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Computational Experiments (computational + experiment)
Selected AbstractsRobust optimum design of SAW filters by the penalty function methodELECTRICAL ENGINEERING IN JAPAN, Issue 3 2007Kiyoharu Tagawa Abstract In order to increase the reliability of surface acoustic wave (SAW) filters, a robust optimum design technique is presented. The frequency response characteristics of SAW filters are governed primarily by their geometrical structures, that is, the configurations of the interdigital transducers (IDTs) and reflectors fabricated on piezoelectric substrates. To choose desirable structures of SAW filters through computer simulation, conventional design techniques utilize the equivalent circuit model of the IDT. However, they have rarely considered the accuracy of the underlying model, which may be degraded by the dispersion of the circuit parameters. In this paper, considering the errors of these parameters, the robust optimum design of SAW filters is formulated as a constrained optimization problem. Then, a penalty function method combined with an improved variable neighborhood search is proposed and applied to the problem. Computational experiments conducted on a practical design problem of a resonator type SAW filter demonstrate the usefulness of the proposed method. © 2006 Wiley Periodicals, Inc. Electr Eng Jpn, 158(3): 45,54, 2007; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/eej.20469 [source] A numerical study of an unsteady laminar flow in a doubly constricted 3D vesselINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 12 2002B. V. Rathish Kumar Abstract Unsteady flow dynamics in doubly constricted 3D vessels have been investigated under pulsatile flow conditions for a full cycle of period T. The coupled non-linear partial differential equations governing the mass and momentum of a viscous incompressible fluid has been numerically analyzed by a time accurate Finite Volume Scheme in an implicit Euler time marching setting. Roe's flux difference splitting of non-linear terms and the pseudo-compressibility technique employed in the current numerical scheme makes it robust both in space and time. Computational experiments are carried out to assess the influence of Reynolds' number and the spacing between two mild constrictions on the pressure drop across the constrictions. The study reveals that the pressure drop across a series of mild constrictions can get physiologically critical and is also found to be sensitive both to the spacing between the constrictions and the oscillatory nature of the inflow profile. The flow separation zone on the downstream constriction is seen to detach from the diverging wall of the constriction leading to vortex shedding with 3D features earlier than that on the wall in the spacing between the two constrictions. Copyright © 2002 John Wiley & Sons, Ltd. [source] An adaptive survivability admission control algorithm using backup path for high-speed networksINTERNATIONAL JOURNAL OF NETWORK MANAGEMENT, Issue 6 2003Chi-Chun Lo In this paper, we propose an adaptive survivability admission control algorithm using a backup path for high-speed networks. For each call request, the proposed algorithm selects a combination of working path and backup path. Two BP selection methods, min-cost and min-expectation, are suggested. Computational experiments indicate that the proposed algorithm significantly reduces the consumption of backup capacity while still maintaining 100% survivability upon a single link failure and near 80% survivability upon double link failures.,Copyright © 2003 John Wiley & Sons, Ltd. [source] Scheduling activities at oil wells with resource displacementINTERNATIONAL TRANSACTIONS IN OPERATIONAL RESEARCH, Issue 6 2008Arnaldo V. Moura Abstract Before promising locations at petroliferous basins become productive oil wells, it is necessary to complete development activities at these locations. The scheduling of such activities must satisfy several conflicting constraints and attain a number of goals. Moreover, resource displacements between wells are important and must also be taken into account. The problem is NP-hard, as can be seen by a simple poly-time reduction from the Job Shop problem. This paper describes Greedy Randomized Adaptive Search Procedures (GRASPs) for the scheduling of oil well development activities with resource displacement. The heuristics were tested on real instances from a major oil company, recognized for its expertise in offshore oil exploration. Computational experiments over real instances revealed that the GRASP implementations are competitive, outperforming the software currently being used by the company. [source] A hybrid search combining interior point methods and metaheuristics for 0,1 programmingINTERNATIONAL TRANSACTIONS IN OPERATIONAL RESEARCH, Issue 6 2002Agnčs Plateau Our search deals with methods hybridizing interior point processes and metaheuristics for solving 0,1 linear programs. This paper shows how metaheuristics can take advantage of a sequence of interior points generated by an interior point method. After introducing our work field, we present our hybrid search which generates a diversified population. Next, we explain the whole method combining the solutions encountered in the previous phase through a path