混合群搜索优化算法及其应用研究.pdf

中 文 摘 要

群搜索优化算法是 S. He，Q. H. Wu 和 J. R. 2006 年共同提出的，来源于
对动物觅食行为和群居形态的一种模仿，并首次利用了生物学的视觉搜索原理。但标准
群搜索优化算法在处理多模态优化问题时易陷于局部极小值，此外，它在优化后期的收
敛速度明显变慢，甚至处于停滞状态，难以获很好的全局最优解，因此本文针对上述两
类问题，分别提出两种混合群搜索优化算法以提高优化性能。
针对群搜索优化算法在多模态优化问题上容易陷于过早收敛，本文将 Metropolis 准
则引入发现者的搜索模式，使得算法能以一定的概率接受劣解，从而强化算法的全局搜
索能力，使其能有效跳出局部极值点。通过七个典型测试函数的测试，结果表明该算法
的性能明显优于标准群搜索优化算法，尤其在求解高维多峰函数问题上有独特优势。
针对一类特殊具有导数信息的优化问题，本文将限域拟牛顿法引入群搜索优化算法
中，提出了群搜索优化算法与限域拟牛顿法的混合算法，并以七个典型测试函数的高维
数值优化问题进行仿真，结果证明了其有效性。许多工程问题均可表示为非线性方程组
的求解，本文针对四个典型的非线性方程组求解，利用上述两个改进的混合算法进行求
解，结果均表明了群搜索优化算法与限域拟牛顿法的混合算法性能最佳。

关键词：群搜索优化算法；Metropolis 准则；限域拟牛顿法
ABSTRACT

Group Search Optimization (GSO) is a new population-based swarm
intelligent algorithm, firstly proposed in 2006 by S. He, Q. H. Wu and J. R.
Saunders. It is inspired by animal seeking behaviors, and incorporated the
visional search mechanism. However, compared with the advantages, there exist
some shortcomings for GSO. Firstly, it is easily trapped into local optima when
dealing with multi-modal problems. Secondly, the computational efficiency is
poor in the final stage of GSO. Therefore, in this article, two hybrid algorithms
of GSO are proposed aiming to improve the performance.
To overcome the premature convergence phenomenon, the metropolis rule
is introduced into producer’s search pattern to enhance the global search
capability. Different from original random search pattern, in this new variant
hybrid with Metropolis rule, the producer can accept the bad solution with a
certain probability. Simulation results show it superior to the standard version in
multi-modal benchmarks.
To solve a special kind optimization problem with differential information,
the Limited Storage Quasi-Newton Method is hybrid with GSO to increase the
local search capability. Numerical results show it is effect