Abstract: Gravitational search algorithm (GSA) is a novel optimization algorithm based on the law of gravity and mass interactions. Some studies show that GSA can obtain more superior results than classical optimization algorithms in most cases. But the standard GSA is easy to be trapped into local optimum and premature convergence. This paper proposes an improved weighted algorithm based on Lévy Flight and inertia weight, named QmuGSA, to strength global search capacity of GSA. The new algorithm can expand agents’ search space and increase the diversity of population by using the characteristics of random walk of Lévy Flight, it is easier to jump out of local optimal point. The numerical results in four benchmark functions demonstrate that the new algorithm can effectively overcome the defects of premature and low convergence precision of the standard GSA, has better optimization precision and global convergence performance, and can solve some complex function optimization problems.

Key words: gravitational search algorithm (GSA), Lévy Flight, inertia weight

摘要： 引力搜索算法（gravitational search algorithm，GSA）是模拟万有引力定律进行搜索的一种新颖的优化算法，已有研究表明GSA算法相比一些传统的优化算法拥有较好的收敛性能，但其缺乏有效的全局寻优机制，易于被局部极值吸引，从而陷入早熟收敛。因此提出了一种基于Lévy Flight和权值惯性递减的引力搜索算法QmuGSA，以加强算法的全局寻优能力。该算法通过Lévy Flight独特的不均匀随机游走的机制扩大粒子的搜索范围，增加种群多样性，从而更容易跳出局部最优点。通过4个标准测试函数对所提算法进行了仿真测试，结果表明所提算法能够有效克服基本引力搜索算法易早熟、收敛精度低等缺陷，具有较好的寻优精度和全局收敛性能，能够解决一些复杂函数的优化问题。

关键词: 引力搜索算法（GSA）, Lé, vy Flight, 惯性权重