Multiscale Chaotic SPSA and Smoothed Functional Algorithms for Simulation Optimization

The authors propose a two-timescale version of the one-simulation smoothed functional (SF) algorithm with extra averaging. They also propose the use of a chaotic simple deterministic iterative sequence for generating random samples for averaging. This sequence is used for generating the N independent and identically distributed (i.i.d.), Gaussian random variables in the SF algorithm. The convergence analysis of the algorithms is also briefly presented. The authors show numerical experiments on the chaotic sequence and compare performance with a good pseudo-random generator. Next they show experiments in two different settings—a network of M/G/1 queues with feedback and the problem of finding a closed-loop optimal policy (within a prespecified class) in the available bit rate (ABR) service in asynchronous transfer mode (ATM) networks, using all the algorithms. The authors observe that algorithms that use the chaotic sequence show better performance in most cases than those that use the pseudo-random generator.