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Convergence analysis and performance of the extended artificial physics optimization algorithm
Authors:Liping Xie  Jianchao Zeng
Affiliation:a Complex System and Computational Intelligence Laboratory, Taiyuan University of Science and Technology, Taiyuan, Shanxi 030024, PR China
b Registered Patent Attorney and Consulting Engineer, Cataldo and Fisher, LLC, 400 TradeCenter, Suite 5900, Woburn, MA 01801, USA
Abstract: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 {miwG}. EAPO is tested against several benchmark functions with excellent results. The algorithm converges more quickly than APO and with better diversity.
Keywords:Extended artificial physics optimization (EAPO)   Proof of convergence   Artificial physics optimization (APO)   Physicomimetics   Global optimization   Gravitational force   Virtual force   Newton&rsquo  s law
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