On statistical bounds of heuristic solutions to location problems

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. 

Proceedings from the 2nd seminar on Development of Modular Products : December 13-14, 2004, Campus Framtidsdalen, Dalarna University, Sweden

Companies are focusing on efforts increasing the overall efficiency at the same time as the ability to meet customer needs becomes even more important. There is a need to improve the organisation and the product design at the same time through the visualisation of how a product family design should be performed in order to adapt to customers, company internal issues, and long-term strategy. Therefore, there is a need for qualified personnel in today’s companies with the knowledge of product development and modularity. The graduate course Development of Modular Products at Högskolan Dalarna has the objective to provide such knowledge. As a part of the course, each student will individually perform extensive research within a chosen area with respect to Product Development and Modularity. This proceeding is the result of the students own work and was presented during a two day seminar at Dalarna University. The contents of the papers cover many areas, from the identification of customer needs to cost effective manufacturing, and benefits of modularisation. The reader of this proceeding will not only benefit from many areas within Product Development and Modularity but also from the colour of many cultures. In this proceeding, students from nine countries are represented (Bangladesh, China, Costa Rica, Germany, Holland, India, Luxembourg Nigeria, and Sweden). Enjoy the reading.

Statistical bound of genetic solutions to quadratic assignment problems

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. 

A computational comparison of different algorithms for very large p-median problems

In this paper, we propose a new method for solving large scale p-median problem instances based on real data. We compare different approaches in terms of runtime, memory footprint and quality of solutions obtained. In order to test the different methods on real data, we introduce a new benchmark for the p-median problem based on real Swedish data. Because of the size of the problem addressed, up to 1938 candidate nodes, a number of algorithms, both exact and heuristic, are considered. We also propose an improved hybrid version of a genetic algorithm called impGA. Experiments show that impGA behaves as well as other methods for the standard set of medium-size problems taken from Beasley’s benchmark, but produces comparatively good results in terms of quality, runtime and memory footprint on our specific benchmark based on real Swedish data.

Health problems in elderly patients during the first post-stroke year

BACKGROUND: A wide range of health problems has been reported in elderly post-stroke patients. AIM: The aim of this study was to analyse the prevalence and timing of health problems identified by patient interviews and scrutiny of primary health care and municipality elderly health care records during the first post-stroke year. METHODS: A total of 390 consecutive patients, ≥65 years, discharged alive from hospital after a stroke event, were followed for 1 year post-admission. Information on the health care situation during the first post-stroke year was obtained from primary health care and municipal elderly health care records and through interviews with the stroke survivors, at 1 week after discharge, and 3 and 12 months after hospital admission. RESULTS: More than 90% had some health problem at some time during the year, while based on patient record data only 4-8% had problems during a given week. The prevalence of interview-based health problems was generally higher than record-based prevalence, and the ranking order was moderately different. The most frequently interview-reported problems were associated with perception, activity, and tiredness, while the most common record-based findings indicated pain, bladder and bowel function, and breathing and circulation problems. There was co-occurrence between some problems, such as those relating to cognition, activity, and tiredness. CONCLUSIONS: Almost all patients had a health problem during the year, but few occurred in a given week. Cognitive and communication problems were more common in interview data than record data. Co-occurrence may be used to identify subtle health problems.