Optimization heuristic solutions, how good can they be? : With empirical applications in location problems

Combinatorial optimization problems, are one of the most important types of problems in operational research. Heuristic and metaheuristics algorithms are widely applied to find a good solution. However, a common problem is that these algorithms do not guarantee that the solution will coincide with the optimum and, hence, many solutions to real world OR-problems are afflicted with an uncertainty about the quality of the solution. The main aim of this thesis is to investigate the usability of statistical bounds to evaluate the quality of heuristic solutions applied to large combinatorial problems. The contributions of this thesis are both methodological and empirical. From a methodological point of view, the usefulness of statistical bounds on p-median problems is thoroughly investigated. The statistical bounds have good performance in providing informative quality assessment under appropriate parameter settings. Also, they outperform the commonly used Lagrangian bounds. It is demonstrated that the statistical bounds are shown to be comparable with the deterministic bounds in quadratic assignment problems. As to empirical research, environment pollution has become a worldwide problem, and transportation can cause a great amount of pollution. A new method for calculating and comparing the CO2-emissions of online and brick-and-mortar retailing is proposed. It leads to the conclusion that online retailing has significantly lesser CO2-emissions. Another problem is that the Swedish regional division is under revision and the border effect to public service accessibility is concerned of both residents and politicians. After analysis, it is shown that borders hinder the optimal location of public services and consequently the highest achievable economic and social utility may not be attained.

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.

Herbrand's Theorem and Equational Reasoning: Problems and Solutions

The famous Herbrand's theorem of mathematical logic plays an important role in automated theorem proving. In the first part of this article, we recall the theorem and formulate a number of natural decision problems related to it. Somewhat surprisingly, these problems happen to be equivalent. One of these problems is the so-called simultaneous rigid E-unification problem. In the second part, we survey recent result on the simultaneous rigid E-unification problem.