relinking template. Computational experiments are reported on 0,1 multiconstraint knapsack problems. [source] Two new cases of rank reversals when the AHP and some of its additive variants are used that do not occur with the multiplicative AHPJOURNAL OF MULTI CRITERIA DECISION ANALYSIS, Issue 1 2001Evangelos Triantaphyllou Abstract Many researchers have long observed some cases in which certain ranking irregularities can occur when the original analytic hierarchy process (AHP), or some of its variants, are used. This paper presents two new categories of ranking irregularities which defy common intuition. These ranking irregularities occur when one decomposes a decision problem into a set of smaller problems each defined on two alternatives and the same criteria as the original problem. These irregularities are possible when the original AHP, or some of its additive variants, are used. Computational experiments on random test problems and an examination of some real-life case studies suggest that these ranking irregularities are dramatically likely to occur. This paper also proves that these ranking irregularities are not possible when a multiplicative variant of the AHP is used. Copyright © 2001 John Wiley & Sons, Ltd. [source] Single-warehouse multi-retailer inventory systems with full truckload shipmentsNAVAL RESEARCH LOGISTICS: AN INTERNATIONAL JOURNAL, Issue 5 2009Yue Jin Abstract We consider a multi-stage inventory system composed of a single warehouse that receives a single product from a single supplier and replenishes the inventory of n retailers through direct shipments. Fixed costs are incurred for each truck dispatched and all trucks have the same capacity limit. Costs are stationary, or more generally monotone as in Lippman (Management Sci 16, 1969, 118,138). Demands for the n retailers over a planning horizon of T periods are given. The objective is to find the shipment quantities over the planning horizon to satisfy all demands at minimum system-wide inventory and transportation costs without backlogging. Using the structural properties of optimal solutions, we develop (1) an O(T2) algorithm for the single-stage dynamic lot sizing problem; (2) an O(T3) algorithm for the case of a single-warehouse single-retailer system; and (3) a nested shortest-path algorithm for the single-warehouse multi-retailer problem that runs in polynomial time for a given number of retailers. To overcome the computational burden when the number of retailers is large, we propose aggregated and disaggregated Lagrangian decomposition methods that make use of the structural properties and the efficient single-stage algorithm. Computational experiments show the effectiveness of these algorithms and the gains associated with coordinated versus decentralized systems. Finally, we show that the decentralized solution is asymptotically optimal. © 2009 Wiley Periodicals, Inc. Naval Research Logistics 2009 [source] A refined deterministic linear program for the network revenue management problem with customer choice behaviorNAVAL RESEARCH LOGISTICS: AN INTERNATIONAL JOURNAL, Issue 6 2008Sumit Kunnumkal Abstract We present a new deterministic linear program for the network revenue management problem with customer choice behavior. The novel aspect of our linear program is that it naturally generates bid prices that depend on how much time is left until the time of departure. Similar to the earlier linear program used by van Ryzin and Liu (2004), the optimal objective value of our linear program provides an upper bound on the optimal total expected revenue over the planning horizon. In addition, the percent gap between the optimal objective value of our linear program and the optimal total expected revenue diminishes in an asymptotic regime where the leg capacities and the number of time periods in the planning horizon increase linearly with the same rate. Computational experiments indicate that when compared with the linear program that appears in the existing literature, our linear program can provide tighter upper bounds, and the control policies that are based on our linear program can obtain higher total expected revenues. © 2008 Wiley Periodicals, Inc. Naval Research Logistics, 2008 [source] The ,-reliable mean-excess regret model for stochastic facility location modelingNAVAL RESEARCH LOGISTICS: AN INTERNATIONAL JOURNAL, Issue 7 2006Gang Chen Abstract In this paper, we study a strategic facility location problem under uncertainty. The uncertainty associated with future events is modeled by defining alternative future scenarios with probabilities. We present a new model called the ,-reliable mean-excess model that minimizes the expected regret with respect to an endogenously selected subset of worst-case scenarios whose collective probability of occurrence is no more than 1 , ,. Our mean-excess risk measure is coherent and computationally efficient. Computational experiments also show that the ,-reliable mean-excess criterion matches the ,-reliable minimax criterion closely. © 2006 Wiley Periodicals, Inc. Naval Research Logistics 2006 [source] Quay crane scheduling at container terminals to minimize the maximum relative tardiness of vessel departuresNAVAL RESEARCH LOGISTICS: AN INTERNATIONAL JOURNAL, Issue 1 2006Jiyin Liu Abstract In this paper, we study the problem of scheduling