Genetic Algorithms and the Optimal Allocation of Trials

Abstract

This study gives a formal setting to the difficult optimization problems characterized by the conjunction of (1) substantial complexity and initial uncertainty, (2) the necessity of acquiring new information rapidly to reduce the uncertainty, and (3) a requirement that the new information be exploited as acquired so that average performance increases at a rate consistent with the rate of acquisition of information. The setting has as its basis a set $\mathcal{A}$ of structures to be searched or tried and a performance function $\mu :\mathcal{A} \to $ real numbers. Within this setting it is determined how to allocate trials to a set of random variables so as to maximize expected performance. This result is then transformed into a criterion against which to measure the performance of a robust and easily implemented set of algorithms called reproductive plans. It is shown that reproductive plans can in fact surpass the criterion because of a phenomenon called intrinsic parallelism—a single trial (individual $A \in \mathcal{A}$) simultaneously tests and exploits many random variables.