Computational study of the step size parameter of the subgradient optimization method

The subgradient optimization method is a simple and flexible linear programming iterative algorithm. It is much simpler than Newton's method and can be applied to a wider variety of problems. It also converges when the objective function is non-differentiable. Since an efficient algorithm will not only produce a good solution but also take less computing time, we always prefer a simpler algorithm with high quality. In this study a series of step size parameters in the subgradient equation is studied. The performance is compared for a general piecewise function and a specific p-median problem. We examine how the quality of solution changes by setting five forms of step size parameter.

Rule versus interaction function : evaluating regional aggregations of commuting flows in Sweden

The aim of this paper is to evaluate the performance of two divergent methods for delineating commuting regions, also called labour market areas, in a situation that the base spatial units differ largely in size as a result of an irregular population distribution. Commuting patterns in Sweden have been analyzed with geographical information system technology by delineating commuting regions using two regionalization methods. One, a rule-based method, uses one-way commuting flows to delineate local labour market areas in a top-down procedure based on the selection of predefined employment centres. The other method, the interaction-based Intramax analysis, uses two-way flows in a bottom-up procedure based on numerical taxonomy principles. A comparison of these methods will expose a number of strengths and weaknesses. For both methods, the same data source has been used. The performance of both methods has been evaluated for the country as a whole using resident employed population, self-containment levels and job ratios for criteria. A more detailed evaluation has been done in the Goteborg metropolitan area by comparing regional patterns with the commuting fields of a number of urban centres in this area. It is concluded that both methods could benefit from the inclusion of additional control measures to identify improper allocations of municipalities.