一种求解图着色问题的优化组合遗传算法①

图着色算法是一种典型的NP-完全问题。在逆序算子、对偶算子和矩阵遗传算子的性能研究基础上,采用自然数与二进制相互转换的编码方案,应用图着色问题的约束条件建立适应度评价函数,将具有良好局部搜索性能的矩阵遗传算子与具有良好局部搜索性能的逆序与对偶组合算子优化组合应用,构造了一种用于求解图着色问题的优化组合遗传算法,保证了算法的全局收敛性。与基本遗传算法相比较,实验结果表明,该算法对图着色问题有较好的求解性能。

Optimization Combination Genetic Algorithm for Graph Coloring Problem

Graph coloring is a NP-Complete problem. In this paper, based on the research result of Matrix genetic operator, inverse and dual combination operator, an optimization combination genetic algorithm is constructed through the inverse and dual combination genetic operator combined with matrix genetic operator to solve Graph Coloring problem. A transform coding between integer and binary is introduced to make good use of the combination operators. Fitness function based on constraint of Graph Coloring problem is designed, and the convergence of algorithm is proved. Better efficiency of the optimization combination genetic algorithm for solving Graph Coloring problem is verified compared with current genetic algorithm.