3 resultados para Multiplicity of positive solutions

em Dalarna University College Electronic Archive


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The main objective for this degree project was to analyze the Endpoint Security Solutions developed by Cisco, Microsoft and a third minor company solution represented by InfoExpress. The different solutions proposed are Cisco Network Admission Control, Microsoft Network Access Protection and InfoExpress CyberGatekeeper. An explanation of each solution functioning is proposed as well as an analysis of the differences between those solutions. This thesis work also proposes a tutorial for the installation of Cisco Network Admission Control for an easier implementation. The research was done by reading articles on the internet and by experimenting the Cisco Network Admission Control solution. My background knowledge about Cisco routing and ACL was also used. Based on the actual analysis done in this thesis, a conclusion was drawn that all existing solutions are not yet ready for large-scale use in corporate networks. Moreover all solutions are proprietary and incompatible. The future possible standard for Endpoint solution might be driven by Cisco and Microsoft and a rude competition begins between those two giants.

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Quadratic assignment problems (QAPs) are commonly solved by heuristic methods, where the optimum is sought iteratively. Heuristics are known to provide good solutions but the quality of the solutions, i.e., the confidence interval of the solution is unknown. This paper uses statistical optimum estimation techniques (SOETs) to assess the quality of Genetic algorithm solutions for QAPs. We examine the functioning of different SOETs regarding biasness, coverage rate and length of interval, and then we compare the SOET lower bound with deterministic ones. The commonly used deterministic bounds are confined to only a few algorithms. We show that, the Jackknife estimators have better performance than Weibull estimators, and when the number of heuristic solutions is as large as 100, higher order JK-estimators perform better than lower order ones. Compared with the deterministic bounds, the SOET lower bound performs significantly better than most deterministic lower bounds and is comparable with the best deterministic ones. 

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Solutions to combinatorial optimization problems, such as problems of locating facilities, frequently rely on heuristics to minimize the objective function. The optimum is sought iteratively and a criterion is needed to decide when the procedure (almost) attains it. Pre-setting the number of iterations dominates in OR applications, which implies that the quality of the solution cannot be ascertained. A small, almost dormant, branch of the literature suggests using statistical principles to estimate the minimum and its bounds as a tool to decide upon stopping and evaluating the quality of the solution. In this paper we examine the functioning of statistical bounds obtained from four different estimators by using simulated annealing on p-median test problems taken from Beasley’s OR-library. We find the Weibull estimator and the 2nd order Jackknife estimator preferable and the requirement of sample size to be about 10 being much less than the current recommendation. However, reliable statistical bounds are found to depend critically on a sample of heuristic solutions of high quality and we give a simple statistic useful for checking the quality. We end the paper with an illustration on using statistical bounds in a problem of locating some 70 distribution centers of the Swedish Post in one Swedish region.