A Modified Benders' Partitioning Algorithm for Mixed Integer Programming

McDaniel, Dale; Devine, Michael D.

doi:10.1287/mnsc.24.3.312

Cited by 183 publications

(120 citation statements)

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“…Many other applications of Benders decomposition have been proposed since then (see, for example, Richardson 1976;Magnanti et al 1986;Cordeau et al 2000;Cordeau et al 2001). Methodologies for improving the performance of the method have been proposed in McDaniel and Devine (1977) and Magnanti and Wong (1981). Kouvelis and Yu (1997) derived an algorithm for the scenario version of the robust shortest path problem (see Yu and Jang 1998) by adapting Benders decomposition.…”

Section: A Benders Decomposition Approachmentioning

confidence: 99%

The robust shortest path problem with interval data via Benders decomposition

Montemanni

Gambardella

2005

4OR

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Abstract. Many real problems can be modelled as robust shortest path problems on digraphs with interval costs, where intervals represent uncertainty about real costs and a robust path is not too far from the shortest path for each possible configuration of the arc costs.In this paper we discuss the application of a Benders decomposition approach to this problem.Computational results confirm the efficiency of the new algorithm. It is able to clearly outperform state-of-the-art algorithms on many classes of networks. For the remaining classes we identify the most promising algorithm among the others, depending of the characteristics of the networks.

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Section: A Benders Decomposition Approachmentioning

confidence: 99%

The robust shortest path problem with interval data via Benders decomposition

Montemanni

Gambardella

2005

4OR

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“…This formulation involves an exponential number of connectivity constraints that cannot be represented explicitly for real life sized instances. To address this, we present a Bender's decomposition approach that iteratively adds connectivity constraints to a relaxed master problem [1,12].…”

Section: Introductionmentioning

confidence: 99%

Solving Connected Subgraph Problems in Wildlife Conservation

Dilkina

Gomes

2010

Integration of AI and OR Techniques in Constraint Programming for Combinatorial Optimization Problems

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Abstract. We investigate mathematical formulations and solution techniques for a variant of the Connected Subgraph Problem. Given a connected graph with costs and profits associated with the nodes, the goal is to find a connected subgraph that contains a subset of distinguished vertices. In this work we focus on the budget-constrained version, where we maximize the total profit of the nodes in the subgraph subject to a budget constraint on the total cost. We propose several mixed-integer formulations for enforcing the subgraph connectivity requirement, which plays a key role in the combinatorial structure of the problem. We show that a new formulation based on subtour elimination constraints is more effective at capturing the combinatorial structure of the problem, providing significant advantages over the previously considered encoding which was based on a single commodity flow. We test our formulations on synthetic instances as well as on real-world instances of an important problem in environmental conservation concerning the design of wildlife corridors. Our encoding results in a much tighter LP relaxation, and more importantly, it results in finding better integer feasible solutions as well as much better upper bounds on the objective (often proving optimality or within less than 1% of optimality), both when considering the synthetic instances as well as the real-world wildlife corridor instances.

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“…Instead of considering all the variables and the constraints of PP1 simultaneously, OJTM decomposes the PP1 into a Master Problem (MP) and a Slave Problem (SP), which are solved iteratively through a feedback loop. By doing so, the computational complexity of the solution is significantly reduced [23], [30], even if the PP1 is non-convex. The structure of OJTM is shown in Fig.…”

Section: B Optimal Joint Dvfs Task Mappingmentioning

confidence: 99%

Energy-Quality-Time Optimized Task Mapping on DVFS-Enabled Multicores

Kritikakou

Sentieys

2018

IEEE Trans. Comput.-Aided Des. Integr. Circuits Syst.

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Abstract-Multicore architectures have great potential for energy-constrained embedded systems, such as energy-harvesting wireless sensor networks. Some embedded applications, especially the real-time ones, can be modeled as imprecise computation tasks. A task is divided into a mandatory subtask that provides a baseline Quality-of-Service (QoS) and an optional subtask that refines the result to increase the QoS. Combining dynamic voltage and frequency scaling, task allocation and task adjustment, we can maximize the system QoS under real-time and energy supply constraints. However, the nonlinear and combinatorial nature of this problem makes it difficult to solve. This work first formulates a mixed-integer non-linear programming problem to concurrently carry out task-to-processor allocation, frequencyto-task assignment and optional task adjustment. We provide a mixed-integer linear programming form of this formulation without performance degradation and we propose a novel decomposition algorithm to provide an optimal solution with reduced computation time compared to state-of-the-art optimal approaches (22.6% in average). We also propose a heuristic version that has negligible computation time.

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A Modified Benders' Partitioning Algorithm for Mixed Integer Programming

Cited by 183 publications

References 4 publications

The robust shortest path problem with interval data via Benders decomposition

The robust shortest path problem with interval data via Benders decomposition

Solving Connected Subgraph Problems in Wildlife Conservation

Energy-Quality-Time Optimized Task Mapping on DVFS-Enabled Multicores

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