Feedback algorithm for switch location : analysis of complexity and application to network design

An accelerated feedback algorithm to solve the single-facility minisum problem is studied with application to designing networks with the star topology. The algorithm, in which the acceleration with respect to the Weiszfeld procedure is achieved by multiplying the current Weiszfeld iterate by an accelerating feedback factor, is shown to converge faster than the accelerating procedures available in the literature. Singularities encountered in the algorithm are discussed in detail. A simple practical exception handling subroutine is developed. Several applications of the algorithm to designing computer networks with the star topology are demonstrated. Applications of the algorithm as a subroutine for multi-switch location problems are considered. Various engineering aspects involved in acquiring and processing coordinates for geographic locations are discussed. A complete algorithm in pseudocode along with the source code listing in Mathematica 4.1 is presented

Revisiting several problems and algorithms in continuous location with lp norms

This paper addresses the general continuous single facility location problems in finite dimension spaces under possibly different ℓp norms in the demand points. We analyze the difficulty of this family of problems and revisit convergence properties of some well-known algorithms. The ultimate goal is to provide a common approach to solve the family of continuous ℓp ordered median location problems in dimension d (including of course the ℓp minisum or Fermat-Weber location problem for any p ≥ 1). We prove that this approach has a polynomial worse case complexity for monotone lambda weights and can be also applied to constrained and even non-convex problems.Junta de AndalucíaFondo Europeo de Desarrollo RegionalMinisterio de Ciencia e Innovació

The optimal location of facilities on a network

Imperial Users onl

Improvements and comparison of heuristics for solving the uncapacitated multisource Weber problem

Copyright @ 2000 INFORMSThe multisource Weber problem is to locate simultaneously m facilities in the Euclidean plane to minimize the total transportation cost for satisfying the demand of n fixed users, each supplied from its closest facility. Many heuristics have been proposed for this problem, as well as a few exact algorithms. Heuristics are needed to solve quickly large problems and to provide good initial solutions for exact algorithms. We compare various heuristics, i.e., alternative location-allocation (Cooper 1964), projection (Bongartz et al. 1994), Tabu search (Brimberg and Mladenovic 1996a), p-Median plus Weber (Hansen ct al. 1996), Genetic search and several versions of Variable Neighbourhood search. Based on empirical tests that are reported, it is found that most traditional and some recent heuristics give poor results when the number of facilities to locate is large and that Variable Neighbourhood search gives consistently best results, on average, in moderate computing time.This study was supported by the Department of National Defence (Canada) Academic Research; Office of Naval Research Grant N00014-92-J-1194, Natural Sciences and Engineering Research Council of Canada Grant GPO 105574 and Fonds pour la Formation des Chercheurs et l’Aide a la Recherche Grant 32EQ 1048; and by an International Postdoctoral Fellowship of the Natural Sciences and Engineering Research Council of Canada, Grant OGPOO 39682

A MODELING FRAMEWORK ON DISTANCE PREDICTING FUNCTIONS FOR LOCATION MODELS IN CONTINUOUS SPACE

Continuous location models are the oldest models in locations analysis dealing with the geometrical representations of reality, and they are based on the continuity of location area. The classical model in this area is the Weber problem. Distances in the Weber problem are often taken to be Euclidean distances, but almost all kinds of the distance functions can be employed. In this survey, we examine an important class of distance predicting functions (DPFs) in location problems all of practical relevance. This paper provides a review on recent efforts and development in modeling travel distances based on the coordinates they use and their applicability in certain practical settings. Very little has been done to include special cases of the class of metrics and its classification in location models and such merit further attention. The new metrics are discussed in the well-known Weber problem, its multi-facility case and distance approximation problems. We also analyze a variety of papers related to the literature in order to demonstrate the effectiveness of the taxonomy and to get insights for possible research directions. Research issues which we believe to be worthwhile exploring in the future are also highlighted

Stochastic Multifacility Location Problem under Triangular Area Constraint with Euclidean Norm

