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. 

Characterization of residential chimney conditions for flue gas flow measurements

A literature survey and a theoretical study were performed to characterize residential chimney conditions for flue gas flow measurements. The focus is on Pitot-static probes to give sufficient basis for the development and calibration of a velocity pressure averaging probe suitable for the continuous dynamic (i.e. non steady state) measurement of the low flow velocities present in residential chimneys. The flow conditions do not meet the requirements set in ISO 10780 and ISO 3966 for Pitot-static probe measurements, and the methods and their uncertainties are not valid. The flow velocities in residential chimneys from a heating boiler under normal operating condi-tions are shown to be so low that they in some conditions result in voiding the assumptions of non-viscous fluid justifying the use of the quadratic Bernoulli equation. A non-linear Reynolds number dependent calibration coefficient that is correcting for the viscous effects is needed to avoid significant measurement errors. The wide range of flow velocity during normal boiler operation also results in the flow type changing from laminar, across the laminar to turbulent transition region, to fully turbulent flow, resulting in significant changes of the velocity profile during dynamic measurements. In addition, the short duct lengths (and changes of flow direction and duct shape) used in practice are shown to result in that the measurements are done in the hydrodynamic entrance region where the flow velocity profiles most likely are neither symmetrical nor fully developed. A measurement method insensitive to velocity profile changes is thus needed, if the flow velocity profile cannot otherwise be determined or predicted with reasonable accuracy for the whole measurement range. Because of particulate matter and condensing fluids in the flue gas it is beneficial if the probe can be constructed so that it can easily be taken out for cleaning, and equipped with a locking mechanism to always ensure the same alignment in the duct without affecting the calibration. The literature implies that there may be a significant time lag in the measurements of low flow rates due to viscous effects in the internal impact pressure passages of Pitot probes, and the significance in the discussed application should be studied experimentally. The measured differential pressures from Pitot-static probes in residential chimney flows are so low that the calibration and given uncertainties of commercially available pressure transducers are not adequate. The pressure transducers should be calibrated specifically for the application, preferably in combination with the probe, and the significance of all different error sources should be investigated carefully. Care should be taken also with the temperature measurement, e.g. with averaging of several sensors, as significant temperature gradients may be present in flue gas ducts.

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.