scholarly journals Stabilized Benders Methods for Large-Scale Combinatorial Optimization, with Application to Data Privacy

2020 ◽  
Vol 66 (7) ◽  
pp. 3051-3068 ◽  
Author(s):  
Daniel Baena ◽  
Jordi Castro ◽  
Antonio Frangioni
Keyword(s):  
Data Privacy ◽  
Large Scale ◽  
Benders Decomposition ◽  
Mixed Integer ◽  
Master Problem ◽  
Continuous Variables ◽  
Typical Structure ◽  
Disclosure Control ◽  
Current State ◽  
Statistical Disclosure

The cell-suppression problem (CSP) is a very large mixed-integer linear problem arising in statistical disclosure control. However, CSP has the typical structure that allows application of the Benders decomposition, which is known to suffer from oscillation and slow convergence, compounded with the fact that the master problem is combinatorial. To overcome this drawback, we present a stabilized Benders decomposition whose master is restricted to a neighborhood of successful candidates by local-branching constraints, which are dynamically adjusted, and even dropped, during the iterations. Our experiments with synthetic and real-world instances with up to 24,000 binary variables, 181 million (M) continuous variables, and 367M constraints show that our approach is competitive with both the current state-of-the-art code for CSP and the Benders implementation in CPLEX 12.7. In some instances, stabilized Benders provided a very good solution in less than 1 minute, whereas the other approaches found no feasible solution in 1 hour. This paper was accepted by Yinyu Ye, optimization.

scholarly journals A Redesigned Benders Decomposition Approach for Large-Scale In-Transit Freight Consolidation Operations

2018 ◽  
Vol 11 (2) ◽  
pp. 1-15 ◽  
Author(s):  
Abdulkader S. Hanbazazah ◽  
Luis E. Abril ◽  
Nazrul I. Shaikh ◽  
Murat Erkoc
Keyword(s):  
Large Scale ◽  
Benders Decomposition ◽  
Scale Up ◽  
Third Party ◽  
Mixed Integer ◽  
Continuous Variables ◽  
Due Dates ◽  
Decomposition Approach ◽  
Freight Consolidation ◽  
In Transit

The growth in online shopping and third-party logistics has caused a revival of interest in finding optimal solutions to the large-scale, in-transit freight consolidation problem. Given the shipment date, size, origin, destination, and due dates of multiple shipments distributed over space and time, the problem requires determining when to consolidate some of these shipments into one shipment at an intermediate consolidation point so as to minimize shipping costs while satisfying the due date constraints. In this article, the authors develop a mixed-integer programming formulation for a multi-period freight consolidation problem that involves multiple products, suppliers, and potential consolidation points. Benders decomposition is then used to replace a large number of integer freight-consolidation variables by a small number of continuous variables that reduce the size of the problem without impacting optimality. The results show that Benders decomposition provides a significant scale-up in the performance of the solver. The authors demonstrate their approach using a large-scale case with more than 27.5 million variables and 9.2 million constraints.

scholarly journals Optimal Torpedo Scheduling

2018 ◽  
Vol 63 ◽  
pp. 955-986 ◽  
Author(s):  
Adrian Goldwaser ◽  
Andreas Schutt
Keyword(s):  
Large Scale ◽  
Benders Decomposition ◽  
Steel Production ◽  
Planning Horizon ◽  
Mixed Integer ◽  
Hot Metal ◽  
Rail Network ◽  
Sulfur Level ◽  
First Time ◽  
Resource Capacity

We consider the torpedo scheduling problem in steel production, which is concerned with the transport of hot metal from a blast furnace to an oxygen converter. A schedule must satisfy, amongst other considerations, resource capacity constraints along the path and the locations traversed as well as the sulfur level of the hot metal. The goal is first to minimize the number of torpedo cars used during the planning horizon and second to minimize the time spent desulfurizing the hot metal. We propose an exact solution method based on Logic based Benders Decomposition using Mixed-Integer and Constraint Programming, which optimally solves and proves, for the first time, the optimality of all instances from the ACP Challenge 2016 within 10 minutes. In addition, we adapted our method to handle large-scale instances and instances with a more general rail network. This adaptation optimally solved all challenge instances within one minute and was able to solve instances of up to 100,000 hot metal pickups.

