Solving multi-level capacitated lot-sizing problems is still a challenging task, in spite of increasing computational power and faster algorithms. In this paper a new approach combining an ant-based algorithm with an ...
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Solving multi-level capacitated lot-sizing problems is still a challenging task, in spite of increasing computational power and faster algorithms. In this paper a new approach combining an ant-based algorithm with an exact solver for (mixed-integer) linear programs is presented. A MAX-MIN ant system is developed to determine the principal production decisions, a LP/MIP solver is used to calculate the corresponding production quantities and inventory levels. Two different local search methods and an improvement strategy based on reduced mixed-integer problems are developed and integrated into the ant algorithm. This hybrid approach provides superior results for small and medium-sized problems in comparison to the existing approaches in the literature. For large-scale problems the performance of this method is among the best. (C) 2009 Elsevier B.V. All rights reserved.
This paper presents a new hybrid algorithm for a classical capacitated plant location problem. Benders' decomposition algorithm has been successfully applied in many areas. A major difficulty with this decompositi...
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This paper presents a new hybrid algorithm for a classical capacitated plant location problem. Benders' decomposition algorithm has been successfully applied in many areas. A major difficulty with this decomposition lies in the solution of master problem, which is a "hard" problem, costly to compute. Our proposed algorithm, instead of using a costly branch-and-bound method, incorporates a genetic algorithm to obtain "good" suboptimal solutions to the master problem at a tremendous saving in the computational effort. The performance of the proposed algorithm is tested on randomly generated data and also well-known existing data. The computational results indicate that the proposed algorithm is effective and efficient for the capacitated plant location problem and competitive with the Benders' decomposition algorithm. (C) 2010 Elsevier Ltd. All rights reserved.
Quantum key distribution (QKD) is regarded as a key-technology for the upcoming decades. Its practicability has been demonstrated through various experimental implementations. Wide-area QKD networks are a natural next...
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Quantum key distribution (QKD) is regarded as a key-technology for the upcoming decades. Its practicability has been demonstrated through various experimental implementations. Wide-area QKD networks are a natural next step and should inherit the selling point of provable security. However, most research in QKD focuses on point-to-point connections, leaving end-to-end security to the trustworthiness of intermediate repeater nodes, thus defeating any formal proof of security: why bother outwitting QKD, if the repeater node is an easy prey, and an equally valuable target? We discuss methods of designing QKD networks with provable end-to-end security at provably optimized efforts. We formulate two optimization problems, along with investigations of computational difficulty: First, what is the minimal cost for a desired security? Second, how much security is achievable under given (budget-)constraints? Both problems permit applications of commercial optimization software, so allow taking a step towards an economic implementation of a globally spanning QKD network.
This paper proposes a novel integrated model for yard truck and yard crane scheduling problems for loading operations in container terminal. The problem is formulated as a mixed-integer programming model. Due to the c...
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This paper proposes a novel integrated model for yard truck and yard crane scheduling problems for loading operations in container terminal. The problem is formulated as a mixed-integer programming model. Due to the computational intractability, two efficient solution methods, based on Benders' decomposition, are developed for problem solution;namely, the general Benders' cut-based method and the combinatorial Benders' cut-based method. Computational experiments are conducted to evaluate the effectiveness of the proposed solution methods. (C) 2009 Elsevier Ltd. All rights reserved.
When a branch and bound method is used to solve a linear mixedinteger program (MIP), the order in which the nodes of the branch and bound tree are explored significantly affects how quickly the MIP is solved. In this...
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When a branch and bound method is used to solve a linear mixedinteger program (MIP), the order in which the nodes of the branch and bound tree are explored significantly affects how quickly the MIP is solved. In this paper, new methods are presented that exploit correlation and distribution characteristics of branch and bound trees to trigger backtracking and to choose the next node to solve when backtracking. A new method is also presented that determines when the cost of using a node selection method outweighs its benefit, in which case it is abandoned in favor of a simpler method. Empirical experiments show that these proposed methods outperform the current state of the art. (C) 2009 Elsevier Ltd. All rights reserved.
We address in this article a problem that is of significance to the chemical industry, namely, the optimal design of a multi-echelon supply chain and the associated inventory systems in the presence of uncertain custo...
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We address in this article a problem that is of significance to the chemical industry, namely, the optimal design of a multi-echelon supply chain and the associated inventory systems in the presence of uncertain customer demands. By using the guaranteed service approach to model the multi-echelon stochastic inventory system, we develop an optimization model to simultaneously determine the transportation, inventory, and network structure of a multi-echelon supply chain. The model is an MINLP with a non-convex objective function including bilinear, trilinear, and square root terms. By exploiting the properties of the basic model, we reformulate this problem as a separable concave minimization program. A spatial decomposition algorithm based on the integration of Lagrangean relavation and piecewise linear approximation is proposed to obtain near global optimal solutions with reasonable computational expense. Examples for specialty chemicals and industrial gas supply chains with up to 15 plants, 100 potential distribution centers, and 200 markets are presented. (C) 2009 American Institute of Chemical Engineers AIChE J, 56: 419-440, 2010
We consider a network of cognitive users (also referred to as secondary users (SUs)) coexisting and sharing the spectrum with primary users (PUs) in an underlay cognitive radio network (CRN). Specifically, we consider...
