Optimizing Global-Local Search Hybrids

This paper develops a framework for optimizing global-local hybrids of search or optimization procedures. The paper starts by idealizing the search problem as a search by a global algorithm G for either (1) acceptable targets|solutions that meet a speci ed criterion|or for (2) basins of attraction that then lead to acceptable targets under a speci ed local search algorithm L. The paper continues by abstracting two sets of parameters|probabilities of successfully hitting targets and basins and time-to-criterion coe cients|and writing equations to account for the total time of search and for the reliability in reaching an acceptable solution. A two-basin optimality criterion is derived and applied to important representative problems. Continuations and extensions of the work are suggested, but the theory appears to be useful immediately in better understanding the economy of e ective hybridization.