A novel heuristics optimization inspired by the Lorentz transformation

Abstract

We propose a novel population-based heuristics optimization strategy involving the Lorentz transformation. All of the currently available meta-heuristics optimization strategies are basically categorized into a sort of neighbor search. We have adopted the Lorentz transformation in determining the neighbors in the search domain. Although the Lorentz transformation was originally used for the mathematical interpretation of the special relativity, we recognized that the Lorentz transformation could be utilized for optimization problems. The key idea of the proposed algorithm is that an additional, dummy time variable was assigned to the decision variable and thereby the neighbor search took place not in the conventional Euclidean space but in so-called space-time based on the Minkowski metric. Besides the time variable, the speed and direction of the virtual moving frame have been shown to act as a key parameter to determine the neighbor. The relative speed of the virtual moving frame was varied in the range from 0 to 1, and the direction was randomly decided but in some cases we used the first Eigen vector direction of the covariance matrix of instantaneous decision variables. The objective function was regarded as invariant to the reference frame, something like a transcendental entity in the space time. We investigated two different algorithms according to the control of time, speed and direction. The proposed, novel heuristics optimization worked properly in the continuous n-dimensional search space when we executed test experiments using several well-known benchmark functions.