Benders decomposition algorithms for the fixed-charge relay network design in telecommunications
TL;DR: This study considers a fixed-charge relay network design problem whose applications are found mainly in long distance translucent optical telecommunication networks and devise Benders decomposition based solution methodologies in which the algorithmic performance is further enhanced by devising strengthened and disaggregated Benders cuts.
Abstract: In translucent networks, signal regenerators that operate based on optical/electrical/optical (O/E/O) conversion are employed to handle the problems of physical impairments and resulting signal quality issues in long-distance transmissions. Regenerators are placed at the relay nodes in a translucent network in such a way that the optical signals are not transmitted farther than a threshold distance without a 3R regeneration (reamplification-reshaping-retiming).
In this study, we consider a fixed-charge relay network design (FCRND) problem whose applications are found mainly in long distance translucent optical telecommunication networks. From a modeling perspective, FCRND combines prominent features of the uncapacitated single-assignment hub location (location of relays points) and the fixed-charge network design problems (choice of transmission links in the network and routing of signals) while additionally considering distance-based coverage constraints. We devise Benders decomposition based solution methodologies in which the algorithmic performance is further enhanced by devising strengthened and disaggregated Benders cuts, surrogate constraints for the master problem, and an upper bound heuristic to both obtain and tighten optimality Benders cuts. We obtain solutions within 2.0 % of optimality in very reasonable times as we illustrate in our computational study.
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TL;DR: A state-of-the-art survey of the Benders Decomposition algorithm, emphasizing its use in combinatorial optimization and introducing a taxonomy of algorithmic enhancements and acceleration strategies based on the main components of the algorithm.
506 citations
Cites background or methods from "Benders decomposition algorithms fo..."
...Kewcharoenwong and Üster (2014) obtained an encouraging speedup with this approach in the context of fixed-charge relay network design in telecommunications....
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...Many researchers therefore apply heuristic procedures to generate solutions or, as a subordinate method, improve previously generated ones (Gelareh et al., 2015; Kewcharoenwong and Üster, 2014; Oliveira et al., 2014; Botton et al., 2013; Taşkın and Cevik, 2013)....
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...For other uses of VI see Taşkın and Cevik (2013), Kewcharoenwong and Üster (2014), Pishvaee et al. (2014), Jenabi et al. (2015), Emami et al. (2016), and Jeihoonian et al. (2016)....
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...Many researchers therefore apply heuristic procedures to generate solutions or, as a subordinate method, improve previously generated ones (Gelareh et al., 2015; Kewcharoenwong and Üster, 2014; Oliveira et al., 2014; Botton et al., 2013; Taşkın and Cevik, 2013)....
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TL;DR: In this article, the regenerator placement problem is revisited from the hub location perspective for applications arising in transportation settings, and two new dimensions involving the challenges of survivability are introduced to the problem.
Abstract: In a telecommunications network the reach of an optical signal is the maximum distance it can traverse before its quality degrades. Regenerators are devices to extend the optical reach. The regenerator placement problem seeks to place the minimum number of regenerators in an optical network so as to facilitate the communication of a signal between any node pair. In this study, the Regenerator Location Problem is revisited from the hub location perspective directing our focus to applications arising in transportation settings. Two new dimensions involving the challenges of survivability are introduced to the problem. Under partial survivability, our designs hedge against failures in the regeneration equipment only, whereas under full survivability failures on any of the network nodes are accounted for by the utilization of extra regeneration equipment. All three variations of the problem are studied in a unifying framework involving the introduction of individual flow-based compact formulations as well as cut formulations and the implementation of branch and cut algorithms based on the cut formulations. Extensive computational experiments are conducted in order to evaluate the performance of the proposed solution methodologies and to gain insights from realistic instances.
29 citations
Cites methods from "Benders decomposition algorithms fo..."
...…this analysis of Campbell and O’Kelly (2012), RLP literature discussed in this paper as well as a closely related network design problem with relays of Cabral et al. (2007), Laporte and Pascoal (2011) and Kewcharoenwong and Uster (2014) seem to be confined to the field of telecommunications....
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...Under partial survivability, our designs hedge against failures in the regeneration equipment only, whereas under full survivability failures on any of the network nodes are accounted for by the utilization of extra regeneration equipment....
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TL;DR: This paper introduces a flow shipment scheduling and hub location-routing problem in which the hub network is not fully interconnected, with the aim of maximizing the total amount of flow delivered by a predetermined latest arrival time and minimizing total fixed and routing costs.
22 citations
TL;DR: This study proposes a two-stage mixed-integer linear programming (MILP) model capturing the aforementioned issues, along with specific concern to the perishable product storage and transportation, and proposes a hybrid decomposition algorithm combining the enhanced Benders decomposition algorithms and sample average approximation to solve the large size test instances of this complex problem.
21 citations
TL;DR: The results show that, making routing, bandwidth allocation, modulation selection, and regenerator placement decisions in a joint manner, it is possible to obtain drastic capacity enhancements when only a very modest portion of the nodes is endowed with the signal regeneration capability.
