Minimum cost multicommodity network flow problem in time-varying networks: by decomposition principle

Khodayifar, Salman

doi:10.1007/s11590-019-01519-5

Cited by 9 publications

(5 citation statements)

References 14 publications

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“…On the other hand CPLEX takes more than 10 seconds to find a solution, which is two orders of magnitude longer than Algorithm 2. Note that state-of-the-art methods for multi-commodity flows can typically not be expected to improve the run time by more than an order of magnitude as compared to standard LP solvers [4,52,40]. Our proposed algorithm is thus competitive with specialized state-of-the-art methods for network flow problems.…”

Section: Simulationsmentioning

confidence: 95%

“…In the setting of one commodity, let P denote the set of feasible paths in the time-expanded network N exp , i.e., p ∈ P if p is a path that starts in a source, p 1 ∈ S + , and ends in a sink, p T ∈ S − . The corresponding cost of unit flow on the path p ∈ P is then (4) see [40] for a similar problem formulation.…”

Section: Dynamic Network Flowmentioning

confidence: 99%

“…Between each (ordered) pair of nodes we create a directed edge with probability 1/2. The expected value of the number of edges in the network is thus 40 2 = 780. Moreover, we allow for intermediate storage in the nodes, but not in the edges.…”

Section: 2mentioning

confidence: 99%

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Scalable computation of dynamic flow problems via multi-marginal graph-structured optimal transport

Haasler¹,

Ringh²,

Chen³

et al. 2021

Preprint

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In this work, we develop a new framework for dynamic network flow problems based on optimal transport theory. We show that the dynamic multi-commodity minimum-cost network flow problem can be formulated as a multi-marginal optimal transport problem, where the cost function and the constraints on the marginals are associated with a graph structure. By exploiting these structures and building on recent advances in optimal transport theory, we develop an efficient method for such entropy-regularized optimal transport problems. In particular, the graph structure is utilized to efficiently compute the projections needed in the corresponding Sinkhorn iterations, and we arrive at a scheme that is both highly computationally efficient and easy to implement. To illustrate the performance of our algorithm, we compare it with a state-of-the-art Linear programming (LP) solver. We achieve good approximations to the solution at least one order of magnitude faster than the LP solver. Finally, we showcase the methodology on a traffic routing problem with a large number of commodities.

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Section: Simulationsmentioning

confidence: 95%

Section: Dynamic Network Flowmentioning

confidence: 99%

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Scalable computation of dynamic flow problems via multi-marginal graph-structured optimal transport

Haasler¹,

Ringh²,

Chen³

et al. 2021

Preprint

View full text Add to dashboard Cite

show abstract

“…The research of Fleischer and Skutella (2002), Glover and Sherali (2005), and Khodayifar (2021) are most related to our work. Fleischer and Skutella (2002) and Glover and Sherali (2005) both take a multi-period approach to solve the dynamic network flow problems, in which they determine flows over a sequence of discretized time periods.…”

Section: Dynamic Flowsmentioning

confidence: 98%

Minimum‐cost flow problems having arc‐activation costs

Curry

Smith

2021

Naval Research Logistics

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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.

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“…Our solution approach is to formulate the studied problem as a min-cost multicommodity network flow problem. Problems of this type are studied by (Ahuja et al 1993), (Karzanov 1994), and recently by (Grande et al 2018) and (Khodayifar 2021), to name a few. The typical application is to find the best delivery plan of several products from the manufacturing sites to the warehouses though a given road network with arc capacities and costs.…”

Section: Literature Reviewmentioning

confidence: 99%

Cost minimizing planning of container inspection and repair in multiple facilities

2022

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A problem of optimal mid-term or long-term planning of inspection and repair of freight containers in multiple facilities is introduced and investigated. The containers are of different types and quality levels, which define their repair costs and workforce requirements. The objective function includes the total holding, inspection, repair, transportation and rejection costs. We propose a deterministic, time-dependent, integer linear min-cost multi-commodity network-flow formulation. The problem is shown to be polynomially solvable if there is a single facility, a single time period and all the containers are repairable and have to be repaired. It is shown to be NP-hard for three important special cases. The computational results of our experiments on randomly generated instances based on real data show that instances of sizes 3 facilities, 4 container types and up to 9 container quality levels can be solved with CPLEX in 5 minutes on a conventional PC, even for 30 periods, with an optimality gap of less than 3%. This is sufficient for medium-term or weekly planning or for short-term recovery planning. However, there are instances of the same magnitude, but with 360 periods of a considerably longer planning horizon, for which an optimality gap of 28% remained even after 10 hours of CPLEX computation.

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Minimum cost multicommodity network flow problem in time-varying networks: by decomposition principle

Cited by 9 publications

References 14 publications

Scalable computation of dynamic flow problems via multi-marginal graph-structured optimal transport

Scalable computation of dynamic flow problems via multi-marginal graph-structured optimal transport

Minimum‐cost flow problems having arc‐activation costs

Cost minimizing planning of container inspection and repair in multiple facilities

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