quay cranes (QCs) at container terminals where incoming vessels have different ready times. The objective is to minimize the maximum relative tardiness of vessel departures. The problem can be formulated as a mixed integer linear programming (MILP) model of large size that is difficult to solve directly. We propose a heuristic decomposition approach to breakdown the problem into two smaller, linked models, the vessel-level and the berth-level models. With the same berth-level model, two heuristic methods are developed using different vessel-level models. Computational experiments show that the proposed approach is effective and efficient. © 2005 Wiley Periodicals, Inc. Naval Research Logistics, 2006 [source] A branch-and-cut algorithm for partition coloringNETWORKS: AN INTERNATIONAL JOURNAL, Issue 3 2010Yuri Frota Abstract Let G = (V, E, Q) be a undirected graph, where V is the set of vertices, E is the set of edges, and Q = {Q1,,,Qq} is a partition of V into q subsets. We refer to Q1,,,Qq as the components of the partition. The partition coloring problem (PCP) consists of finding a subset V, of V with exactly one vertex from each component Q1,,,Qq and such that the chromatic number of the graph induced in G by V, is minimum. This problem is a generalization of the graph coloring problem. This work presents a branch-and-cut algorithm proposed for PCP. An integer programing formulation and valid inequalities are proposed. A tabu search heuristic is used for providing primal bounds. Computational experiments are reported for random graphs and for PCP instances originating from the problem of routing and wavelength assignment in all-optical WDM networks. © 2009 Wiley Periodicals, Inc. NETWORKS, 2010 [source] Cycle-based algorithms for multicommodity network flow problems with separable piecewise convex costsNETWORKS: AN INTERNATIONAL JOURNAL, Issue 2 2008Mauricio C. de Souza Abstract We present cycle-based algorithmic approaches to find local minima of a nonconvex and nonsmooth model for capacity expansion of a network supporting multicommodity flows. By exploiting complete optimality conditions for local minima, we give the convergence analysis of the negative-cost cycle canceling method. The cycle canceling method is embedded in a tabu search strategy to explore the solution space beyond the first local optimum. Reaching a local optimum, the idea is to accept a cost-increasing solution by pushing flow around a positive-cost cycle, and then to make use of the cycle cancelling method incorporating tabu search memory structures to find high quality local optima. Computational experiments on instances of the literature show that the tabu search algorithm can significantly improve feasible solutions obtained by the local optimization procedure, and it outperforms the capacity and flow assignment heuristic in terms of solution quality. © 2007 Wiley Periodicals, Inc. NETWORKS, 2008 [source] Path inequalities for the vehicle routing problem with time windowsNETWORKS: AN INTERNATIONAL JOURNAL, Issue 4 2007Brian Kallehauge Abstract In this paper we introduce a new formulation of the vehicle routing problem with time windows (VRPTW) involving only binary variables. The new formulation is based on the formulation of the asymmetric traveling salesman problem with time windows by Ascheuer et al. (Networks 36 (2000) 69,79) and has the advantage of avoiding additional variables and linking constraints. In the new formulation, time windows are modeled using path inequalities that eliminate time and capacity infeasible paths. We present a new class of strengthened path inequalities based on the polyhedral results obtained by Mak (Ph.D. Thesis, 2001) for a variant of the TSP. We study the VRPTW polytope and determine its dimension. We show that the lifted path inequalities are facet defining under certain assumptions. We also introduce precedence constraints in the context of the VRPTW. Computational experiments are performed with a branch and cut algorithm on the Solomon test problems with wide time windows. Based on results on 25-node problems, the outcome is promising compared to leading algorithms in the literature. In particular, we report a solution to a previously unsolved 50-node Solomon test problem R208. The conclusion is therefore that a polyhedral approach to the VRPTW is a viable alternative to the path formulation of Desrochers et al. (Oper Res 40 (1992), 342,354). © 2007 Wiley Periodicals, Inc. NETWORKS, Vol. 49(4), 273,293 2007 [source] Minimizing the cost of placing and sizing wavelength division multiplexing and optical crossconnect equipment in a telecommunications networkNETWORKS: AN INTERNATIONAL JOURNAL, Issue 4 2005Belén Melián Abstract Cost reduction is a major concern when designing optical fiber networks. Multiwavelength optical devices are new technology for increasing the capacity of fiber networks while reducing costs, when compared to installing traditional (e.g., SONET) equipment and new fiber. In this article we discuss the development of a metaheuristic method that seeks to optimize the location of Wavelength Division Multiplexing (WDM) and Optical Crossconnect (OXC) equipment in fiber networks. The procedure combines ideas from the scatter search, tabu search, and multistart methodologies. Computational experiments with both real-world and