Solving a class of simulation-based optimization problems using “optimality in probability”

We consider a class of simulation-based optimization problems using optimality in probability, an approach which yields what is termed a “champion solution”. Compared to the traditional optimality in expectation, this approach favors the solution whose actual performance is more likely better than that of any other solution; this is an alternative complementary approach to the traditional optimality sense, especially when facing a dynamic and nonstationary environment. Moreover, using optimality in probability is computationally promising for a class of simulation-based optimization problems, since it can reduce computational complexity by orders of magnitude compared to general simulation-based optimization methods using optimality in expectation. Accordingly, we have developed an “Omega Median Algorithm” in order to effectively obtain the champion solution and to fully utilize the efficiency of well-developed off-line algorithms to further facilitate timely decision making. An inventory control problem with nonstationary demand is included to illustrate and interpret the use of the Omega Median Algorithm, whose performance is tested using simulations.