Selecting the best stochastic system for large scale problems in DEDS. (Q1427727)

The problem of selecting a stochastic system that has the best expected performance is considered. The performance of the stochastic system is measured by a real-valued function \(g(x,y)\), where \(x\) is an element of a finite set of feasible solutions \(S\), and \(y=Y_x\) is a random variable. Therefore, the mathematical expectation \(E(g(x,Y_x))\) should be minimized over the set of feasible solutions \(S\). The problem is that, for a sufficiently large set \(S\), simulating each system to estimate all values \(E(g(x,Y_x))\) would be very expensive in terms of computer time. A two-phase optimization procedure is proposed that uses a standard clock simulation technique and consequently allows to simulate simultaneously all considered systems. In the first phase, non-competing alternatives are screened and a confidence set is constructed that contains the best alternative with a pre-specified large probability. In the second phase, the best alternative is selected among the survivals of the first stage. The algorithm is applied to a practical example.