Mathematical function optimization using a novel algorithm based on Newtonian field theory

Over the past several decades, function optimization has been a growing topic in the field of computational intelligence. This is partly down to the myriad of real world problems that function optimization can be applied to, but also the fact there are a number of issues facing optimization algorithms that are still yet to be solved. Such problems include getting stuck in local optima, and balancing exploration and exploitation. This paper introduces a novel approach to solving the function optimization problem that utilizes the equations of Newtonian field theory to find good solutions. Like a number of existing optimization algorithms, this approach models a number of particles and their positions in solution space. However, the algorithm proposed in this paper introduces a number of interesting behaviours that can help solve some of the aforementioned issues. The algorithm is explained using both formal mathematics and pseudocode, and the emergent behaviours of the algorithm are discussed. In addition to this, the approach is compared to other optimization algorithms using a set of different functions. The results of these experiments, as well as potential improvements to the proposed algorithm are discussed.