Large scale mixed-integer optimization: A solution method with supply chain applications

Vujanic, Robin; Esfahani, Peyman Mohajerin; Goulart, Paul J.; Morari, Manfred

doi:10.1109/med.2014.6961472

Cited by 11 publications

(10 citation statements)

References 17 publications

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“…In power systems, scheduling operations of power generation plants [Yam04] is a decision problem in which the subsystems are the generating units, integer variables in the local models arise due to, e.g., start-up and shut-down costs, and the coupling constraints are related to the requirement that generation must match load. In supply chain management, models fitting P appear in the problem of partial shipments [DGT06,VEGM14b]. Portfolio optimization for small investors, for which mixed-integer models have been proposed, is another example application [BT13].…”

Section: (P)mentioning

confidence: 99%

“…Furthermore, note that while the structural properties of x LP appeared in the literature [BLSP83,Ber09,VEGM14b], the contribution here is to ensure that, under Assumption 2.4, these advantageous properties are transferred to the inner solutions x(λ ). This is of substantial practical interest, because it is the inner solutions that one has direct access to when solving the dual.…”

Section: Duality For Problem Pmentioning

confidence: 99%

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A decomposition method for large scale MILPs, with performance guarantees and a power system application

et al. 2016

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Abstract. Lagrangian duality in mixed integer optimization is a useful framework for problems decomposition and for producing tight lower bounds to the optimal objective, but in contrast to the convex counterpart, it is generally unable to produce optimal solutions directly. In fact, solutions recovered from the dual may be not only suboptimal, but even infeasible. In this paper we concentrate on large scale mixed-integer programs with a specific structure that is of practical interest, as it appears in a variety of application domains such as power systems or supply chain management. We propose a solution method for these structures, in which the primal problem is modified in a certain way, guaranteeing that the solutions produced by the corresponding dual are feasible for the original unmodified primal problem. The modification is simple to implement and the method is amenable to distributed computations. We also demonstrate that the quality of the solutions recovered using our procedure improves as the problem size increases, making it particularly useful for large scale instances for which commercial solvers are inadequate. We illustrate the efficacy of our method with extensive experimentations on a problem stemming from power systems.

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Section: (P)mentioning

confidence: 99%

Section: Duality For Problem Pmentioning

confidence: 99%

A decomposition method for large scale MILPs, with performance guarantees and a power system application

et al. 2016

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“…This situation occurs for very structured problems, such as in the case study analyzed in [15], for which our restriction can be obtained by scaling (12) by (S + 1)/S. Finally, in certain problem set-ups, such as in partial shipments [19], the local constraint sets are such that 0 ∈ X i and A i x i 0 for all x i ∈ X i . Then, by construction, L i = 0 and˜ i = 0 for all i ∈ {1, .…”

Section: Tight Restriction For Asymptotic Feasibilitymentioning

confidence: 99%

A Primal Decomposition Method with Suboptimality Bounds for Distributed Mixed-Integer Linear Programming

Camisa

Notarnicola

Notarstefano

2018

2018 IEEE Conference on Decision and Control (CDC)

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In this paper we deal with a network of agents seeking to solve in a distributed way Mixed-Integer Linear Programs (MILPs) with a coupling constraint (modeling a limited shared resource) and local constraints. MILPs are NP-hard problems and several challenges arise in a distributed framework, so that looking for suboptimal solutions is of interest. To achieve this goal, the presence of a linear coupling calls for tailored decomposition approaches. We propose a fully distributed algorithm based on a primal decomposition approach and a suitable tightening of the coupling constraints. Agents repeatedly update local allocation vectors, which converge to an optimal resource allocation of an approximate version of the original problem. Based on such allocation vectors, agents are able to (locally) compute a mixed-integer solution, which is guaranteed to be feasible after a sufficiently large time. Asymptotic and finite-time suboptimality bounds are established for the computed solution. Numerical simulations highlight the efficacy of the proposed methodology. * This result is part of a project that has received funding

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“…Ekeland and Temam [13], Bertsekas and coauthors [4,7], Pappalardo [35], Wang [45], Kerdreux et al [24], Bi and Tang [8]). These theoretical results have found applications in engineering, such as the large-scale unit commitment problem [3,25] and optimization of Plug-in Electric Vehicles charging [44] in the electricity system, optimization of multicarrier communication systems [48], supply-chain management [43], and spatial graphical model estimation [15].…”

Section: Introductionmentioning

confidence: 99%

Approximate Nash equilibria in large nonconvex aggregative games

Liu,

Oudjane,

Wan

2020

Preprint

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This paper shows the existence of O( 1 n γ )-Nash equilibria in n-player noncooperative aggregative games where the players' cost functions depend only on their own action and the average of all the players' actions, and is lower semicontinuous in the former while γ-Hölder continuous in the latter. Neither the action sets nor the cost functions need to be convex. For an important class of aggregative games which includes congestion games with γ being 1, a proximal best-reply algorithm is used to construct an O( 1n )-Nash equilibria with at most O(n 3 ) iterations. These results are applied in a numerical example of demand-side management of the electricity system. The asymptotic performance of the algorithm is illustrated when n tends to infinity.

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Large scale mixed-integer optimization: A solution method with supply chain applications

Cited by 11 publications

References 17 publications

A decomposition method for large scale MILPs, with performance guarantees and a power system application

A decomposition method for large scale MILPs, with performance guarantees and a power system application

A Primal Decomposition Method with Suboptimality Bounds for Distributed Mixed-Integer Linear Programming

Approximate Nash equilibria in large nonconvex aggregative games

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