Abstract: In this study, we introduce the regenerator location problem in flexible optical networks. With a given traffic demand, the regenerator location problem in flexible optical networks considers the r...
20 citations
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TL;DR: In this article, the 8th International Meeting of the Institute of Management Sciences, Brussels, August 23-26, 1961, the authors presented a paper entitled "The International Journal of Management Science and Management Sciences".
Abstract: Paper presented to the 8th International Meeting of the Institute of Management Sciences, Brussels, August 23-26, 1961.
2,782 citations
TL;DR: In this paper, a multicommodity capacitated single-period version of the problem is formulated as a mixed integer linear program, and a solution technique based on Benders Decomposition is developed, implemented, and successfully applied to a real problem for a major food firm with 17 commodity classes, 14 plants, 45 possible distribution center sites, and 121 customer zones.
Abstract: A commonly occurring problem in distribution system design is the optimal location of intermediate distribution facilities between plants and customers. A multicommodity capacitated single-period version of this problem is formulated as a mixed integer linear program. A solution technique based on Benders Decomposition is developed, implemented, and successfully applied to a real problem for a major food firm with 17 commodity classes, 14 plants, 45 possible distribution center sites, and 121 customer zones. An essentially optimal solution was found and proven with a surprisingly small number of Benders cuts. Some discussion is given concerning why this problem class appears to be so amenable to solution by Benders’ method, and also concerning what we feel to be the proper professional use of the present computational technique.
1,201 citations
"Benders decomposition algorithms fo..." refers background or methods in this paper
...We then randomly assign a demand value wij to each node pair [i, j ] ∈Q using a uniform distribution U[10,20]....
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...1: Let So and Sc be the set of the opened and closed link obtained from MP; 2: Let UB(So) be the upper bound associated with So (from Algorithm 3); 3: Let S̄c = Sc; 4: while S̄c =∅ do 5: Sort S̄c in descending order of Ukl ; 6: q = min{|S̄c|,R}, R is randomly drawn from U[5,10]; 7: Let Sq be the first q closed links in the sorted closed links S̄c; 8: if UB(So ∪ Sq) < UB(So) then 9: Update So, Sc , and Ukl ; 10: else...
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...Another approach to decreasing the excessive master problem runtime is through the utilization of the ε-optimal approach [10]....
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Book•
01 Jan 2001
TL;DR: The Weber Problem, a study of location problems in the public sector, and an Efficient Genetic Algorithm for the p-Median Problem, provide insights into the design of location models.
Abstract: 1 The Weber Problem.- 2 Continuous Covering Location Problems.- 3 Discrete Network Location Models.- 4 Location Problems in the Public Sector.- 5 Consumers in Competitive Location Models.- 6 An Efficient Genetic Algorithm for the p-Median Problem.- 7 Demand Point Aggregation for Location Models.- 8 Location Software and Interface with GIS and Supply Chain Management.- 9 Telecommunication and Location.- 10 Reserve Design and Facility Siting.- 11 Facility Location Problems with Stochastic Demands and Congestion.- 12 Hub Location Problems.- 13 Location and Robotics.- 14 The Quadratic Assignment Problem.
1,124 citations
08 Jun 2015
TL;DR: In this article, the authors proposed a novel association algorithm and proved its superiority w.r.t. prior art by means of simulations that are based on Vodafone's small cell trial network and employing a high resolution pathloss prediction and realistic user distributions.
Abstract: Until the 4th Generation (4G) cellular 3GPP systems, a user equipment's (UE) cell association has been based on the downlink received power from the strongest base station. Recent work has shown that - with an increasing degree of heterogeneity in emerging 5G systems - such an approach is dramatically suboptimal, advocating for an independent association of the downlink and uplink where the downlink is served by the macro cell and the uplink by the nearest small cell. In this paper, we advance prior art by explicitly considering the cell-load as well as the available backhaul capacity during the association process. We introduce a novel association algorithm and prove its superiority w.r.t. prior art by means of simulations that are based on Vodafone's small cell trial network and employing a high resolution pathloss prediction and realistic user distributions. We also study the effect that different power control settings have on the performance of our algorithm.
756 citations
TL;DR: A new technique for accelerating the convergence of the algorithm and theory for distinguishing “good” model formulations of a problem that has distinct but equivalent mixed integer programming representations is introduced.
Abstract: This paper proposes methodology for improving the performance of Benders decomposition when applied to mixed integer programs. It introduces a new technique for accelerating the convergence of the algorithm and theory for distinguishing “good” model formulations of a problem that has distinct but equivalent mixed integer programming representations. The acceleration technique is based upon selecting judiciously from the alternate optima of the Benders subproblem to generate strong or pareto-optimal cuts. This methodology also applies to a much broader class of optimization algorithms that includes Dantzig-Wolfe decomposition for linear and nonlinear programs and related “cutting plane” type algorithms that arise in resource directive and price decomposition. When specialized to network location problems, this cut generation technique leads to very efficient algorithms that exploit the underlying structure of these models. In discussing the “proper” formulation of mixed integer programs, we suggest criteri...
655 citations