ABSTRACT
This chapter involves some advanced topics on the QPSO algorithm. Readers who are not interested in the theory of QPSO should skip this chapter except the last section. First, the behaviour of an individual particle is analysed using probability theory and stochastic simulation to validate the theoretical results. Second, the global convergence of QPSO is proved by using probability measures, Markov processes and œxed-point theorems in probabilistic metric (PM) spaces. ¢ird, the deœnitions of computational complexity and the rate of convergence of a stochastic search algorithm are introduced and applied to the QPSO algorithm, and tested experimentally against the sphere function. Finally, parameter selection of the QPSO algorithm is discussed, and numerical tests of several benchmark functions are performed and analysed.
