Lagrangian based heuristics for the multicommodity network flow problem with fixed costs on paths

Holmberg, Kaj; Joborn, Martin; Melin, K. L.

doi:10.1016/j.ejor.2007.04.029

Cited by 17 publications

(11 citation statements)

References 5 publications

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“…The Lagrange relaxation technique that we use is not always guaranteed to satisfy the corresponding constraints (as observed in Sections 3 and 4). Hence, one future direction is to develop a Lagrange heuristic [14][15][16] specific to our problem to avoid this behavior. Another future direction involves finding more efficient algorithms for solving this BILP, which we know is an NP-complete problem.…”

Section: Discussionmentioning

confidence: 99%

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ParaLarPD: Parallel FPGA Router Using Primal-Dual Sub-Gradient Method

et al. 2019

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In the field programmable gate array (FPGA) design flow, one of the most time-consuming steps is the routing of nets. Therefore, there is a need to accelerate it. In a recent work by Hoo et al., the authors have developed a linear programming (LP)-based framework that parallelizes this routing process to achieve significant speed-ups (the resulting algorithm is termed as ParaLaR). However, this approach has certain weaknesses. Namely, the constraints violation by the solution and a standard routing metric could be improved. We address these two issues here. In this paper, we use the LP framework of ParaLaR and solve it using the primal-dual sub-gradient method that better exploits the problem properties. We also propose a better way to update the size of the step taken by this iterative algorithm. We call our algorithm as ParaLarPD. We perform experiments on a set of standard benchmarks, where we show that our algorithm outperforms not just ParaLaR but the standard existing algorithm VPR as well. We perform experiments with two different configurations. We achieve 20% average improvement in the constraints violation and the standard metric of the minimum channel width (both of which are related) when compared with ParaLaR. When compared to VPR, we get average improvements of 28% in the minimum channel width (there is no constraints violation in VPR). We obtain the same value for the total wire length as by ParaLaR, which is 49% better on an average than that obtained by VPR. This is the original metric to be minimized, for which ParaLaR was proposed. Next, we look at the third and easily measurable metric of critical path delay. On an average, ParaLarPD gives 2% larger critical path delay than ParaLaR and 3% better than VPR. We achieve maximum relative speed-ups of up to seven times when running a parallel version of our algorithm using eight threads as compared to the sequential implementation. These speed-ups are similar to those as obtained by ParaLaR.CAD (computer-aided design) tools. This can be achieved in two ways. First, by parallelizing the routing algorithms for hardware having multiple cores. However, the pathfinder algorithm [3], which is one of the most commonly used FPGA routing algorithm is intrinsically sequential. Hence, this approach seems inappropriate for parallelizing all types of FPGA routing algorithms.Second, instead of compiling the entire design together, the users can partition their design, compile partitions progressively, and then assemble all the partitions to form the entire design. Some existing works have proposed this approach [4,5]. However, the routing resources required by one partition may be held by another partition, i.e., there is no guarantee to have balanced partitions. In other words, in this approach, there is a need to tackle the difficulties arising in sharing of routing resources.The authors in ParaLaR [6] overcome the limitations of existing approaches by formulating the FPGA routing problem as an optimization problem [7]. Here, the objective function is linear an...

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Section: Discussionmentioning

confidence: 99%

“…The Lagrange relaxation [11] is a technique well suited for problems where the constraints can be relaxed by incorporating them into an objective function. If this is not possible, then a Lagrange heuristic can be developed [14][15][16].…”

Section: The Channel Width Constraintsmentioning

confidence: 99%

ParaLarPD: Parallel FPGA Router Using Primal-Dual Sub-Gradient Method

et al. 2019

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“…Jo et al (2007) proposed the spanning tree-based GA approach for solving non-linear FCTP. Holmberg et al (2008) studied the multi-commodity network flow problem with fixed costs on paths, with specific application to the empty freight car distribution process of a rail operator. Sheu (2008) presented a hybrid neuro fuzzy methodology to identify appropriate global logistics operational modes used for global supply chain management.…”

Section: Literature Reviewmentioning

confidence: 99%

Genetic Algorithm for optimisation of distribution system in a single stage supply chain network with fixed charges

Manimaran¹,

Selladurai²,

Ranganathan³

et al. 2011

IJISE

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This paper proposes a single stage supply chain network fixed charge transportation problem (FCTP) and a solution procedure. The objective is to find the optimum set of suppliers to be opened and determine the quantities to be supplied, so that the total cost of distribution can be minimised. The problem chosen goes beyond the traditional mathematical programming and it becomes a non-polynomial (NP) hard problem, particularly while considering the fixed charges. Genetic Algorithm (GA) approach is proposed in this paper for solving. GA is applied for optimisation of the distribution network to provide optimal or near optimal solution. To demonstrate the efficiency of the proposed method in FCTP, GA is compared with spanning tree-based GA with the aid of numerical examples. Following application and analysis of this methodology, the proposed method is identified to be efficient concerning the total distribution cost. Further, the accuracy and procedure of selecting the suitable suppliers for meeting the customer needs are found simple and systematic in approach.

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“…In Section 3, we introduce a greedy randomized Lagrangian repair heuristic paired with a standard subgradient optimization algorithm. Lagrangian relaxation is a classical approach and it has been paired with a variety of heuristic mechanism to obtain high-quality feasible solutions for many problems, e.g., see Galvȃo andReVelle (1996), Haddadi (1997), Tragantalerngsak et al (1997), Lim and Kim (1998), Klose (2000), Jeet and Kutanoglu (2007), Larsson et al (2008), andHolmberg et al (2008). The integration of greedy randomized repair mechanisms and Lagrangian relaxations is not as widely documented, although recently Pessôa et al (2008) propose the use of a greedy randomized adaptive search procedure (GRASP) and path-relinking to achieve feasibility from solutions to a Lagrangian relaxation of the k-set covering problem.…”

Section: Introductionmentioning

confidence: 99%