Mixed-Integer Rounding Enhanced Benders Decomposition for Multiclass Service-System Staffing and Scheduling with Arrival Rate Uncertainty

2017 ◽  
Vol 63 (7) ◽  
pp. 2073-2091 ◽  
Author(s):  
Merve Bodur ◽  
James R. Luedtke
Keyword(s):  
Benders Decomposition ◽  
Service System ◽  
Arrival Rate ◽  
Mixed Integer ◽  
Mixed Integer Rounding ◽  
Integer Rounding

scholarly journals Conic mixed-integer rounding cuts

2008 ◽  
Vol 122 (1) ◽  
pp. 1-20 ◽  
Author(s):  
Alper Atamtürk ◽  
Vishnu Narayanan
Keyword(s):  
Mixed Integer ◽  
Mixed Integer Rounding ◽  
Integer Rounding

Aggregation and Mixed Integer Rounding to Solve MIPs

2001 ◽  
Vol 49 (3) ◽  
pp. 363-371 ◽  
Author(s):  
Hugues Marchand ◽  
Laurence A. Wolsey
Keyword(s):  
Mixed Integer ◽  
Mixed Integer Rounding ◽  
Integer Rounding

scholarly journals Mingling: mixed-integer rounding with bounds

2009 ◽  
Vol 123 (2) ◽  
pp. 315-338 ◽  
Author(s):  
Alper Atamtürk ◽  
Oktay Günlük
Keyword(s):  
Mixed Integer ◽  
Mixed Integer Rounding ◽  
Integer Rounding

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.

scholarly journals Security Constrained Unit Commitment in a Power System based on Benders Decomposition and Mixed Integer Non-linear Programming

2018 ◽  
Vol 7 (2.6) ◽  
pp. 283 ◽  
Author(s):  
Pranda Prasanta Gupta ◽  
Prerna Jain ◽  
Suman Sharma ◽  
Rohit Bhakar
Keyword(s):  
Linear Programming ◽  
Network Security ◽  
Power System ◽  
Optimal Power Flow ◽  
Benders Decomposition ◽  
Optimal Solution ◽  
Mixed Integer ◽  
Reserve Requirement ◽  
Non Linear Programming ◽  
Non Linear

In deregulated power markets, Independent System Operators (ISOs) maintains adequate reserve requirement in order to respond to generation and system security constraints. In order to estimate accurate reserve requirement and handling non-linearity and non-convexity of the problem, an efficient computational framework is required. In addition, ISO executes SCUC in order to reach the consistent operation. In this paper, a novel type of application which is Benders decomposition (BD) and Mixed integer non linear programming (MINLP) can be used to assess network security constraints by using AC optimal power flow (ACOPF) in a power system. It performs ACOPF in network security check evaluation with line outage contingency. The process of solving modified system would be close to optimal solution, the gap between the close to optimal and optimal solution is expected to determine whether a close to optimal solutionis accepetable for convenientpurpose. This approach drastically betters the fast computational requirement in practical power system .The numerical case studies are investigated in detail using an IEEE 118-bus system. 

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.

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