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In this chapter, we establish a framework for formal comparisons of several leading optimization algorithms, providing guidance to practitioners for when to use or not use a particular method. The focus in this chapter is five general algorithm forms: random search, simultaneous perturbation stochastic approximation, simulated annealing, evolution strategies, and genetic algorithms. We summarize the available theoretical results on rates of convergence for the five algorithm forms and then use the theoretical results to draw some preliminary conclusions on the relative efficiency. Our aim is to sort out some of the competing claims of efficiency and to suggest a structure for comparison that is more general and transferable than the usual problem-specific numerical studies.

Abstract-A stochastic approximation method for optimizing a class of discrete functions is considered. The procedure is a version of the Simultaneous Perturbation Stochastic Approximation (SPSA) method that has been modified to obtain a stochastic optimization method for cost functions defined on a grid of points in Euclidean p-space having integer components. We discuss the algorithm and examine its convergence properties.

The cost of delay i s a serious and increasing problem in the airline industry. Air travel is increasing, and already domestic airports incur thousands of hours of delay daily, costing the industry $2 billion a year. One strategy for reducing total delay costs is to hold planes for a short time at the gate in order to reduce costly airborne congestion. In a network of airports involving hundreds of ights, it is dicult to determine the amount to hold each ight at the gate. This paper discusses how the optimization procedure simultaneous perturbation stochastic approximation (SPSA) can be used to process delay cost measurements from air trac simulation packages and produce an optimal gate holding schedule. As a test case, the SIMMOD air trac simulation package was used to model a simple four-airport network. Initial delay costs are reduced up to 10.3%.