The multifacility location issue is an augmentation of the single-location problem in which we might be keen on finding the location of various new facilities concerning different existing locations. In the present study, multifacility location under triangular zone limitation with probabilistic methodology for the weights considered in the objective function and the Euclidean distances between the locations has been presented. Scientific detailing and the explanatory arrangement have been acquired by utilizing Kuhn-Tucker conditions. The arrangement strategy has been represented with the assistance of a numerical illustration. Two sub-instances of the issue in each of which the new locations are to be situated in semi-open rectangular zone have likewise been talked about

Solution Methods for the \u3cem\u3ep\u3c/em\u3e-Median Problem: An Annotated Bibliography

The p-median problem is a graph theory problem that was originally designed for, and has been extensively applied to, facility location. In this bibliography, we summarize the literature on solution methods for the uncapacitated and capacitated p-median problem on a graph or network

Generalized Weiszfeld algorithms for Lq optimization

In many computer vision applications, a desired model of some type is computed by minimizing a cost function based on several measurements. Typically, one may compute the model that minimizes the L₂ cost, that is the sum of squares of measurement errors with respect to the model. However, the Lq solution which minimizes the sum of the qth power of errors usually gives more robust results in the presence of outliers for some values of q, for example, q = 1. The Weiszfeld algorithm is a classic algorithm for finding the geometric L1 mean of a set of points in Euclidean space. It is provably optimal and requires neither differentiation, nor line search. The Weiszfeld algorithm has also been generalized to find the L1 mean of a set of points on a Riemannian manifold of non-negative curvature. This paper shows that the Weiszfeld approach may be extended to a wide variety of problems to find an Lq mean for 1 ≤ q <; 2, while maintaining simplicity and provable convergence. We apply this problem to both single-rotation averaging (under which the algorithm provably finds the global Lq optimum) and multiple rotation averaging (for which no such proof exists). Experimental results of Lq optimization for rotations show the improved reliability and robustness compared to L₂ optimization.This research has been funded by National ICT Australia

Qualitative Characteristics and Quantitative Measures of Solution's Reliability in Discrete Optimization: Traditional Analytical Approaches, Innovative Computational Methods and Applicability

The purpose of this thesis is twofold. The first and major part is devoted to sensitivity analysis of various discrete optimization problems while the second part addresses methods applied for calculating measures of solution stability and solving multicriteria discrete optimization problems. Despite numerous approaches to stability analysis of discrete optimization problems two major directions can be single out: quantitative and qualitative. Qualitative sensitivity analysis is conducted for multicriteria discrete optimization problems with minisum, minimax and minimin partial criteria. The main results obtained here are necessary and sufficient conditions for different stability types of optimal solutions (or a set of optimal solutions) of the considered problems. Within the framework of quantitative direction various measures of solution stability are investigated. A formula for a quantitative characteristic called stability radius is obtained for the generalized equilibrium situation invariant to changes of game parameters in the case of the H¨older metric. Quality of the problem solution can also be described in terms of robustness analysis. In this work the concepts of accuracy and robustness tolerances are presented for a strategic game with a finite number of players where initial coefficients (costs) of linear payoff functions are subject to perturbations. Investigation of stability radius also aims to devise methods for its calculation. A new metaheuristic approach is derived for calculation of stability radius of an optimal solution to the shortest path problem. The main advantage of the developed method is that it can be potentially applicable for calculating stability radii of NP-hard problems. The last chapter of the thesis focuses on deriving innovative methods based on interactive optimization approach for solving multicriteria combinatorial optimization problems. The key idea of the proposed approach is to utilize a parameterized achievement scalarizing function for solution calculation and to direct interactive procedure by changing weighting coefficients of this function. In order to illustrate the introduced ideas a decision making process is simulated for three objective median location problem. The concepts, models, and ideas collected and analyzed in this thesis create a good and relevant grounds for developing more complicated and integrated models of postoptimal analysis and solving the most computationally challenging problems related to it.Siirretty Doriast