Pseudorandomness in Central Force Optimization

Central Force Optimization is a deterministic metaheuristic for an evolutionary algorithm that searches a decision space by flying probes whose trajectories are computed using a gravitational metaphor. CFO benefits substantially from the inclusion of a pseudorandom component (a numerical sequence that is precisely known by specification or calculation but otherwise arbitrary). The essential requirement is that the sequence is uncorrelated with the decision space topology, so that its effect is to pseudorandomly distribute probes throughout the landscape. While this process may appear to be similar to the randomness in an inherently stochastic algorithm, it is in fact fundamentally different because CFO remains deterministic at every step. Three pseudorandom methods are discussed (initial probe distribution, repositioning factor, and decision space adaptation). A sample problem is presented in detail and summary data included for a 23-function benchmark suite. CFO’s performance is quite good compared to other highly developed, state-of-the-art algorithms. Ver. 2 (typographical errors in Step (c) of Fig. 1 and discussion of Fig. 8 corrected; clarification of definition of best R r ; error in Table 2 test function f12 corrected; f12 source code in Appendix 3, page 60 corrected). 3 February 2010 Saint Augustine, Florida