The Optimal Controlled Partitioning Strategy for Power System Based on Master-Slave Problem

2013 ◽  
Vol 385-386 ◽  
pp. 999-1006
Author(s):  
Wei Wang ◽  
Ting Yu ◽  
Tian Jiao Pu ◽  
Ai Zhong Tian ◽  
Ji Keng Lin
Keyword(s):  
Large Scale ◽  
Optimization Method ◽  
Mixed Integer ◽  
Master Problem ◽  
Decomposition Algorithms ◽  
Integer Programming Problem ◽  
Complete Model ◽  
New Approach ◽  
Mixed Integer Programming Problem ◽  
Partitioning Strategy

Controlled partitioning strategy is one of the effective measures taken for the situation when system out-of-step occurs. The complete splitting model, mostly solved by approximate decomposition algorithms, is a large-scale nonlinear mixed integer programming problem. A new alternate optimization method based on master-slave problem to search for optimal splitting strategy is proposed hereby. The complete model was converted into master-slave problems based on CGKP (Connected Graph Constrained Knapsack Problem). The coupling between master problem and slave problem is achieved through load adjustment. A better splitting strategy can be obtained through the alternating iteration between the master problem and the salve problem. The results of the examples show that the method can obtain better splitting strategy with less shed load than other approximate algorithms, which verifies the feasibility and effectiveness of the new approach presented.

scholarly journals Providing Data With High Utility And No Disclosure Risk For The Public and Researchers: An Evaluation By Advanced Statistical Disclosure Risk Methods

2014 ◽  
Vol 43 (4) ◽  
pp. 247-254
Author(s):  
Matthias Templ
Keyword(s):  
Data Privacy ◽  
Data Sets ◽  
Real World Data ◽  
Data Set ◽  
The Public ◽  
Disclosure Control ◽  
High Data ◽  
Disclosure Risk ◽  
Statistical Disclosure ◽  
High Utility

The demand of data from surveys, registers or other data sets containing sensibleinformation on people or enterprises have been increased significantly over the last years.However, before providing data to the public or to researchers, confidentiality has to berespected for any data set containing sensible individual information. Confidentiality canbe achieved by applying statistical disclosure control (SDC) methods to the data. Theresearch on SDC methods becomes more and more important in the last years because ofan increase of the awareness on data privacy and because of the fact that more and moredata are provided to the public or to researchers. However, for legal reasons this is onlyvisible when the released data has (very) low disclosure risk.In this contribution existing disclosure risk methods are review and summarized. Thesemethods are finally applied on a popular real-world data set - the Structural EarningsSurvey (SES) of Austria. It is shown that the application of few selected anonymisationmethods leads to well-protected anonymised data with high data utility and low informationloss.

scholarly journals Micro Grid Energy Management using DE Algorithm with BDC theorem

2019 ◽  
Vol 8 (4S2) ◽  
pp. 334-338
Keyword(s):  
Power Plants ◽  
Large Scale ◽  
Benders Decomposition ◽  
Reactive Power ◽  
Differential Evolution Algorithm ◽  
Decomposition Theorem ◽  
Drop Out ◽  
Mixed Integer ◽  
De Algorithm ◽  
Micro Grid

this paper evaluates combination of DE algorithm and benders decomposition theorem of VMG is used to solving the large scale mixed integer programming problems. DE algorithm is implemented in Village area Micro grids. Village area micro grid and the required load is calculated regarding the sold out power or purchase power with the help of DE algorithm. Differential evolution algorithm is applied in the village area micro grid and measure the real power, reactive power of various power plants. . In this DE algorithm is implemented in village area micro grid and the survey period is two years. Final survey shows which month produce more power and sold out power in nearest city area electricity board, But in power shortage in village area micro grid ,it purchase the power from nearest electricity board.DE algorithm determine the one month power survey and benders decomposition determine the individual value of the power plants. But the benders decomposition theorem is not accept the non linearity items. To overcome this problem BDCT and DEA is implemented in village area micro grid. This combination is used to maintain the drop out voltage of any power plants.

