الگوریتم ژنتیک با جهش آشوبی هوشمند و ترکیب چند‌نقطه‌ای مکاشفه‌ای برای حل مسئله رنگ‌آمیزی گراف

Graph coloring is a way of coloring the vertices of a graph such that no two adjacent vertices have the same color. Graph coloring problem (GCP) is about finding the smallest number of colors needed to color a given graph. The smallest number of colors needed to color a graph G, is called its chromatic number. GCP is a well-known NP-hard problems and, therefore, heuristic algorithms are usually used to solve it. GCP has many applications such as: bandwidth allocation, register allocation, VLSI design, scheduling, Sudoku, map coloring and so on. We try genetic algorithm (GA) and chaos theory to solve GCP. We proposed a heuristic algorithm called CMHn to implement multi-point crossover operation in GA. To generate initial population, a fast greedy algorithm is used. In this algorithm, the degree of each node and the number colors in its neighbor is used to assign a color to each node. Mutation operation in GA is used to explore the search space and scape from the local optima. In this study, a chaotic mutation operation is presented to select some vertices and change their color.  The crossover and mutation parameters in the proposed algorithm is tuned based on some experiment. To evaluate the proposed algorithm, some experiment is conducted on DIMACS data set. Among DIMACS sample graphs, DSJ, Queen, Le450, Wap are well-known challenging samples for graph coloring. The proposed algorithm is executed 10 times on each sample and the best, worst and mean results are reported. Results show that the proposed algorithm can effectively solve GCP and have comparable outcome with the recent studies in this field. The proposed method outperforms other algorithms on very large graphs (Wap graphs).