A Manifold-Guided Gravitational Search Algorithm for High-Dimensional Global Optimization Problems

Abstract

Gravitational Search Algorithm (GSA) is a well-known physics-based meta-heuristic algorithm inspired by Newton’s law of universal gravitation and performs well in solving optimization problems. However, when solving high-dimensional optimization problems, the performance of GSA may deteriorate dramatically due to severe interference of redundant dimensional information in the high-dimensional space. To solve this problem, this paper proposes a Manifold-Guided Gravitation Search Algorithm, called MGGSA. First, based on the Isomap, an effective dimension extraction method is designed. In this mechanism, the effective dimension is extracted by comparing the dimension differences of the particles located in the same sorting position both in the original space and the corresponding low-dimensional manifold space. Then, the gravitational adjustment coefficient is designed, so that the particles can be guided to move in a more appropriate direction by increasing the effect of effective dimension, reducing the interference of redundant dimension on particle motion. The performance of the proposed algorithm is tested on 35 high-dimensional (dimension is 1000) benchmark functions from CEC2010 and CEC2013, and compared with eleven state-of-art meta-heuristic algorithms, the original GSA and four latest GSA’s variants, as well as three well-known large-scale global optimization algorithms. The experimental results demonstrate that MGGSA not only has a fast convergence rate but also has high solution accuracy. Besides, MGGSA is applied to three real-world application problems, which verifies the effectiveness of MGGSA on practical applications.