Manifold learning for efficient gravitational search algorithm

Metaheuristic algorithms provide a practical tool for optimization in a high-dimensional search space. Some mimic phenomenons of nature such as swarms and flocks. Prominent one is the Gravitational Search Algorithm (GSA) inspired by Newton's law of gravity to manipulate agents modeled as point masses in the search space. The law of gravity states that interaction forces are inversely proportional to the squared distance in the Euclidean space between two objects. In this paper we claim that when the set of solutions lies in a lower-dimensional manifold, the Euclidean distance would yield unfitted forces and bias in the results, thus causing suboptimal and slower convergence. We propose to modify the algorithm and utilize geodesic distances gained through manifold learning via diffusion maps. In addition, we incorporate elitism by storing exploration data. We show the high performance of this approach in terms of the final solution value and the rate of convergence compared to other meta-heuristic algorithms including the original GSA. In this paper we also provide a comparative analysis of the state-of-the-art optimization algorithms on a large set of standard benchmark functions.