A quadtree-based allocation method for a class of large discrete Euclidean location problems: large location problems

A special data compression approach using a quadtree-based method is proposed for allocating very large demand points to their nearest facilities while eliminating aggregation error. This allocation procedure is shown to be extremely effective when solving very large facility location problems in the Euclidian space. Our method basically aggregates demand points where it eliminates aggregation-based allocation error, and disaggregates them if necessary. The method is assessed first on the allocation problems and then embedded into the search for solving a class of discrete facility location problems namely the p-median and the vertex p-centre problems. We use randomly generated and TSP datasets for testing our method. The results of the experiments show that the quadtree-based approach is very effective in reducing the computing time for this class of location problems

Location models in the public sector

The past four decades have witnessed an explosive growth in the field of networkbased facility location modeling. This is not at all surprising since location policy is one of the most profitable areas of applied systems analysis in regional science and ample theoretical and applied challenges are offered. Location-allocation models seek the location of facilities and/or services (e.g., schools, hospitals, and warehouses) so as to optimize one or several objectives generally related to the efficiency of the system or to the allocation of resources. This paper concerns the location of facilities or services in discrete space or networks, that are related to the public sector, such as emergency services (ambulances, fire stations, and police units), school systems and postal facilities. The paper is structured as follows: first, we will focus on public facility location models that use some type of coverage criterion, with special emphasis in emergency services. The second section will examine models based on the P-Median problem and some of the issues faced by planners when implementing this formulation in real world locational decisions. Finally, the last section will examine new trends in public sector facility location modeling.Location analysis, public facilities, covering models

p-Median problems in a fuzzy environment

In this paper a formulation for the fuzzy p-median model in a fuzzy environment is presented. The model allows to find optimal locations of p facilities and their related cost when data related to the node demands and the edge distances are imprecise and uncertain and also to know the degree of certainty of the solution. For the sake of illustration, the proposed model is applied in a reduced map of Kinshasa (Democratic Republic of Congo) obtaining results which are rather than realistic one

Master of Science

thesisThe algebraic multigrid (AMG) method is often used as a preconditioner in Krylov subspace solvers such as the conjugate gradient method. An AMG preconditioner hierarchically aggregates the degrees of freedom during the coarsening phase in order to eciently account for lower-frequency errors. Each degree of freedom in the coarser level corresponds to one of the aggregates in the ner level. The aggregation in each level in the hierarchy has a signicant impact on the eectiveness of AMG as a preconditioner. The aggregation can be formulated as a partitioning problem on the graph induced from the matrix representation of a linear system. The contributions of this work are as follows: rst, a GPU implementation of a \bottom-up" partitioning scheme based on maximal independent sets (MIS), including an ecient conditioning scheme for enforcing partition size constraints; second, three novel topological metrics, convexity, eccentricity, and minimum enclosing ball, for measuring partition quality; third, empirical test results comparing our MIS-Based aggregation methods with the MeTis graph partioning library, showing that the metrics correlate more strongly with AMG performance than the commonly used edge-cut metric, and that for ner aggregations, MIS-based aggregation is better suited for AMG coarsening than is the \top down" MeTis graph partitioning library, but that for coarser aggregations, MeTis performs better

