  In this paper, we propose a relaxation to the stochastic ruler method
originally described by Yan and Mukai in 1992 for asymptotically determining
the global optima of discrete simulation optimization problems. The `original'
version of the stochastic ruler and its variants require that a candidate for
the next estimate of the optimal solution pass a certain number of tests with
respect to the stochastic ruler to be selected as the next estimate of the
optimal solution. This requirement - that all tests need to be passed - can
lead to promising candidate solutions being rejected and can slow down the
convergence of the algorithm. Our proposed modification to the stochastic ruler
algorithm relaxes this requirement, and we show analytically that our proposed
variant of the stochastic ruler method incurs lesser computational overhead
when a new solution in the neighborhood of the current solution is a
`successful' candidate for the next estimate of the current solution. We then
show numerically that this can yield accelerated convergence to the optimal
solution via multiple numerical examples. We also provide the theoretical
grounding for the asymptotic convergence in probability of the variant to the
global optimal solution under the same set of assumptions as those underlying
the original stochastic ruler method.
