4,489 research outputs found
Validating Sample Average Approximation Solutions with Negatively Dependent Batches
Sample-average approximations (SAA) are a practical means of finding
approximate solutions of stochastic programming problems involving an extremely
large (or infinite) number of scenarios. SAA can also be used to find estimates
of a lower bound on the optimal objective value of the true problem which, when
coupled with an upper bound, provides confidence intervals for the true optimal
objective value and valuable information about the quality of the approximate
solutions. Specifically, the lower bound can be estimated by solving multiple
SAA problems (each obtained using a particular sampling method) and averaging
the obtained objective values. State-of-the-art methods for lower-bound
estimation generate batches of scenarios for the SAA problems independently. In
this paper, we describe sampling methods that produce negatively dependent
batches, thus reducing the variance of the sample-averaged lower bound
estimator and increasing its usefulness in defining a confidence interval for
the optimal objective value. We provide conditions under which the new sampling
methods can reduce the variance of the lower bound estimator, and present
computational results to verify that our scheme can reduce the variance
significantly, by comparison with the traditional Latin hypercube approach
Latin hypercube sampling with dependence and applications in finance
In Monte Carlo simulation, Latin hypercube sampling (LHS) [McKay et al. (1979)] is a well-known variance reduction technique for vectors of independent random variables. The method presented here, Latin hypercube sampling with dependence (LHSD), extends LHS to vectors of dependent random variables. The resulting estimator is shown to be consistent and asymptotically unbiased. For the bivariate case and under some conditions on the joint distribution, a central limit theorem together with a closed formula for the limit variance are derived. It is shown that for a class of estimators satisfying some monotonicity condition, the LHSD limit variance is never greater than the corresponding Monte Carlo limit variance. In some valuation examples of financial payoffs, when compared to standard Monte Carlo simulation, a variance reduction of factors up to 200 is achieved. LHSD is suited for problems with rare events and for high-dimensional problems, and it may be combined with Quasi-Monte Carlo methods. --Monte Carlo simulation,variance reduction,Latin hypercube sampling,stratified sampling
Experimental Design of a Prescribed Burn Instrumentation
Observational data collected during experiments, such as the planned Fire and
Smoke Model Evaluation Experiment (FASMEE), are critical for progressing and
transitioning coupled fire-atmosphere models like WRF-SFIRE and WRF-SFIRE-CHEM
into operational use. Historical meteorological data, representing typical
weather conditions for the anticipated burn locations and times, have been
processed to initialize and run a set of simulations representing the planned
experimental burns. Based on an analysis of these numerical simulations, this
paper provides recommendations on the experimental setup that include the
ignition procedures, size and duration of the burns, and optimal sensor
placement. New techniques are developed to initialize coupled fire-atmosphere
simulations with weather conditions typical of the planned burn locations and
time of the year. Analysis of variation and sensitivity analysis of simulation
design to model parameters by repeated Latin Hypercube Sampling are used to
assess the locations of the sensors. The simulations provide the locations of
the measurements that maximize the expected variation of the sensor outputs
with the model parameters.Comment: 35 pages, 4 tables, 28 figure
A Study For Efficiently Solving Optimisation Problems With An Increasing Number Of Design Variables
Coupling optimisation algorithms to Finite Element Methods (FEM) is a very promising way to achieve optimal metal forming processes. However, many optimisation algorithms exist and it is not clear which of these algorithms to use. This paper investigates the sensitivity of a Sequential Approximate Optimisation algorithm (SAO) proposed in [1-4] to an increasing number of design variables and compares it with two other algorithms: an Evolutionary Strategy (ES) and an Evolutionary version of the SAO (ESAO). In addition, it observes the influence of different Designs Of Experiments used with the SAO. It is concluded that the SAO is very capable and efficient and its combination with an ES is not beneficial. Moreover, the use of SAO with Fractional Factorial Design is the most efficient method, rather than Full Factorial Design as proposed in [1-4]
- âŠ