Continuous multifacility ordered median location problems

In this paper we propose a general methodology for solving a broad class of continuous, multifacility location problems, in any dimension and with ℓτ -norms proposing two different methodologies: 1) by a new second order cone mixed integer programming formulation and 2) by formulating a sequence of semidefinite programs that converges to the solution of the problem; each of these relaxed problems solvable with SDP solvers in polynomial time. We apply dimensionality reductions of the problems by sparsity and symmetry in order to be able to solve larger problems. Continuous multifacility location and Ordered median problems and Semidefinite programming and Moment problem.Junta de AndalucíaFondo Europeo de Desarrollo RegionalMinisterio de Ciencia e Innovació

An interior-point method for the single-facility location problem with mixed norms using a conic formulation

We consider the single-facility location problem with mixed norms, i.e. the problem of minimizing the sum of the distances from a point to a set of fixed points in R, where each distance can be measured according to a different p-norm.We show how this problem can be expressed into a structured conic format by decomposing the nonlinear components of the objective into a series of constraints involving three-dimensional cones. Using the availability of a self-concordant barrier for these cones, we present a polynomial-time algorithm (a long-step path-following interior-point scheme) to solve the problem up to a given accuracy. Finally, we report computational results for this algorithm and compare with standard nonlinear optimization solvers applied to this problem.nonsymmetric conic optimization, conic reformulation, convex optimization, sum of norm minimization, single-facility location problems, interior-point methods

Sensitivity analysis of distance constraints and of multifacility minimax location on tree networks

Ankara : The Department of Industrial Engineering and the Institute of Engineering and Sciences of Bilkent Univ. ,1989.Thesis (Master's) -- Bilkent University, 1989.Includes bibliographical references leaves 77-79.In this thesis, the main concern is to investigate the use of consistency conditions of distance constraints in sensitivity analysis of certain network location problems. The interest is in minimax type of objective functions. A single parametric approach is adopted in the sensitivity analysis for the m-facility minimax location problem on tree networks. Apart from the traditional sensitivity analysis approach, a conceptual framework for imprecision in distance constraints is developed.Doğan, EsraM.S

Polynomially solvable cases of multifacility distance constraints on cyclic networks

Ankara : The Department of Industrial Engineering and the Institute of Engineering and Sciences of Bilkent Univ., 1993.Thesis (Master's) -- Bilkent University, 1993.Includes bibliographical references leaves 79-81Distance Constraints Problem is to locate one or more new facilities on a network so that the distances between new and existing facilities as well as between pairs of new facilities do not exceed given upper bounds. The problem is AfV-Complete on cyclic networks and polynomially solvable on trees. Although theory for tree networks is well-developed, there is virtually no theory for cyclic networks. In this thesis, we identify a special class of instances for which we develop theory and algorithms that are applicable to any metric space defining the location space. We require that the interaction between new facilities has a tree structure. The method is based on successive applications of EXPANSION and INTERSECTION operations defined on subsets of the location space. Application of this method to general networks yields strongly polynomial algorithms. Finally, we give an algorithm that constructs an e-optimal solution to a related minimax problem.Yeşilkökçen, Naile GülcanM.S

Applications of network optimization

Includes bibliographical references (p. 41-48).Ravindra K. Ahuja ... [et al.]

Discrete Convex Functions on Graphs and Their Algorithmic Applications

The present article is an exposition of a theory of discrete convex functions on certain graph structures, developed by the author in recent years. This theory is a spin-off of discrete convex analysis by Murota, and is motivated by combinatorial dualities in multiflow problems and the complexity classification of facility location problems on graphs. We outline the theory and algorithmic applications in combinatorial optimization problems