An investigation of multilevel refinement in routing and location problems

Multilevel refinement is a collaborative hierarchical solution technique. The multilevel technique aims to enhance the solution process of optimisation problems by improving the asymptotic convergence in the quality of solutions produced by its underlying local search heuristics and/or improving the convergence rate of these heuristics. To these aims, the central methodologies of the multilevel technique are filtering solutions from the search space (via coarsening), reducing the amount of problem detail considered at each level of the solution process and providing a mechanism to the underlying local search heuristics for efficiently making large moves around the search space. The neighbourhoods accessible by these moves are typically inaccessible if the local search heuristics are applied to the un-coarsened problems. The methodologies combine to meet the multilevel technique's aims, because, as the multilevel technique iteratively coarsens, extends and refines a given problem, it reduces the possibility of the local search heuristic becoming trapped in local optima of poor quality. The research presented in this thesis investigates the application of multilevel refinement to classes of location and routing problems and develops numerous multilevel algorithms. Some of these algorithms are collaborative techniques for metaheuristics and others are collaborative techniques for local search heuristics. Additionally, new methods of coarsening for location and routing problems and enhancements for the multilevel technique are developed. It is demonstrated that the multilevel technique is suited to a wide array of problems. By extending the investigations of the multilevel technique across routing and location problems, the research was able to present generalisations regarding the multilevel technique's suitability, for these and similar types of problems. Finally, results on a number of well known benchmarking suites for location and routing problem are presented, comparing equivalent single-level and multilevel algorithms. These results demonstrate that the multilevel technique provides significant gains over its single-level counterparts. In all cases, the multilevel algorithm was able to improve the asymptotic convergence in the quality of solutions produced by the standard (single-level) local search heuristics or metaheuristics. The multilevel technique did not improve the convergence rate of the single-level's local search heuristics in all cases. However, for large-scale problems the multilevel variants scaled in a manner superior to the single-level techniques. The research also demonstrated that for sufficiently large problems, the multilevel technique was able to improve the asymptotic convergence in the quality of solutions at a sufficiently fast rate, such that the multilevel algorithms were able to produce superior results compared to the single-level versions, without refining the solution down to the most detailed level

An investigation into machine learning approaches for forecasting spatio-temporal demand in ride-hailing service

In this paper, we present machine learning approaches for characterizing and forecasting the short-term demand for on-demand ride-hailing services. We propose the spatio-temporal estimation of the demand that is a function of variable effects related to traffic, pricing and weather conditions. With respect to the methodology, a single decision tree, bootstrap-aggregated (bagged) decision trees, random forest, boosted decision trees, and artificial neural network for regression have been adapted and systematically compared using various statistics, e.g. R-square, Root Mean Square Error (RMSE), and slope. To better assess the quality of the models, they have been tested on a real case study using the data of DiDi Chuxing, the main on-demand ride hailing service provider in China. In the current study, 199,584 time-slots describing the spatio-temporal ride-hailing demand has been extracted with an aggregated-time interval of 10 mins. All the methods are trained and validated on the basis of two independent samples from this dataset. The results revealed that boosted decision trees provide the best prediction accuracy (RMSE=16.41), while avoiding the risk of over-fitting, followed by artificial neural network (20.09), random forest (23.50), bagged decision trees (24.29) and single decision tree (33.55).Comment: Currently under review for journal publicatio

Optimizing the two-step floating catchment area method for measuring spatial accessibility to medical clinics in Montreal

<p>Abstract</p> <p>Background</p> <p>Reducing spatial access disparities to healthcare services is a growing priority for healthcare planners especially among developed countries with aging populations. There is thus a pressing need to determine which populations do not enjoy access to healthcare, yet efforts to quantify such disparities in spatial accessibility have been hampered by a lack of satisfactory measurements and methods. This study compares an optimised and the conventional version of the two-step floating catchment area (2SFCA) method to assess spatial accessibility to medical clinics in Montreal.</p> <p>Methods</p> <p>We first computed catchments around existing medical clinics of Montreal Island based on the shortest network distance. Population nested in dissemination areas were used to determine potential users of a given medical clinic. To optimize the method, medical clinics (supply) were weighted by the number of physicians working in each clinic, while the previous year's medical clinic users were computed by ten years age group was used as weighting coefficient for potential users of each medical clinic (demand).</p> <p>Results</p> <p>The spatial accessibility score (SA) increased considerably with the optimisation method. Within a distance of 1 Km, for instance, the maximum clinic accessible for 1,000 persons is 2.4 when the conventional method is used, compared with 27.7 for the optimized method. The t-test indicates a significant difference between the conventional and the optimized 2SFCA methods. Also, results of the differences between the two methods reveal a clustering of residuals when distance increases. In other words, a low threshold would be associated with a lack of precision.</p> <p>Conclusion</p> <p>Results of this study suggest that a greater effort must be made ameliorate spatial accessibility to medical clinics in Montreal. To ensure that health resources are allocated in the interest of the population, health planners and the government should consider a strategy in the sitting of future clinics which would provide spatial access to the greatest number of people.</p