Heuristic optimization of the p-median problem and population re-distribution

This thesis contributes to the heuristic optimization of the p-median problem and Swedish population redistribution.   The p-median model is the most representative model in the location analysis. When facilities are located to a population geographically distributed in Q demand points, the p-median model systematically considers all the demand points such that each demand point will have an effect on the decision of the location. However, a series of questions arise. How do we measure the distances? Does the number of facilities to be located have a strong impact on the result? What scale of the network is suitable? How good is our solution? We have scrutinized a lot of issues like those. The reason why we are interested in those questions is that there are a lot of uncertainties in the solutions. We cannot guarantee our solution is good enough for making decisions. The technique of heuristic optimization is formulated in the thesis.   Swedish population redistribution is examined by a spatio-temporal covariance model. A descriptive analysis is not always enough to describe the moving effects from the neighbouring population. A correlation or a covariance analysis is more explicit to show the tendencies. Similarly, the optimization technique of the parameter estimation is required and is executed in the frame of statistical modeling. 

Refraction in spacetime

Refraction, interference, and diffraction are distinguishing features of wavelike phenomena. Although they are usually associated only with a purely spatial wave-propagation pattern, analogs to interference and diffraction involving the spatio-temporal dynamics of waves in one dimension have been discussed. We complete the triplet of analogies by discussing how spatio-temporal analogs to refraction are exhibited by a quantum particle in one dimension that is scattering off a step barrier. Similarly, birefringence in spacetime occurs for a spin-1/2 particle in a magnetic field.

How do neighbouring populations affect local population change over time?

This study covers a period when society changed from a pre-industrial agricultural society to a post-industrial service-producing society. Parallel with this social transformation, major population changes took place. In this study, we analyse how local population changes are affected by neighbouring populations. To do so we use the last 200 years of local population change that redistributed population in Sweden. We use literature to identify several different processes and spatial dependencies in the redistribution between a parish and its surrounding parishes. The analysis is based on a unique unchanged historical parish division, and we use an index of local spatial correlation to describe different kinds of spatial dependencies that have influenced the redistribution of the population. To control inherent time dependencies, we introduce a non-separable spatial temporal correlation model into the analysis of population redistribution. Hereby, several different spatial dependencies can be observed simultaneously over time. The main conclusions are that while local population changes have been highly dependent on the neighbouring populations in the 19th century, this spatial dependence have become insignificant already when two parishes is separated by 5 kilometres in the late 20th century. Another conclusion is that the time dependency in the population change is higher when the population redistribution is weak, as it currently is and as it was during the 19th century until the start of industrial revolution.