The convergence analysis of artificial physics optimisation algorithm

Artificial physics optimisation (APO) algorithm is a novel population-based stochastic algorithm based on physicomimetics framework for multidimensional search and optimisation. APO invokes 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 APO is guaranteed to converge. These convergence conditions indicate that some individuals have convergence behaviours whereas other individuals have divergent behaviours in APO system. According to the character, it can be proved that APO algorithm converge to the vicinity of global optimum with probability one based on the related knowledge of probability theory, which is proposed in brief. By regarding each individual|s position on each evolutionary step as a stochastic vector, APO algorithm determined by non-negative real parameter tuple {m i, w, G} is analysed using discrete-time linear system theory. The convergent condition of APO algorithm and corresponding parameter selection guidelines are derived. The simulation results show that the convergent condition is effective in guiding the parameter selection of APO algorithm and can help to explain why those parameters work well.