A Barzilai-Borwein-based heuristic algorithm for locating multiple facilities with regional demand

Jiang, Jianlin; Yuan, Xiaoming

doi:10.1007/s10589-010-9392-9

Cited by 11 publications

(8 citation statements)

References 40 publications

(45 reference statements)

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“…One strategy has focused on modeling such demand as one or multiple continuous regions, and search for the optimal facility sites is complex often involving integration overall an two‐dimensional (2D) region. To simplify the problem, certain assumptions are usually made, such as a uniform demand distribution (Love ) and rectangle or circle shaped regions (Love ; Aly and Marucheck ; Jiang and Yuan ). For irregularly shaped regions, heuristic approaches are then relied upon.…”

Section: Introductionmentioning

confidence: 99%

Regional Coverage Maximization: Alternative Geographical Space Abstraction and Modeling

Tong

Wei

2016

Geographical Analysis

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Analysis results are often found to vary with the way we abstract geographical space. When continuous geographic phenomena are abstracted, processed, and stored in a digital environment, some level of discretization is often employed. Information loss in a discretization process brings about uncertainty/error, and as a result research findings may be highly dependent on the particular discretization method used. This article examines one spatial problem concerning how to achieve the maximal regional coverage given a limited number of service facilities. Two widely used geographical space abstraction approaches are examined, the point‐based representation and the area‐based representation, and issues associated with each representation scheme are analyzed. To accommodate the limitations of the existing representation schemes, a mixed representation strategy is proposed along with a new maximal covering model. Experiments are conducted to site warning sirens in Dublin, Ohio. Results demonstrate the effectiveness of the mixed representation scheme in finding high‐quality solutions when the regional coverage level is medium or high.

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Section: Introductionmentioning

confidence: 99%

Regional Coverage Maximization: Alternative Geographical Space Abstraction and Modeling

Tong

Wei

2016

Geographical Analysis

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“…When demand regions are in consideration, usually there are three ways of measuring the distance between the region and the facility [25]:…”

Section: Introductionmentioning

confidence: 99%

Heuristics for a continuous multi-facility location problem with demand regions

Dinler

Tural

İyigün

2015

Computers & Operations Research

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We consider a continuous multi-facility location problem where the demanding entities are regions in the plane instead of points. Each region may consist of a finite or an infinite number of points. The service point of a station can be anywhere in the region that is assigned to it. We do not allow fractional assignments, that is, each region is assigned to exactly one facility. The problem we consider can be stated as follows: given m demand regions in the plane, find the locations of q facilities and allocate regions to the facilities so as to minimize the sum of squares of the maximum Euclidean distances of the demand regions to the facility locations they are assigned to. We assume that the regions are closed polygons as any region can be approximated within any desired accuracy with a polygon.We first propose mathematical programming formulations of single and multiple facility location problems. The single facility location problem is formulated as a second order cone program (SOCP) which can be solved in polynomial time. The multiple facility location problem is formulated as a mixed integer SOCP. This formulation is weak and does not even solve medium-size problems. We therefore propose heuristics to solve larger instances of the problem. We develop three heuristics that work when the regions are polygons. When the demand regions are rectangles with sides parallel to coordinate axes, a special heuristic is developed. We compare our heuristics in terms of both solution quality and computational time.

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“…We take an interesting facility location problem, which is an extension of Weber problem in [8,14], to show that the study of inverse programming over second-order cones is significant in practice. Motivation.…”

Section: Introductionmentioning

confidence: 99%

A perturbation approach for an inverse quadratic programming problem over second-order cones

Zhang

et al. 2014

Math. Comp.

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This paper is devoted to studying a type of inverse second-order cone quadratic programming problems, in which the parameters in both the objective function and the constraint set of a given second-order cone quadratic programming problem need to be adjusted as little as possible so that a known feasible solution becomes optimal. This inverse problem can be written as a minimization problem with second-order cone complementarity constraints and a positive semidefinite cone constraint. Applying the duality theory, we reformulate this problem as a linear second-order cone complementarity constrained optimization problem with a semismoothly differentiable objective function, which has fewer variables than the original one. A perturbed problem is proposed with the help of the projection operator over second-order cones, whose feasible set and optimal solution set are demonstrated to be continuous and outer semicontinuous, respectively, as the parameter decreases to zero. A smoothing Newton method is constructed to solve the perturbed problem and its global convergence and local quadratic convergence rate are shown. Finally, the numerical results are reported to show the effectiveness for the smoothing Newton method to solve the inverse second-order cone quadratic programming problem.

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A Barzilai-Borwein-based heuristic algorithm for locating multiple facilities with regional demand

Cited by 11 publications

References 40 publications

Regional Coverage Maximization: Alternative Geographical Space Abstraction and Modeling

Regional Coverage Maximization: Alternative Geographical Space Abstraction and Modeling

Heuristics for a continuous multi-facility location problem with demand regions

A perturbation approach for an inverse quadratic programming problem over second-order cones

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