Discrete selfish herd optimizer for solving graph coloring problem

Selfish herd optimizer is a new and effective continuous optimization algorithm, but the algorithm cannot solve the specific discrete problem. Therefore, we design a discrete selfish herd optimizer (DSHO) specifically for solving graph coloring problems. At present, many existing methods cannot effectively solve graph coloring problems. To deal with this difficult problem, in DSHO, we propose an effective step-size updating method. This step-size update method is not random, but is updated based on the conflict matrix of candidate solutions. Moreover, we also add a mechanism to deal with potential color conflict areas. By using these methods, DSHO can effectively reduce the number of conflict areas when calculating the conflict matrix of candidate solutions. To verify DSHO’s optimization performance, we use 83 test cases, they includes five simulated maps, six real maps (China, New York, America, Paris, France and Russia) and 72 test cases of minimum coloring number (They come from DIMACS Implementation Challenge). DSHO compare with the latest coloring algorithms, they are DABC, DFA, GETS, HACO, LGFPA, FROGSIM and SDGC, respectively. The experimental outcomes exhibit that DSHO has minimum number of conflict areas, smaller standard deviation, fewer iterations and higher coloring success rate. Discrete selfish herd optimizer is more competitive than other algorithms. Therefore, it is a new method for solving graph coloring problems effectively.