Mohammad H. Almomani

Subset selection of best simulated systems

In this paper, we consider the problem of selecting a subset of k systems that is contained in the set of the best s simulated systems when the number of alternative systems is huge. We propose a sequential method that uses the ordinal optimization to select a subset G randomly from the search space that contains the best simulated systems with high probability. To guarantee that this subset contains the best systems it needs to be relatively large. Then methods of ranking and selections will be applied to select a subset of k best systems of the subset G with high probability. The remaining systems of G will be replaced by newly selected alternatives from the search space. This procedure is repeated until the probability of correct selection (a subset of the best k simulated systems is selected) becomes very high. The optimal computing budget allocation is also used to allocate the available computing budget in a way that maximizes the probability of correct selection. Numerical experiments for comparing these algorithms are presented.

Selecting a Good Stochastic System for the Large Number of Alternatives

In this article, we present the problem of selecting a good stochastic system with high probability and minimum total simulation cost when the number of alternatives is very large. We propose a sequential approach that starts with the Ordinal Optimization procedure to select a subset that overlaps with the set of the actual best m% systems with high probability. Then we use Optimal Computing Budget Allocation to allocate the available computing budget in a way that maximizes the Probability of Correct Selection. This is followed by a Subset Selection procedure to get a smaller subset that contains the best system among the subset that is selected before. Finally, the Indifference-Zone procedure is used to select the best system among the survivors in the previous stage. The numerical test involved with all these procedures shows the results for selecting a good stochastic system with high probability and a minimum number of simulation samples, when the number of alternatives is large. The results also show that the proposed approach is able to identify a good system in a very short simulation time.

Ordinal Optimization with Computing Budget Allocation for Selecting an Optimal Subset

In this paper, we consider the problem of selecting the top m systems when the number of alternative systems is very large. We propose a sequential procedure that consists of two stages to solve this problem. The procedure is a combination of the ordinal optimization (OO) technique and optimal computing budget allocation (OCBA) method. In the first stage, the OO is used to select a subset that overlaps with the set of actual best k% systems with high probability. Then in the second stage the optimal computing budget is used to select the top m systems from the selected subset. The proposed procedure is tested on two numerical examples. The numerical tests show that the proposed procedure is able to select a subset of best systems with high probability and short simulation time.

On the optimal computing budget allocation problem for large scale simulation optimization

Abstract Selecting a set that contains the best simulated systems is an important area of research. When the number of alternative systems is large, then it becomes impossible to simulate all alternatives, so one needs to relax the problem in order to find a good enough simulated system rather than simulating each alternative. One way for solving this problem is to use two-stage sequential procedure. In the first stage the ordinal optimization is used to select a subset that overlaps with the actual best systems with high probability. Then in the second stage an optimization procedure can be applied on the smaller set to select the best alternatives in it. In this paper, we consider the optimal computing budget allocation (OCBA) in the second stage that distribute available computational budget on the alternative systems in order to get a correct selection with high probability. We also discuss the effect of the simulation parameters on the performance of the procedure by implementing the procedure on three different examples. The numerical results indeed indicate that the choice of these parameters affect its performance.

Asymptotic approximation of the probability of correctly selecting the best systems

Consider the problem of selecting the best stochastic system or the best m systems among a finite but large alternative systems. If a limited computational budget is available to be distributed among the different alternatives, then instead of distributing these computations evenly, the optimal computing budget allocation (OCBA) can be used to distribute this budget in a smart way so as to maximize the probability of correct selection (PCS). However, the OCBA does not tell how large is the PCS. In this paper, we present a procedure that resembles the OCBA, but it gives an approximation of PCS. Thus the user can stop the simulation whenever a precision level is reached.Consider the problem of selecting the best stochastic system or the best m systems among a finite but large alternative systems. If a limited computational budget is available to be distributed among the different alternatives, then instead of distributing these computations evenly, the optimal computing budget allocation (OCBA) can be used to distribute this budget in a smart way so as to maximize the probability of correct selection (PCS). However, the OCBA does not tell how large is the PCS. In this paper, we present a procedure that resembles the OCBA, but it gives an approximation of PCS. Thus the user can stop the simulation whenever a precision level is reached.

Efficient Approach for Selecting the Best Subset of Buffer Profile

One of the main problems with designing a production line is to find the optimal number of buffers between workstations in order to maximizes the throughput. This problem known as buffer allocation problem. Previous work in this problem focus on selecting a single buffer profile that has the maximum throughput. The objective in this paper would be to selecting from a large number of alternatives, the best subset of buffer profiles where its throughput are at its maximum. The ordinal optimization with optimal computing budget allocation approaches will be used to isolating the best subset of buffer profile, where its throughput is maximum, from the set of all alternatives. Numerical results show that the proposed algorithm finds the best subset of the puffer allocation with high probability and small replications numbers of samples.

Sequential selection approach for selecting the best system

Consider the problem of selecting the best simulated system with high probability, from a finite and huge set of alternative systems. The best system might be the one that has the maximum or minimum performance measure. In this paper, we present a sequential method that uses the Ordinal Optimization procedure to select randomly a subset that overlaps with the set of the actual best m% systems with high probability from the search space. The next step, we use Optimal Computing Budget Allocation technique to allocate the available computing budget in a way that maximizes the probability of correct selection. This follows by a Subset Selection procedure to get a smaller subset that contains the best system from the subset that is selected before. Finally, we use the Indifference-Zone procedure to select the best system among the survivors in the previous stage. The results of the empirical experiments show that this approach selects the best simulated system with high probability and a minimum number of simulation replication, when the number of alternatives is huge.