artificial data show the effectiveness of the proposed procedure. The experiments include a comparison with a permutation-based approach and with lower bounds generated with CPLEX. © 2005 Wiley Periodicals, Inc. NETWORKS, Vol. 45(4), 199,209 2005 [source] Optimization of Internet Protocol network design and routingNETWORKS: AN INTERNATIONAL JOURNAL, Issue 1 2004Kaj Holmberg Abstract We consider network design and routing for Internet Protocol (IP) traffic. The design problem concerns capacity dimensioning of communication links, where the design cost consists of fixed charges and linear capacity expansion costs. The optimization problem also concerns determining the amount of traffic demand to be carried by the network and the metric used by a shortest path routing protocol. We present a novel linear mixed-integer mathematical formulation and two heuristic solution procedures. The first heuristic uses mixed-integer programming to generate a sequence of routing solutions. The second solution approach is a simulated annealing meta heuristic. Computational experiments for synthesized and real-life networks show that high-quality solutions can be obtained by both approaches. © 2003 Wiley Periodicals, Inc. [source] Local search with perturbations for the prize-collecting Steiner tree problem in graphsNETWORKS: AN INTERNATIONAL JOURNAL, Issue 1 2001S. A. Canuto Abstract Given an undirected graph with prizes associated with its nodes and weights associated with its edges, the prize-collecting Steiner tree problem consists of finding a subtree of this graph which minimizes the sum of the weights of its edges plus the prizes of the nodes not spanned. In this paper, we describe a multistart local search algorithm for the prize-collecting Steiner tree problem, based on the generation of initial solutions by a primal-dual algorithm using perturbed node prizes. Path-relinking is used to improve the solutions found by local search and variable neighborhood search is used as a post-optimization procedure. Computational experiments involving different algorithm variants are reported. Our results show that the local search with perturbations approach found optimal solutions on nearly all of the instances tested. © 2001 John Wiley & Sons, Inc. [source] Impact of Price Postponement on Capacity and Flexibility Investment DecisionsPRODUCTION AND OPERATIONS MANAGEMENT, Issue 2 2006Stephan Biller Investments in dedicated and flexible capacity have traditionally been based on demand forecasts obtained under the assumption of a predetermined product price. However, the impact on revenue of poor capacity and flexibility decisions can be mitigated by appropriately changing prices. While investment decisions need to be made years before demand is realized, pricing decisions can easily be postponed until product launch, when more accurate demand information is available. We study the effect of this price decision delay on the optimal investments on dedicated and flexible capacity. Computational experiments show that considering price postponement at the planning stage leads to a large reduction in capacity investments, especially in the more expensive flexible capacity, and a significant increase in profits. Its impact depends on demand correlation, elasticity and diversion, ratio of fixed to variable capacity costs, and uncertainty remaining at the times the pricing and production decisions are made. [source] The pair-functional method for direct solution of molecular structures.ACTA CRYSTALLOGRAPHICA SECTION A, Issue 2 2001The new pair-functional direct method has been implemented and tested. Like the Patterson function, the pairing force has valuable imaging properties at high resolution. Two simple iterative algorithms were designed to refine on the total pair potential and the normalized intensity correlation coefficient of an atomic model. The first algorithm is a peak-picking method which selects the best-paired high peaks from a density map and then uses the strong reflections to generate a new Fourier filtered map. The second algorithm, the pair-and-square method, uses a tangent formula step instead of the Fourier and is a little more efficient. Computational experiments on a point-atom grid model, with perfect data, reached exact ab initio solutions for up to 600 atoms. Point-atom models were also solved by searching for reduced structures that contained as few as one quarter of the atoms. Seeded searches, guided by a small known fragment, solved up to 30000 atoms on the grid. Realistic tests on actual molecules showed that Sheldrick's [Acta Cryst. (1990), A46, 467,473] test structures of 50,200 atoms can be solved under a variety of conditions. [source] A numerical approach revealing the impact of rheological properties on mouthfeel caused by foodINTERNATIONAL JOURNAL OF FOOD SCIENCE & TECHNOLOGY, Issue 6 2007Katrin Mathmann Summary In contrast to the static chemoreceptor-related flavour perception, texture of food capable of flow is detected dynamically with oral mechanoreceptors while the food is manipulated in the mouth. The resulting sensation called mouthfeel strongly depends on the different physical properties of food. Aim of the current study is to determine numerically the occurring fluid mechanical forces in food suspensions using a simplified tongue-palate model system