Facility location: concepts, models, algorithms and case studies. Series: Contributions to Management Science

Wolf, Gert W.

doi:10.1080/13658816.2010.528422

Cited by 42 publications

(34 citation statements)

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“…We now give another example: the sum of norms optimization problems, which are generally nonconvex. Such problems have applications, for example, in facility location, where locations of new facilities should be decided by analyzing the distance between the new and the existing facilities [24]. Moreover, the problem of the following example can be applied not only to the minimization of the distance but also maximization of it by taking the constant λ i as −λ i .…”

Section: Examples Of Positively Homogeneous Optimization Problemsmentioning

confidence: 99%

Duality of nonconvex optimization with positively homogeneous functions

Yamanaka

Yamashita

2018

Comput Optim Appl

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We consider an optimization problem with positively homogeneous functions in its objective and constraint functions. Examples of such positively homogeneous functions include the absolute value function and the p-norm function, where p is a positive real number. The problem, which is not necessarily convex, extends the absolute value optimization proposed in [O. L. Mangasarian, Absolute value programming, Computational Optimization and Applications 36 (2007) pp. [43][44][45][46][47][48][49][50][51][52][53]. In this work, we propose a dual formulation that, differently from the Lagrangian dual approach, has a closed-form and some interesting properties. In particular, we discuss the relation between the Lagrangian duality and the one proposed here, and give some sufficient conditions under which these dual problems coincide. Finally, we show that some well-known problems, e.g., sum of norms optimization and the group Lasso-type optimization problems, can be reformulated as positively homogeneous optimization problems.Recently, the so-called absolute value equations (AVE) and absolute value optimization (AVO) problems have been attracted much attention. The AVE were introduced in 2004 by Rohn [21]. Basically, ifÃ,B are given matrices, andb is a given vector, one should find a vector x that satisfiesÃx +B|x| =b, where |x| is a vector whose i-th entry is the absolute value of the i-th entry of x. It is known that AVE are equivalent to the linear complementarity problems (LCP) [9,16,20], which include many real-world applications. As an extension of AVE, Mangasarian [14] proposed in 2007 the AVO problems, which have the absolute value of variables in their objective and constraint functions. More precisely, the AVO problem considered is given by+K|x| ≥p, whereÃ,B,H,K are given matrices, andc,d,b,p are vectors with appropriate dimensions. Since AVE and LCP are equivalent, the AVO include the mathematical programs with linear complementarity constraints [12], which are one of the formulations of equilibrium problems. As another application of AVO, Yamanaka and Fukushima [26] presented facility location problems. Since 2007, some methods for solving AVE have been presented in the literature. For example, Rohn [22] considered an iterative algorithm using the sign of variables for the case thatÃ andB are square matrices. For more generalÃ andB, Mangasarian [14] provided a method involving successive linearization techniques. Another methods include a concave minimization approach, given by Mangasarian [13], and Newton-type methods, proposed by Caccetta et al. [3], Mangasarian [15], and Zhang and Wei [28]. Some generalizations of AVE were also proposed. For example, Hu et al. [10] considered an AVE involving the absolute value of variables associated to the second-order cones. Miao et al. [18]investigated an AVE with the so-called circular cones. In both papers, quasi-Newton based algorithms were used.As for AVO problems, Yamanaka and Fukushima [26] proposed to use a branch-andbound technique. In the branching procedure, ...

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Section: Examples Of Positively Homogeneous Optimization Problemsmentioning

confidence: 99%

Duality of nonconvex optimization with positively homogeneous functions

Yamanaka

Yamashita

2018

Comput Optim Appl

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“…In a NP-complete problem, there are no known general efficient algorithms that output an exact solution(s) other than an (almost) exhaustive search. Therefore, when faced with the NP-complete problems, a typical approach is to find an approximation rather than seeking an exact solution by using heuristics that can be applied to a particular problem [23] [24]. Depending on the chosen heuristics, the solutions could be a local optimum.…”

Section: Uwb Indoor Positioning Network Optimization Algorithmmentioning

confidence: 99%

Planning of UWB indoor positioning network using binary integer linear programming

Kim

Choi

2016

IJUWBCS

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The Ultra Wide Band (UWB) is a promising indoor positioning sensor. Its precise range measurement and wall penetration capability are well suited for indoor navigation. UWB anchor locations must also be carefully determined to achieve the optimal performance of a UWB positioning. However, previous approaches on the UWB anchor placement resulted in poor positioning accuracy around corners of an indoor environment and ignored UWB wall penetration effects. To overcome those shortcomings, this paper introduces an advanced method of an UWB anchor network design that provides high positioning accuracy in all user space and minimizes uncertainty due to UWB signal wall penetrations with a binary integer linear programming. It is expected that the presented method would provide a reliable positioning performance that is needed for the navigation of autonomous systems.

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“…In 2011, Goswami et al [9] studied the methods for optimizing offsite passenger service facilities. The optimization of CAT locations is similar to a multiple facility location problem (MFLP) [10] and the best routes between passengers and CATs should be found, which corresponds to a many-tomany path optimization problem [11]. For solving a largescale problem, heuristic or meta-heuristics algorithms should be adopted.…”

Section: Introductionmentioning

confidence: 99%

An Efficient Genetic Method for Multi-Objective Location Optimization of Multiple City Air Terminals

Zhou

et al. 2021

IEEE Access

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Multi-objective location optimization methods play an important role in intelligent planning the locations of city air terminals. The objectives are to improve passenger experience and enhance the competitiveness of air transportation. A mathematical model for the problem is introduced at first. The model takes three factors into accounted as the optimization objectives, including the average path length from passengers to city air terminals, the maximum tolerable distance of passengers, and the service capacity limit of a station. Secondly, an efficient hybrid evolutionary method is presented for efficiently optimizing the locations of city air terminals, which includes an improved ripple-spreading algorithm for solving the many-to-many path optimization problem and a genetic algorithm for optimizing the facility location problem. A case study based on a large city in China is performed to test the proposed method for configuring city air terminals in city urban area and to show its effectiveness and efficiency.INDEX TERMS Multi-objective optimization, hybrid evolutionary method, ripple spreading algorithm, adaptive genetic algorithm, city air terminal, optimization method.Recently, researchers have shown an increased interest in

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Facility location: concepts, models, algorithms and case studies. Series: Contributions to Management Science

Cited by 42 publications

References 0 publications

Duality of nonconvex optimization with positively homogeneous functions

Duality of nonconvex optimization with positively homogeneous functions

Planning of UWB indoor positioning network using binary integer linear programming

An Efficient Genetic Method for Multi-Objective Location Optimization of Multiple City Air Terminals

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