细菌觅食算法求解高维优化问题

Bacterial foraging algorithm for solving high-dimensional optimization problems

针对细菌觅食优化算法中,以往的自适应步长公式引入参数过多,统一的经验性参数无法适应各类不同问题的情况,提出了改进的自适应步长公式,通过在步长公式中引入当前细菌的进化代数、寻优范围,并发挥当前最优细菌的引导作用,灵活地调整步长,真正达到自适应调整步长的目的;其次对高维优化问题进行分析,将其分为可分解可分组、不可分解可分组和不可分解不可分组三大类,针对不同类型的问题,采用不同的分组方式,降维、细化来求解,将复杂问题简单化,极大地提高了求解的效率和精度。将改进的自适应步长公式应用于高维优化问题的求解方法中,通过对多个标准测试函数在多维空间特别是超高维空间(500维、800维、1000维)进行测试,并将其结果与其他算法进行比较,实验证明该改进算法在寻得最优解的精度和效率上比其他改进方案有显著提高。

Firstly,according to the situation that there are too many parameters in adaptive step size formula and the unified empirical parameters cannot adapt to various problems in bacterial foraging optimization algorithm,this paper proposed an improved adaptive step size formula by which introduced the evolution generations of current bacteria,the guide of optimal bacteria and the range of each dimension optimization to adjust the step size flexibly. Secondly,to analyze the problem of high-dimensional optimization,which divided into decomposable,indecomposable but grouping and indecomposable not grouping class,it had been found the way to simplify complex problem by grouping of fractal dimension and detailing according to the different kinds of problems so greatly improved the efficiency and accuracy of solving problem. Based on the number of standard test functions in multidimensional space,especially high-dimensional space（ 500 dimension and 800 dimension and 1000dimension）,the experimental results show that the improved algorithm significantly improves in the accuracy and efficiency than others.