Stochastic Approximation to Understand Simple Simulation Models

This paper illustrates how a deterministic approximation of a stochastic process can be usefully applied to analyse the dynamics of many simple simulation models. To demonstrate the type of results that can be obtained using this approximation, we present two illustrative examples which are meant to serve as methodological references for researchers exploring this area. Finally, we prove some convergence results for simulations of a family of evolutionary games, namely, intra-population imitation models in n-player games with arbitrary payoffs.Ministerio de Educación (JC2009- 00263), Ministerio de Ciencia e Innovación (CONSOLIDER-INGENIO 2010: CSD2010-00034, DPI2010-16920

Stochastic programming approaches to stochastic scheduling

Practical scheduling problems typically require decisions without full information about the outcomes of those decisions. Yields, resource availability, performance, demand, costs, and revenues may all vary. Incorporating these quantities into stochastic scheduling models often produces diffculties in analysis that may be addressed in a variety of ways. In this paper, we present results based on stochastic programming approaches to the hierarchy of decisions in typical stochastic scheduling situations. Our unifying framework allows us to treat all aspects of a decision in a similar framework. We show how views from different levels enable approximations that can overcome nonconvexities and duality gaps that appear in deterministic formulations. In particular, we show that the stochastic program structure leads to a vanishing Lagrangian duality gap in stochastic integer programs as the number of scenarios increases.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/44935/1/10898_2004_Article_BF00121682.pd

Characterization of the probabilistic traveling salesman problem

We show that stochastic annealing can be successfully applied to gain new results on the probabilistic traveling salesman problem. The probabilistic "traveling salesman" must decide on an a priori order in which to visit n cities (randomly distributed over a unit square) before learning that some cities can be omitted. We find the optimized average length of the pruned tour follows E((L) over bar (pruned))=rootnp(0.872-0.105p)f(np), where p is the probability of a city needing to be visited, and f(np)-->1 as np-->infinity. The average length of the a priori tour (before omitting any cities) is found to follow E(L-a priori)=rootn/pbeta(p), where beta(p)=1/[1.25-0.82 ln(p)] is measured for 0.05less than or equal topless than or equal to0.6. Scaling arguments and indirect measurements suggest that beta(p) tends towards a constant for p<0.03. Our stochastic annealing algorithm is based on limited sampling of the pruned tour lengths, exploiting the sampling error to provide the analog of thermal fluctuations in simulated (thermal) annealing. The method has general application to the optimization of functions whose cost to evaluate rises with the precision required

A lower bound on convergence rates of nonadaptive algorithms for univariate optimization with noise

Global optimization, Wiener process, Noisy information,

Estimation of Total Body Water from Foot-To-Foot Bioelectrical Impedance Analysis in Patients with Cancer Cachexia - Agreement Between Three Prediction Methods and Deuterium Oxide Dilution

Introduction: Bioelectrical impedance analysis (BIA) is a useful bedside measure to estimate total body water (TBW). The aim of this study was to determine the agreement between three equations for the prediction of TBW using BIA against the criterion method, deuterium oxide dilution, in patients with cancer cachexia. Methods: Eighteen measurements of TBW using foot-to-foot BIA in seven outpatients with cancer cachexia (five male and two female, age 56.4 +/- 6.7 years) at an Australian hospital. Three prediction formulae were used to estimate TBW - TBWca-radiotherapy developed in patients with cancer undergoing radiotherapy, TBWca-underweight and TBWca-normal weight developed in underweight and normal weight patients with cachexia. TBW was measured using the deuterium oxide dilution technique as the gold standard. Results: Mean measured TBW was 39.5 +/- 6.0 L. There was no significant difference in measured TBW and estimates from prediction equations TBWca-underweight and TBWca-radiotherapy. There was a significant difference in measured TBW and TBWca-normal weight. All prediction equations overestimated TBW in comparison with measured TBW. The smallest bias was observed with TBWca-underweight (0.38 L). The limits of agreement are wide (> 7.4 L) for each of the prediction equations compared with measured TBW. Conclusions: At a group level, TBWca-underweight is the best predictor of measured TBW in patients with cancer cachexia. For an individual however, the limits of agreement are wide for all prediction equations and are unsuitable for use. Practitioners need to be aware of the limitations of using TBW prediction equations for individuals