Convergence analysis and performance of an extended central force optimization algorithm

Keywords: Extended/enhanced central force optimization (ECFO) Global optimization Convergence analysis Simple central force optimization (SCFO) Gravitational force a b s t r a c t Simple central force optimization (SCFO) algorithm is a novel physically-inspired optimization algorithm as simulating annealing (SA). To enhance the global search ability of SCFO and accelerate its convergence, a novel extended/enhanced central force optimization (ECFO) algorithm is proposed through both adding the historical information and defining an adaptive mass. SCFO and ECFO are all motivated by gravitational kinematics, in which the compound gravitation impels particles to the optima. The convergence of ECFO is proved based on a more complex characteristic equation than SCFO, i.e. the second order difference equation. The stability theory of discrete-time-linear system is used to analyze the motion equations of particles. Stability conditions limit their eigenvalues inside the unit cycle in complex plane and corresponding convergence conditions are deduced related with ECFO's parameters. Finally, ECFO are tested against a suite of benchmark functions with deterministic and excellent results. Experiments results show that ECFO converges faster than SCFO with higher global searching ability. In the last decade of the 21st, various nature-inspired heuristic optimization algorithms became the most widely-used optimization methods [1]. Nature-inspired heuristic methods can be commonly divided into two kinds, biologically-inspired heuristics and physically-inspired heuristics, as they respectively imitate biological phenomena and physical principles [2,3]. Nowadays biologically-inspired heuristic optimization algorithms are applied widely in different areas [4–16], e.g. It is known that they all simulate biological interactive mechanisms, e.g. evolutionary, collective, competitive, collaborative, or swarm behaviors. Although certain behaviors are simulated quite perfectly, their deficiencies are still apparent. That is because the uncertainty of macro biological theories on micro individuals is evitable, such as randomness [4–16]. Consequently, the processes and results of optimization are all doubtful [17]; a high computational cost is needed; and a trivial statistical evaluation is indispensable. In addition, due to true random variables in underlying equations, they completely lack repeatability [18]. However, engineers and scientists have always been pursuing certain deterministic heuristic optimization algorithms with simple principles for 0096-3003/$-see front matter Ó 2012 Elsevier Inc. All rights reserved.