Improved solutions to dynamic and stochastic maritime pick-up and delivery problems using local search.

Heuristics for stochastic and dynamic vehicle routing problems are often kept relatively simple, in part due to the high computational burden resulting from having to consider stochastic information in some form. In this work, three existing heuristics are extended by three different local search variations: a first improvement descent using stochastic information, a tabu search using stochastic information when updating the incumbent solution, and a tabu search using stochastic information when selecting moves based on a list of moves determined through a proxy evaluation. In particular, the three local search variations are designed to utilize stochastic information in the form of sampled scenarios. The results indicate that adding local search using stochastic information to the existing heuristics can further reduce operating costs for shipping companies by 0.5–2 %. While the existing heuristics could produce structurally different solutions even when using similar stochastic information in the search, the appended local search methods seem able to make the final solutions more similar in structure.

A search for anisotropy in the arrival directions of ultra high energy cosmic rays recorded at the Pierre Auger Observatory

Observations of cosmic rays arrival directions made with the Pierre Auger Observatory have previously provided evidence of anisotropy at the 99% CL using the correlation of ultra high energy cosmic rays (UHECRs) with objects drawn from the Veron-Cetty Veron catalog. In this paper we report on the use of three catalog independent methods to search for anisotropy. The 2pt-L, 2pt+ and 3pt methods, each giving a different measure of self-clustering in arrival directions, were tested on mock cosmic ray data sets to study the impacts of sample size and magnetic smearing on their results, accounting for both angular and energy resolutions. If the sources of UHECRs follow the same large scale structure as ordinary galaxies in the local Universe and if UHECRs are deflected no more than a few degrees, a study of mock maps suggests that these three method can efficiently respond to the resulting anisotropy with a P-value = 1.0% or smaller with data sets as few as 100 events. using data taken from January 1, 2004 to July 31, 2010 we examined the 20, 30, ... , 110 highest energy events with a corresponding minimum energy threshold of about 49.3 EeV. The minimum P-values found were 13.5% using the 2pt-L method, 1.0% using the 2pt+ method and 1.1% using the 3pt method for the highest 100 energy events. In view of the multiple (correlated) scans performed on the data set, these catalog-independent methods do not yield strong evidence of anisotropy in the highest energy cosmic rays.