格雷码混合加速遗传算法及其性能分析

A GRAY CODE HYBRID ACCELERATING GENETIC ALGORITHM AND ITS PROPERTY ANALYSIS

通过在格雷码遗传算法进化过程中加入单纯形法学习算子 ,并利用格雷码遗传算法和单纯形法所得到的优秀个体群 ,作为变量新的变化范围 ,逐步缩小搜索空间 ,自动向最优解收缩 ,提出了求解非线性规划问题全局解的一种快速算法———格雷码混合加速遗传算法 (GHAGA) .为了在可行域内能得到全局最优解 ,在参数的定义域内投放了大量的均匀随机初始点作为初始群体 .给出了GHAGA算法实施的详细步骤 ,建立了GHAGA相应的收敛定理 ,并分析了该算法的全局优化性能 .理论分析和数值模拟表明 ,GHAGA具有精度高、收敛速度快的特点 ,是一种既可以较大概率搜索全局最优解 ,又能进行局部细致搜索的较好的非线性规划方法 .

Genetic Algorithm is a new kind of effective algorithms for very complex nonlinear programming problems. However, the amount of their computation is often large. In this study, a new method, Gray Code Hybrid Accelerating Genetic Algorithm(GHAGA), and its detailed steps are developed to reduce the amount of the computation and make the algorithm more effective. With the shrinking of searching range, the method gradually directs to optimal result by the excellent individuals obtained by gray code genetic algorithm(GGA) embedding with simplex searching operator and simplex algorithm. In order to cover a wide domain of possible solutions, our algorithm first performs the diversification: it locates the most promising areas, by giving birth to a lot of uniformity random numbers in its definition domain. When the most promising areas are located, the algorithm continues the search by intensification within the interval shrunk by the most promising areas with Nelder-Mead simplex algorithm. Further, the convergence theorem is given and global optimization of GHAGA is discussed theoretically, and its high precision on global optimization is ascertained practically. GHAGA remarkably improves convergence speed and calculation accuracy. It proves a good nonlinear optimal method that can search both global solution and fractional one in greater probability.