Neill E. Bowler

Local search for the probabilistic traveling salesman problem: Correction to the 2-p-opt and 1-shift algorithms

Abstract The probabilistic traveling salesman problem concerns the best way to visit a set of customers located in some metric space, where each customer requires a visit only with some known probability. A solution to this problem is an a priori tour which visits all customers, and the objective is to minimize the expected length of the a priori tour over all customer subsets, assuming that customers in any given subset must be visited in the same order as they appear in the a priori tour. This problem belongs to the class of stochastic vehicle routing problems, a class which has received increasing attention in recent years, and which is of major importance in real world applications. Several heuristics have been proposed and tested for the probabilistic traveling salesman problem, many of which are a straightforward adaptation of heuristics for the classical traveling salesman problem. In particular, two local search algorithms (2-p-opt and 1-shift) were introduced by Bertsimas. In a previous report we have shown that the expressions for the cost evaluation of 2-p-opt and 1-shift moves, as proposed by Bertsimas, are not correct. In this paper we derive the correct versions of these expressions, and we show that the local search algorithms based on these expressions perform significantly better than those exploiting the incorrect expressions.

Comparison of Hybrid-4DEnVar and Hybrid-4DVar Data Assimilation Methods for Global NWP

AbstractThe Met Office has developed an ensemble-variational data assimilation method (hybrid-4DEnVar) as a potential replacement for the hybrid four-dimensional variational data assimilation (hybrid-4DVar), which is the current operational method for global NWP. Both are four-dimensional variational methods, using a hybrid combination of a fixed climatological model of background error covariances with localized covariances from an ensemble of current forecasts designed to describe the structure of “errors of the day.” The fundamental difference between the methods is their modeling of the time evolution of errors within each data assimilation window: 4DVar uses a linear model and its adjoint and 4DEnVar uses a localized linear combination of nonlinear forecasts. Both hybrid-4DVar and hybrid-4DEnVar beat their three-dimensional versions, which are equivalent, in NWP trials. With settings based on the current operational system, hybrid-4DVar performs better than hybrid-4DEnVar. Idealized experiments desig...

On the Reliability and Calibration of Ensemble Forecasts

Abstract An important aspect of ensemble forecasting is that the resulting probabilities are reliable (i.e., the forecast probabilities match the observed frequencies). In the medium-range forecasting context, the literature tends to focus on the requirement that, for a reliable ensemble, the ensemble spread should be representative of the uncertainty in the mean, whereas in the seasonal forecasting context, the literature tends to focus on the requirement that, for a reliable ensemble, the ensemble forecasts should have the same climatological variance as the truth. In this note, the authors emphasize that both of these requirements are necessary for reliability and they clarify that a popular calibration method actually achieves both of these requirements.

The Benefits of Multianalysis and Poor Man's Ensembles

Abstract A new approach to probabilistic forecasting is proposed, based on the generation of an ensemble of equally likely analyses of the current state of the atmosphere. The rationale behind this approach is to mimic a poor man’s ensemble, which combines the deterministic forecasts from national meteorological services around the world. The multianalysis ensemble aims to generate a series of forecasts that are both as skillful as each other and the control forecast. This produces an ensemble mean forecast that is superior not only to the ensemble members, but to the control forecast in the short range even for slowly varying parameters, such as 500-hPa height. This is something that it is not possible with traditional ensemble methods, which perturb a central analysis. The results herein show that the multianalysis ensemble is more skillful than the Met Office’s high-resolution forecast by 4.5% over the first 3 days (on average as measured for RMSE). Similar results are found for different verification ...