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We consider a network of cognitive users (also referred to as secondary users (SUs)) coexisting and sharing the spectrum with primary users (PUs) in an underlay cognitive radio network (CRN). Specifically, we consider a CRN wherein the number of SUs requesting channel access exceeds the number of available frequency bands and spatial modes. In such a setting, we propose a joint fast optimal resource allocation and beamforming algorithm to accommodate maximum possible number of SUs while satisfying quality of service (QoS) requirement for each admitted SU, transmit power limitation at the secondary network basestation (SNBS) and interference constraints imposed by the PUs. Recognizing that the original user maximization problem is a nondeterministic polynomial-time hard (NP), we use a mixed-integer programming framework to formulate the joint user maximization and beamforming problem. Subsequently, an optimal algorithm based on branch and bound (BnB) method has been proposed. In addition, we propose a suboptimal algorithm based on BnB method to reduce the complexity of the proposed algorithm. Specifically, the suboptimal algorithm has been developed based on the first feasible solution it achieves in the fast optimal BnB method. Simulation results have been provided to compare the performance of the optimal and suboptimal algorithms.
In this paper, a strict formulation of a generalization of the classical pickup and delivery problem is presented. Here, we add the flexibility of providing the option for passengers to transfer from one vehicle to an...
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In this paper, a strict formulation of a generalization of the classical pickup and delivery problem is presented. Here, we add the flexibility of providing the option for passengers to transfer from one vehicle to another at specific locations. As part of the mathematical formulation we include transfer nodes where, vehicles may interact interchanging passengers. Additional variables to keep track of customers along their route are considered. The formulation has been proven to work correctly, and by means of a simple example instance, we conclude that there exist some configurations in which a scheme allowing transfers results in better quality optimal solutions. Finally, a solution method based on Benders decomposition is addressed. We compare the computational effort of this application with a straight branch and bound strategy;we also provide insights to develop more efficient set partitioning formulations and associated algorithms for solving real-size problems. (C) 2009 Elsevier B.V. All rights reserved.
Providing a good formulation is an important part of solving a mixed-integer *** suggest measuring the quality of a formulation by whether it is possible to strengthen the coefficients of the formulation. Sequentially...
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Providing a good formulation is an important part of solving a mixed-integer *** suggest measuring the quality of a formulation by whether it is possible to strengthen the coefficients of the formulation. Sequentially strengthening coefficients can then be used as a tool for improving *** believe this method could be useful for analyzing and producing tight formulations of problems that arise in *** illustrate the use of the approach on a problem in production scheduling. We also prove that coefficient strengthening leads to formulations with a desirable property: if no coefficient can be strengthened, then no constraint can be replaced by an inequality that dominates it. The effect of coefficient strengthening is tested on a number of problems in computational experiments. The strengthened formulations are compared to reformulations obtained by the preprocessor of a commercial software package. For several test problems, the formulations obtained by coefficient strengthening are substantially stronger than the formulations obtained by the preprocessor. In particular, we use coefficient strengthening to solve two difficult problems to optimality that have only recently been solved.
Decisions regarding natural gas production, processing and transportation depend on each other, and knowledge about how partial changes in a gas transmission network influence the network capacity and flexibility is c...
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Decisions regarding natural gas production, processing and transportation depend on each other, and knowledge about how partial changes in a gas transmission network influence the network capacity and flexibility is crucial in ensuring efficient system operation. SINTEF has developed a decision support tool, GassOpt, which is based on mixed-integer optimisation. The model objective is to maximise the flow throughput or profit for a given technical state of a natural gas network. The objective of this work has been to develop extensions to the GassOpt model mainly related to modelling of gas processing and energy consumption related to compression, and to analyse their impact on network operation. The extended GassOpt model represents and analyses a gas transport network in more detail, in particular in discovering bottlenecks, related to gas quality, contaminants and energy efficiency, which have obtained increased focus in recent time. GassOpt is a general tool for gas network optimisation, but applied on the Norwegian gas transport network specifically. The GassOpt tool is used to evaluate the current network as well as possible network extensions. Our approach ensures optimal operation of the network by considering the complete system and provides valuable insights in the dependencies between the different parts of the system. Tests show that the model represents actual network operation in a very good way. (C) 2010 Elsevier B.V. All rights reserved.
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