A Physics-based Metaheuristic Algorithm Based on Doppler Effect Phenomenon and Mean Euclidian Distance Threshold

Abstract

Doppler Effect (DE) is a physical phenomenon observed by Doppler, an Austrian mathematician, in 1842. In recent years, the mathematical formulation of this phenomenon has been used to improve the frequency equation of the standard Bat Algorithm (BA) developed by Yang in 2010. In this paper, we use the mathematical formulation of DE with some idealized rules to update the observer velocity existing in the Doppler equation. Thus, a new physics-based Metaheuristic (MH) optimizer is developed. In the proposed algorithm, the observers’ velocities as the algorithm’s search agents are updated based on the DE equation. A new mechanism named Mean Euclidian Distance Threshold (MEDT) is introduced to enhance the quality of the observers. The proposed MEDT mechanism is also employed to avoid the locally optimum solutions and increase the convergence rate of the presented optimizer. Since the proposed algorithm simultaneously utilizes the DE equation and MEDT mechanism, it is called the Doppler Effect-Mean Euclidian Distance Threshold (DE-MEDT) metaheuristic algorithm. The proposed DE-MEDT algorithm’s efficiency is evaluated by solving well-known unconstrained and constrained optimization problems. In the unconstrained optimization problems, 23 well-known optimization functions are used to assess the exploratory, exploitative, and convergence behaviors of the DE-MEDT algorithm.