Lagrangian relaxation for the time-dependent combined network design and routing problem

Papadimitriou, Dimitri; Fortz, Bernard; Gorgone, Enrico

doi:10.1109/icc.2015.7249283

Cited by 8 publications

(5 citation statements)

References 22 publications

(34 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Consequently, the BM presents a large number of iterations and each iteration requires a big computational effort. This observation was computationally confirmed by our experiments reported in , which justify the choice of using the aggregated master problem.…”

Section: The Algorithmsupporting

confidence: 81%

See 1 more Smart Citation

A Lagrangian heuristic algorithm for the time‐dependent combined network design and routing problem

2016

Self Cite

View full text Add to dashboard Cite

During the planning of communication networks, the routing decision process (distributed and online) often remains decoupled from the network design process, that is, resource installation and allocation-planning process (centralized and offline). To reconcile both processes and take into account demand variability, we generalize the capacitated multicommodity fixed charge network design class of problems by including different types of fixed costs (installation and maintenance costs) and variable costs (routing costs) but also variable traffic demands over multiple periods. However, conventional integer programming methods can typically solve only small to medium size instances of this problem. Two major difficulties are encountered when using commercial solvers to solve the associated mixed integer programs: (i) problems are large scale and even solving the linear relaxation of the problem can be challenging; and (ii) the solver hardly find good feasible solutions for medium to large scale instances. As an alternative, we propose a Lagrangian approach for computing a lower bound by relaxing the flow conservation constraints such that the Lagrangian subproblem itself decomposes by node. Though this approach yields one subproblem per network node, solving the Lagrangian dual by means of the bundle method remains a complex computational tasks. However, it always provides a lower bound on the optimal solution. Moreover, based on this relaxation, we propose a Lagrangian heuristic that makes the approach more robust than a black-box usage of a Mixed Integer Programming (MIP) solver. © 2016 Wiley Periodicals, Inc. NETWORKS, Vol. 69(1), 110–123 2017

show abstract

Section: The Algorithmsupporting

confidence: 81%

“…The Lagrangian relaxation problem is solved by means of the BM which aims at overcoming the slow convergence and instability of the Cutting Plane algorithm . A preliminary version of the resolution procedure is documented in . The BM is extended in this article with a LH to produce a feasible solution.…”

Section: The Algorithmmentioning

confidence: 99%

A Lagrangian heuristic algorithm for the time‐dependent combined network design and routing problem

2016

Self Cite

View full text Add to dashboard Cite

show abstract

“…Indeed austria is the largest instance in terms of the number of vertices and arcs but the nominal size of the demands is limited as demonstrated by the 24 unused arcs and the total number of demands proportional to the number of vertices n (instead of n 2 compared to the other instances). A Lagrangian relaxation could also be investigated for comparative purposes; however, experience [36] shows that the resulting problem shall be decomposable per node to yield any potential advantage -which is not the case here due to the delay constraints.…”

Section: Alm With Lp Startmentioning

confidence: 99%

Stochastic Lagrangian-based method for nonconvex optimization with nonlinear constraints

Papadimitriou,

2023

Preprint

View full text Add to dashboard Cite

The Augmented Lagrangian Method (ALM) is one of the most common approaches for solving linear and nonlinear constrained problems. However, for nonconvex objectives, the handling of nonlinear inequality constraints remains challenging. In this paper, we propose a stochastic ALM with Backtracking Line Search that performs on a subset (mini-batch) of randomly selected points for the solving of nonconvex problems. The considered class of problems include both nonlinear equality and inequality constraints. Together with the formal proof of the convergence properties (in expectation) of the proposed algorithm and its computational complexity, the performance of the proposed algorithm are then numerically compared against both exact and inexact state-of-the-art ALM methods. Further, we apply the proposed stochastic ALM method to solve a multi-constrained network design problem. We perform extensive numerical executions on a set of instances extracted from SNDlib to study its behavior and performance as well as potential improvement of this method. Analysis and comparison of the results against those obtained by extending to nonlinear constraints the method developed in [Contardo2021] for the approximation of separable nonconvex optimization programs are then provided. Mathematics Subject Classification (2020) 65K05 · 68Q25 · 90C46 · 90C30 · 90C25

show abstract

“…We next highlight the overlap between dynamic flows and the FCNF. Papadimitriou et al (2015) derive a distributed optimization technique for solving a dynamic version of the capacitated FCNF, in which they assume network parameters vary over time. Unlike our assumptions, the authors do not consider the case in which a fixed-charge could be paid multiple times due to a unique ordering of path-flows.…”

Section: Dynamic Flowsmentioning

confidence: 99%

Minimum‐cost flow problems having arc‐activation costs

Curry

Smith

2021

Naval Research Logistics

View full text Add to dashboard Cite

Time-dependent network applications, such as wireless sensor network and infrastructure optimization settings, may require dynamic flows to be transmitted according to a nonsimultaneous schedule of path-flows. We study a dynamic network flow optimization problem considering the presence of activation costs required to begin transmitting flow on an arc. This problem can be modeled as a dynamic version of the minimum-cost flow problem having arc-activation costs (MCFA). The MCFA is related but not equivalent to the fixed-charge network flow problem. We first discuss the relationship between these two problems, and show how MCFA is unique in the network flow literature. We present a mixed-integer programming (MIP) model along with a series of symmetry-breaking inequalities for solving the MCFA. As an alternative, we employ a relaxation-based algorithm that iteratively obtains upper and lower bounds via the solution of a series of smaller, more tractable MIPs. We show that this algorithm finitely terminates with an optimal MCFA solution. Finally, computational results demonstrate the efficacy of our approach compared to solving a MIP using a state-of-the-art commercial solver.

show abstract

Lagrangian relaxation for the time-dependent combined network design and routing problem

Cited by 8 publications

References 22 publications

A Lagrangian heuristic algorithm for the time‐dependent combined network design and routing problem

A Lagrangian heuristic algorithm for the time‐dependent combined network design and routing problem

Stochastic Lagrangian-based method for nonconvex optimization with nonlinear constraints

Minimum‐cost flow problems having arc‐activation costs

Contact Info

Product

Resources

About