Optimal computing budget allocation for small computing budgets

Abstract

In this paper, we develop an optimal computing budget allocation (OCBA) algorithm for selecting a subset of designs under the restriction of an extremely small computing budget. Such an algorithm is useful in population based Evolutionary Algorithms (EA) and other applications that seek an elite subset of designs. INTRODUCTIONThis paper addresses the problem of selecting the best m out of a finite number of k potential solutions, referred to in this paper as designs. Additionally, the performance measure for each design is stochastic and the simulation budget is extremely small. In the context of a simulation, the objective of the procedure that follows is to determine the best allocation of an extremely small number of simulation replications in order to identify as many of the set of elite designs as possible. By allocating the simulation budget, we resample these designs using multiple evaluations to gain more confidence in the estimated performance measures. This type of ranking and selection (R&S) problem has been considered previously in (Chen, He, and Fu 2008) and (Koenig and Law 1985) except these papers were concerned with selecting all of the top m solutions, and assumed a larger number of simulation replications available. Our primary motivation for this procedure is to use it in conjunction with population based evolution algorithms (EA). An evolution strategy (ES) is a population based direct search algorithm which produces λ offspring (designs) based on mutations of some start point for each generation, evaluates these offspring according to some fitness function (performance measure), selects the µ best of these offspring based on the fitness values to be the parental population of the next generation, and uses the centroid of the parental population to be the starting point of the next generation. The distance travelled toward the optimum in solution space by the population's centroid from one generation to the next is known as the progress rate. For more details, see Beyer and Schwefel (2002). Another potential use of this procedure is screening a set of designs for an elite subset when the number of simulation replications is limited due to time or budget constraints. There are numerous applications of this situation as many simulations have a very high computational effort and decision makers often want more than one design to consider when the number of inputs into the simulation model are high.978-1-4673-4781-5/12/$31.00 ©2012 IEEE

DA-OCBA: Distributed Asynchronous Optimal Computing Budget Allocation Algorithm of Simulation Optimization Using Cloud Computing

“…The OCBA solution can also be used as an approximate solution to the optimization problem defined by the exponential rate of the large deviation probability that maximizes the wrong choice [28,29]. OCBA was also studied in the Bayesian framework [30], but the formula for parameter-optimization problems did not consider order assignment. However, Chen et al [31] showed that the performance of the OCBA algorithm under perfect information (assuming the parameters are known) may be much lower than the performance of the sequential OCBA algorithm.…”

Distributed Particle Swarm Optimization using Optimal Computing Budget Allocation for multi-robot learning

“…OCBA has also been applied in the context of evolutionary algorithms [15], [16]. Schmidt et al [15] used OCBA on an evolutionary algorithm for ranking selection on noisy functions.…”

“…They allocated as many evaluations as needed to obtain an arbitrary quality of the estimations. In [16], the authors used a version of OCBA to select a set of best potential solutions on each iteration of an Evolution Strategy (ES) algorithm and showed with experimental results the effect of different values of the OCBA parameter initial number of samples (n 0 ), which we also analyze in this article. The difference between the ES OCBA and PSO OCBA is that in the ES it is only needed to estimate the performance of the subset with the best solutions while PSO requires to estimate the performance of all candidate solutions.…”

A procedure to select the best subset among simulated systems using economic opportunity cost

“…The procedure, called OCBA-m, allocates a limited computational budget across the k systems to maximize the probability of correct selection (PCS) that the top-m systems are chosen. Zhang et al (2012) present an improved version of this algorithm, called OCBA-m+, while LaPorte et al (2012) extend OCBA for subset selection under very small computing budgets. Ryzhov and Powell (2009) have also recently developed a subset selection algorithm for online problems.…”