A case study for optimal dynamic simulation allocation in ordinal optimization

Ordinal optimization has emerged as an efficient technique for simulation and optimization. Exponential convergence rates can be achieved in many cases. A good allocation of simulation samples across designs can further dramatically improve the efficiency of ordinal optimization by orders of magnitude. However, the allocation problem itself is a big challenge. Most existing methods offer approximations. Assuming the availability of perfect information, we investigate theoretically optimal allocation schemes for some special cases. We compare our theoretically optimal solutions with existing approximation methods using a series of numerical examples. While perfect information is not available in real life, such an optimal solution provides an upper bound for the simulation efficiency we can achieve. The results indicate that the simulation efficiency can still be further improved beyond the existing methods. The numerical testing shows that dynamic allocation is also much more efficient than the static allocation.