混沌优化算法的性能分析

Performance Analysis of Chaos Optimization Algorithm

现代优化算法主要解决全局最优问题,其本质是概率性的.借鉴多种自然现象,人们提出了许多仿生、仿物算法,如禁忌搜索算法(TABU)、模拟退火(SAA)、遗传算法(GA)、进化策略(ES)、蚁群算法(ACA)等.利用混沌的遍历性进行优化搜索就是一种很有趣的研究思路,尤其对于虫口方程人们进行了许多研究,取得了一定的研究成果.但和普通的随机搜索算法相比,其性能之不足也很明显,主要体现在:混沌的遍历性不均匀,在边界处搜索密度高,远不如随机MonteCarlo搜索方法.这就从本质上决定了其搜索性能在普适性上与MonteCarlo算法有差距.仿真计算证实了这个结论.因此对于利用虫口方程进行的混沌优化研究需要谨慎采用.

The main objective of modern optimization algorithm is to deal with the problem of global optimum, which is essentially probabilistic. Many new global algorithms have been put forward such as TABU, simulated annealing algorithm （SAA）,genetic algorithm （GA）, evolutionary strategy （ES） and ant colony algorithm （ACA）, which benefit from many natural phenomena. The ergodicity of chaos is a new and interesting property for optimization, of which the main idea is to search according to a series of successive fields ： first search in the total field, then in a smaller one, and so on. The most famous phenomena of chaos is described by Logistic equation, which have been studied and applied to solve practical problems by many scholars.However, it has some obvious drawbacks in comparison with the ordinary random searching, chaos mainly searches on the edge of searching field, it is not as well as random in homogeneity, so there are apparent differences between chaos optimization and random optimization. The conclusion is confirmed by simulation. Therefore it is of great importance to notice the difference when applying Logistic equation in global optimization.