consisting of two parallel plates. For this purpose, the equations of fluid and particle motion are numerically solved by using structured overlapping grids. In the computational experiment, a density neutral fluid system between the plates is compressed by moving the upper plate with constant velocity down to the other one. It has been found that suspended particles move with the fluid flow but have only minor effect on the global flow field in the applied concentration. [source] Focusing on Customer Time in Field Service: A Normative ApproachPRODUCTION AND OPERATIONS MANAGEMENT, Issue 2 2007Aruna Apte Although customer convenience should be rightfully considered a central element in field services, the customer experience suggests that service enterprises rarely take the customer's preferred time into account in making operational and scheduling decisions. In this paper we present the results of our exploratory research into two interrelated topics: the explicit inclusion of customer time in nonemergency field service delivery decisions and the analysis of trade-off between the customer's convenience and field service provider's cost. Based on prior research in service quality we identify and illustrate two time-based performance metrics that are particularly appropriate for assessing service quality in nonemergency field services: performance and conformance quality. To determine vehicle routes, we develop a hybrid heuristic derived from the existing and proven heuristic methods. A numerical example closely patterned after real-life data is generated and used within a computational experiment to investigate alternate policies for promise time windows. Our experiment shows that over a reasonable range of customer cost parameters the policy of shorter promise time windows reduces the combined total cost incurred by the provider and the customers and should be considered a preferred policy by the field service provider. Managerial implications of this result are discussed. [source] Coordinated Capacitated Lot-Sizing Problem with Dynamic Demand: A Lagrangian HeuristicDECISION SCIENCES, Issue 1 2004E. Powell Robinson Jr. ABSTRACT Coordinated replenishment problems are common in manufacturing and distribution when a family of items shares a common production line, supplier, or a mode of transportation. In these situations the coordination of shared, and often limited, resources across items is economically attractive. This paper describes a mixed-integer programming formulation and Lagrangian relaxation solution procedure for the single-family coordinated capacitated lot-sizing problem with dynamic demand. The problem extends both the multi-item capacitated dynamic demand lot-sizing problem and the uncapacitated coordinated dynamic demand lot-sizing problem. We provide the results of computational experiments investigating the mathematical properties of the formulation and the performance of the Lagrangian procedures. The results indicate the superiority of the dual-based heuristic over linear programming-based approaches to the problem. The quality of the Lagrangian heuristic solution improved in most instances with increases in problem size. Heuristic solutions averaged 2.52% above optimal. The procedures were applied to an industry test problem yielding a 22.5% reduction in total costs. [source] Truck schedule recovery for solid waste collection in Porto Alegre, BrazilINTERNATIONAL TRANSACTIONS IN OPERATIONAL RESEARCH, Issue 5 2008Jing-Quan Li Abstract This paper considers a truck schedule recovery problem in the context of solid waste collection in the city of Porto Alegre, Brazil. When a truck on a scheduled trip breaks down, a backup truck needs to be selected to serve the cargo on that trip and other trucks might be rescheduled in order to gain the minimum operating and delay costs. The problem consists of designing, in the case of a severe disruption in a trip, new schedules taking into account the existing trucks in the system and a set of unfinished and not initiated collection trips, on which the trucks collect the solid waste in fixed routes and empty the loads in one of the several operational recycling facilities. The main objective is to minimize the total distances traveled and delay costs, as well as to obtain balanced assignments of truck unloads into the recycling facilities, due to the social benefits of the solid waste program. We modeled the problem as a mixed-integer linear problem and used CPLEX to solve it. Finally, computational experiments are conducted on real-world data. The results show that our approach successfully reduces the distances traveled and delays, simultaneously balancing the number of trucks unloading at each recycling facility, in comparison with the current manual strategy. [source] Tight bounds for the identical parallel machine-scheduling problem: Part IIINTERNATIONAL TRANSACTIONS IN OPERATIONAL RESEARCH, Issue 1 2008Mohamed Haouari Abstract A companion paper introduces new lower bounds and heuristics for the problem of minimizing makespan on identical parallel machines. The objective of this paper is threefold. First, we describe further enhancements of previously described lower bounds. Second, we propose a new heuristic that requires solving a sequence of 0,1 knapsack problems. Finally, we show that embedding these