Global optimization algorithm for capacitated multi-facility continuous location-allocation problems

Lara, Cristiana L.; Trespalacios, Francisco; Grossmann, Ignacio E.

doi:10.1007/s10898-018-0621-6

Cited by 20 publications

(13 citation statements)

References 18 publications

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“…To solve the above problem, many approaches have been developed previously [21,22], e.g., by Zhang [23]. The earliest approach is an iterative procedure that was offered by Weiszfeld [24], which was followed by some other variants [25][26][27].…”

Section: Literature Reviewmentioning

confidence: 99%

Globally Optimal Facility Locations for Continuous-Space Facility Location Problems

et al. 2021

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The continuous-space single- and multi-facility location problem has attracted much attention in previous studies. This study focuses on determining the globally optimal facility locations for two- and higher-dimensional continuous-space facility location problems when the Manhattan distance is considered. Before we propose the exact method, we start with the continuous-space single-facility location problem and obtain the global minimizer for the problem using a statistical approach. Then, an exact method is developed to determine the globally optimal solution for the two- and higher-dimensional continuous-space facility location problem, which is different from the previous clustering algorithms. Based on the newly investigated properties of the minimizer, we extend it to multi-facility problems and transfer the continuous-space facility location problem to the discrete-space location problem. To illustrate the effectiveness and efficiency of the proposed method, several instances from a benchmark are provided to compare the performances of different methods, which illustrates the superiority of the proposed exact method in the decision-making of the continuous-space facility location problems.

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Section: Literature Reviewmentioning

confidence: 99%

Globally Optimal Facility Locations for Continuous-Space Facility Location Problems

et al. 2021

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“…Integer and outerapproximation cuts (or tailored cuts that can be interpreted as such) are added to the master MILP at each iteration. The convergence behavior of bilevel decomposition strongly depends on the quality of the MILP relaxation and is therefore very application-specific [30,31,32]. Generalized Benders decomposition has been extended to solve two-stage stochastic nonconvex separable MINLPs in which only the continuous variables are involved in the nonconvex terms [33].…”

Section: Literature Reviewmentioning

confidence: 99%

Branch-and-Price for a Class of Nonconvex Mixed-Integer Nonlinear Programs

Allman

Zhang

2020

Preprint

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This work attempts to combine the strengths of two major technologies that have matured over the last three decades: global mixed-integer nonlinear optimization and branch-and-price. We consider a class of generally nonconvex mixed-integer nonlinear programs (MINLPs) with linear complicating constraints and integer linking variables. If the complicating constraints are removed, the problem becomes easy to solve, e.g. due to decomposable structure. Integrality of the linking variables allows us to apply a discretization approach to derive a Dantzig-Wolfe reformulation and solve the problem to global optimality using branch-and-price. It is a remarkably simple idea; but to our surprise, it has barely found any application in the literature. In this work, we show that many relevant problems directly fall or can be reformulated into this class of MINLPs. We present the branch-and-price algorithm and demonstrate its effectiveness (and sometimes ineffectiveness) in an extensive computational study considering multiple large-scale problems of practical relevance, showing that, in many cases, orders-of-magnitude reductions in solution time can be achieved.

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“…BLD algorithm is proposed by Lara, Trespalacios, and Grossmann (2018) to solve the Capacitated Multi-facility Weber Problem (CMWP). The problem is to determine locations in continuous 2-dimensional space for opening new facilities that are connected to supply and customer nodes.…”

Section: Bi-level Decomposition Algorithmmentioning

confidence: 99%

“…Table 1 shows the process. According to the proof (Lara et al, 2018), a lower bound to the MINLP problem is yielded by the MILP model and an upper bound will be yielded by the NLP model. As the number of blocks divided in the area increases, the upper and lower bound will get closer.…”

Section: Bi-level Decomposition Algorithmmentioning

confidence: 99%

Global optimization for multi-stage construction of rescue units in disaster response

Zhang

et al. 2019

Sustainable Cities and Society

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Disasters pose a serious threat to people' lives and urban environment, affecting the sustainable development of society. Then it's crucial to quickly develop an efficient rescue plan for the disaster area. However, disaster rescue is rather difficult due to the requirement to develop the optimal rescue plan as quickly as possible according to the information of trapped people and rescue teams, and the amount of information will continue to increase as the rescue proceeds. At present, most of the rescue plans are manually made based on previous rescue experience. But obviously these plans might be the not optimal one. Considering the real-time location data of trapped people, this paper develops a Mixed Integer Non-linear Programming (MINLP) model to find the highest efficient rescue plan To solve the model accurately and efficiently, a bi-level decomposition (BLD) algorithm is presented to iteratively solve a discretized Mixed Integer Linear Programming (MILP) model and its nonconvex Non-linear Programming (NLP) model until a converged solution is obtained. In addition, since more trapped people could be found over time, the built rescue units should also be considered when making a rescue plan for a new stage. To further improve the solving efficiency, an accelerated bi-level decomposition (ABLD) algorithm is also proposed. Finally, a real-world disaster rescue is given to validate the superiority of the proposed ABLD algorithm relative to particle swarm optimization (PSO) algorithm and BLD algorithm. setting, project design, project selection, organization implementation, and feedback modification (Lei, Wu, Xu, & Fujita, 2017). The process can be simplified into three stages according to the promotion of rescue

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Global optimization algorithm for capacitated multi-facility continuous location-allocation problems

Cited by 20 publications

References 18 publications

Globally Optimal Facility Locations for Continuous-Space Facility Location Problems

Globally Optimal Facility Locations for Continuous-Space Facility Location Problems

Branch-and-Price for a Class of Nonconvex Mixed-Integer Nonlinear Programs

Global optimization for multi-stage construction of rescue units in disaster response

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