The Benders Dual Decomposition Method

2020 ◽  
Vol 68 (3) ◽  
pp. 878-895
Author(s):  
Ragheb Rahmaniani ◽  
Shabbir Ahmed ◽  
Teodor Gabriel Crainic ◽  
Michel Gendreau ◽  
Walter Rei
Keyword(s):  
Decomposition Method ◽  
High Performance ◽  
Large Scale ◽  
Benders Decomposition ◽  
Master Problem ◽  
Computational Results ◽  
Dual Decomposition ◽  
High Quality ◽  
Lagrangian Dual ◽  
Decomposition Strategies

Many methods that have been proposed to solve large-scale MILP problems rely on the use of decomposition strategies. These methods exploit either the primal or dual structures of the problems by applying the Benders decomposition or Lagrangian dual decomposition strategy, respectively. In “The Benders Dual Decomposition Method,” Rahmaniani, Ahmed, Crainic, Gendreau, and Rei propose a new and high-performance approach that combines the complementary advantages of both strategies. The authors show that this method (i) generates stronger feasibility and optimality cuts compared with the classical Benders method, (ii) can converge to the optimal integer solution at the root node of the Benders master problem, and (iii) is capable of generating high-quality incumbent solutions at the early iterations of the algorithm. The developed algorithm obtains encouraging computational results when used to solve various benchmark MILP problems.

scholarly journals Enhancing large neighbourhood search heuristics for Benders’ decomposition

2021 ◽  
Author(s):  
Stephen J. Maher
Keyword(s):  
Integer Programming ◽  
Mixed Integer Programming ◽  
Benders Decomposition ◽  
Trust Region ◽  
Mixed Integer ◽  
Master Problem ◽  
Search Heuristics ◽  
Neighbourhood Search ◽  
Large Neighbourhood ◽  
Large Neighbourhood Search

AbstractA general enhancement of the Benders’ decomposition (BD) algorithm can be achieved through the improved use of large neighbourhood search heuristics within mixed-integer programming solvers. While mixed-integer programming solvers are endowed with an array of large neighbourhood search heuristics, few, if any, have been designed for BD. Further, typically the use of large neighbourhood search heuristics is limited to finding solutions to the BD master problem. Given the lack of general frameworks for BD, only ad hoc approaches have been developed to enhance the ability of BD to find high quality primal feasible solutions through the use of large neighbourhood search heuristics. The general BD framework of SCIP has been extended with a trust region based heuristic and a general enhancement for large neighbourhood search heuristics. The general enhancement employs BD to solve the auxiliary problems of all large neighbourhood search heuristics to improve the quality of the identified solutions. The computational results demonstrate that the trust region heuristic and a general large neighbourhood search enhancement technique accelerate the improvement in the primal bound when applying BD.

A two-stage skilled manpower planning model with demand uncertainty

2018 ◽  
Vol 11 (4) ◽  
pp. 526-551 ◽  
Author(s):  
Mohsen Sadeghi-Dastaki ◽  
Abbas Afrazeh
Keyword(s):  
Large Scale ◽  
Demand Uncertainty ◽  
Benders Decomposition ◽  
Latin Hypercube Sampling ◽  
Sample Average Approximation ◽  
Manpower Planning ◽  
Mixed Integer ◽  
Planning Model ◽  
Two Stage ◽  
Content Type

Purpose Human resources are one of the most important and effective elements for companies. In other words, employees are a competitive advantage. This issue is more vital in the supply chains and production systems, because of high need for manpower in the different specification. Therefore, manpower planning is an important, essential and complex task. The purpose of this paper is to present a manpower planning model for production departments. The authors consider workforce with individual and hierarchical skills with skill substitution in the planning. Assuming workforce demand as a factor of uncertainty, a two-stage stochastic model is proposed. Design/methodology/approach To solve the proposed mixed-integer model in the real-world cases and large-scale problems, a Benders’ decomposition algorithm is introduced. Some test instances are solved, with scenarios generated by Monte Carlo method. For some test instances, to find the number of suitable scenarios, the authors use the sample average approximation method and to generate scenarios, the authors use Latin hypercube sampling method. Findings The results show a reasonable performance in terms of both quality and solution time. Finally, the paper concludes with some analysis of the results and suggestions for further research. Originality/value Researchers have attracted to other uncertainty factors such as costs and products demand in the literature, and have little attention to workforce demand as an uncertainty factor. Furthermore, most of the time, researchers assume that there is no difference between the education level and skill, while they are not necessarily equivalent. Hence, this paper enters these elements into decision making.

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