newly derived bounds in a branch-and-bound procedure yields a very effective exact algorithm. Moreover, this algorithm features a new symmetry-breaking branching strategy. We present the results of computational experiments that were carried out on a large set of instances and that attest to the efficacy of the proposed algorithm. In particular, we report proven optimal solutions for some benchmark problems that have been open for some time. [source] Tight bounds for the identical parallel machine scheduling problemINTERNATIONAL TRANSACTIONS IN OPERATIONAL RESEARCH, Issue 6 2006Mohamed Haouari Abstract We address the problem of minimizing makespan on identical parallel machines. We propose new lower bounding strategies and heuristics for this fundamental scheduling problem. The lower bounds are based on the so-called lifting procedure. In addition, two optimization-based heuristics are proposed. These heuristics require iteratively solving a subset-sum problem. We present the results of computational experiments that provide strong evidence that the new proposed lower and upper bounds consistently outperform the best bounds from the literature. [source] Production planning with resources subject to congestionNAVAL RESEARCH LOGISTICS: AN INTERNATIONAL JOURNAL, Issue 2 2009Jakob Asmundsson Abstract A fundamental difficulty in developing effective production planning models has been accurately reflecting the nonlinear dependency between workload and lead times. We develop a mathematical programming model for production planning in multiproduct, single stage systems that captures the nonlinear dependency between workload and lead times. We then use outer linearization of this nonlinear model to obtain a linear programming formulation and extend it to multistage systems. Extensive computational experiments validate the approach and compare its results to conventional models that assume workload-independent planning lead times. © 2009 Wiley Periodicals, Inc. Naval Research Logistics, 2009 [source] A logistics scheduling model: Inventory cost reduction by batchingNAVAL RESEARCH LOGISTICS: AN INTERNATIONAL JOURNAL, Issue 4 2005Xiangtong Qi Abstract Logistics scheduling refers to the problems where the decisions of job scheduling and transportation are integrated in a single framework. In this paper, we discuss a logistics scheduling model where the raw material is delivered to the shop in batches. By making the batching and scheduling decisions simultaneously, the total inventory and batch setup cost can be reduced. We study different models on this issue, present complexity analysis and optimal algorithms, and conduct computational experiments. Some managerial insights are observed. © 2005 Wiley Periodicals, Inc. Naval Research Logistics, 2005. [source] A branch and bound algorithm for computing optimal replacement policies in consecutive k -out-of- n -systemsNAVAL RESEARCH LOGISTICS: AN INTERNATIONAL JOURNAL, Issue 3 2002James Flynn Abstract This paper presents a branch and bound algorithm for computing optimal replacement policies in a discrete-time, infinite-horizon, dynamic programming model of a binary coherent system with n statistically independent components, and then specializes the algorithm to consecutive k -out-of- n systems. The objective is to minimize the long-run expected average undiscounted cost per period. (Costs arise when the system fails and when failed components are replaced.) An earlier paper established the optimality of following a critical component policy (CCP), i.e., a policy specified by a critical component set and the rule: Replace a component if and only if it is failed and in the critical component set. Computing an optimal CCP is a optimization problem with n binary variables and a nonlinear objective function. Our branch and bound algorithm for solving this problem has memory storage requirement O(n) for consecutive k -out-of- n systems. Extensive computational experiments on such systems involving over 350,000 test problems with n ranging from 10 to 150 find this algorithm to be effective when n , 40 or k is near n. © 2002 Wiley Periodicals, Inc. Naval Research Logistics 49: 288,302, 2002; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/nav.10017 [source] A column generation approach for SONET ring assignmentNETWORKS: AN INTERNATIONAL JOURNAL, Issue 3 2006Elder M. Macambira Abstract In this article we consider the SONET ring assignment problem (SRAP) presented in 7. The authors pointed out the inadequacy of solving SRAP instances using their integer programming formulation and commercial linear programming solvers. Similar experiences with IP models for SRAP are reported in 1. In this article we reformulate SRAP as a set partitioning model with an additional knapsack constraint. This new formulation has an exponential number of columns and, to solve it, we implemented a branch-and-price/column generation algorithm. Extensive computational experiments showed that the new algorithm is orders of magnitude faster than standard branch-and-bound codes running on compact IP models introduced earlier. Instances taken from 1, 7, which could not be solved there in hours of computation were solved here to optimality in just a few seconds. © 2006 Wiley Periodicals, Inc. NETWORKS, Vol. 47(3), 157,171 2006 [source] | |||||||||||||||||||