding graphs in the plane. The algorithms consist of Artificial Bee Colony algorithm, Big Bang-Big Crunch algorithm, Teaching-Learning-Based Optimization algorithm, Cuckoo Search algorithm, Charged System Search algorithm, Tug of War Optimization algorithm, Water Evaporation Optimization algorithm, and Vibrating Particles System algorithm. The performance of the utilized algorithms is investigated through various examples including six complete graphs and eight complete bipartite graphs. Convergence histories of the algorithms are provided to better understanding of their performance. In addition, optimum results at different stages of the optimization process are extracted to enable to compare the meta-heuristics algorithms.