Convergence analysis and performance of the extended artificial physics optimization algorithm

This paper presents extended artificial physics optimization (EAPO), a population‐based, stochastic, evolutionary algorithm (EA) for multidimensional search and optimization. EAPO extends the physicomimetics‐based Artificial Physics Optimization (APO) algorithm by including each individual’s best fitness history. Including the history improves EAPO’s search capability compared to APO. EAPO and APO invoke a gravitational metaphor in which the force of gravity may be attractive or repulsive, the aggregate effect of which is to move individuals toward local and global optima. A proof of convergence is presented that reveals the conditions under which EAPO is guaranteed to converge. Discrete‐time linear system theory is used to develop a second‐order difference equation for an individual’s stochastic position vector as a function of time step. Stable solutions require eigenvalues inside the unit circle, leading to explicit convergence criteria relating the run parameters {m i , w, G}. EAPO is tested against several benchmark functions with excellent results. The algorithm converges more quickly than APO and with better diversity.