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Problem Instances (problem + instance)

Distribution by Scientific Domains
Business, Economics, Finance and Accounting45%
Mathematics and Statistics27%
Engineering18%

Selected Abstracts

Optimal integrated code generation for VLIW architectures

CONCURRENCY AND COMPUTATION: PRACTICE & EXPERIENCE, Issue 11 2006
Christoph Kessler
Abstract We present a dynamic programming method for optimal integrated code generation for basic blocks that minimizes execution time. It can be applied to single-issue pipelined processors, in-order-issue superscalar processors, VLIW architectures with a single homogeneous register set, and clustered VLIW architectures with multiple register sets. For the case of a single register set, our method simultaneously copes with instruction selection, instruction scheduling, and register allocation. For clustered VLIW architectures, we also integrate the optimal partitioning of instructions, allocation of registers for temporary variables, and scheduling of data transfer operations between clusters. Our method is implemented in the prototype of a retargetable code generation framework for digital signal processors (DSPs), called OPTIMIST. We present results for the processors ARM9E, TI C62x, and a single-cluster variant of C62x. Our results show that the method can produce optimal solutions for small and (in the case of a single register set) medium-sized problem instances with a reasonable amount of time and space. For larger problem instances, our method can be seamlessly changed into a heuristic. Copyright © 2006 John Wiley & Sons, Ltd. [source]

A Framework for Facilitating Sourcing and Allocation Decisions for Make-to-Order Items

DECISION SCIENCES, Issue 4 2004
Nagesh N. Murthy
ABSTRACT This paper provides a fundamental building block to facilitate sourcing and allocation decisions for make-to-order items. We specifically address the buyer's vendor selection problem for make-to-order items where the goal is to minimize sourcing and purchasing costs in the presence of fixed costs, shared capacity constraints, and volume-based discounts for bundles of items. The potential suppliers for make-to-order items provide quotes in the form of single sealed bids or participate in a dynamic auction involving open bids. A solution to our problem can be used to determine winning bids amongst the single sealed bids or winners at each stage of a dynamic auction. Due to the computational complexity of this problem, we develop a heuristic procedure based on Lagrangian relaxation technique to solve the problem. The computational results show that the procedure is effective under a variety of scenarios. The average gap across 2,250 problem instances is 4.65%. [source]

Multi-Period Planning of Survivable WDM Networks

EUROPEAN TRANSACTIONS ON TELECOMMUNICATIONS, Issue 1 2000
Mario Pickavet
This paper presents a new heuristic algorithm useful for long-term planning of survivable WDM networks. A multi-period model is formulated that combines network topology design and capacity expansion. The ability to determine network expansion schedules of this type becomes increasingly important to the telecommunications industry and to its customers. The solution technique consists of a Genetic Algorithm that allows to generate several network alternatives for each time period simultaneously and shortest-path techniques to deduce from these alternatives a least-cost network expansion plan over all time periods. The multi-period planning approach is illustrated on a realistic network example. Extensive simulations on a wide range of problem instances are carried out to assess the cost savings that can be expected by choosing a multi-period planning approach instead of an iterative network expansion design method. [source]

An online active set strategy to overcome the limitations of explicit MPC

INTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL, Issue 8 2008
H. J. Ferreau
Abstract Nearly all algorithms for linear model predictive control (MPC) either rely on the solution of convex quadratic programs (QPs) in real time, or on an explicit precalculation of this solution for all possible problem instances. In this paper, we present an online active set strategy for the fast solution of parametric QPs arising in MPC. This strategy exploits solution information of the previous QP under the assumption that the active set does not change much from one QP to the next. Furthermore, we present a modification where the CPU time is limited in order to make it suitable for strict real-time applications. Its performance is demonstrated with a challenging test example comprising 240 variables and 1191 inequalities, which depends on 57 parameters and is prohibitive for explicit MPC approaches. In this example, our strategy allows CPU times of well below 100 ms per QP and was about one order of magnitude faster than a standard active set QP solver. Copyright © 2007 John Wiley & Sons, Ltd. [source]

Sensitivity analysis of the knapsack sharing problem: perturbation of the profit of an item

INTERNATIONAL TRANSACTIONS IN OPERATIONAL RESEARCH, Issue 1 2008
T. Belgacem
Abstract In this paper, we study the sensitivity of the optimum of a max,min combinatorial optimization problem, namely the knapsack sharing problem, to the perturbation of the profit of an arbitrary item. We mainly establish the interval limits of each perturbed item by applying a reduction of the original problem into a series of single knapsack problems. We propose a solution procedure in order to establish these interval limits. The principle of the method is to stabilize the optimal solution in the perturbed problem, following two cases: (i) when the item belongs to an optimal class and (ii) when the item belongs to a non-optimal class. We also consider either the problem admits a unique or multiple optimal classes. Finally, we evaluate the effectiveness of the proposed method on several problem instances in the literature. [source]

Direct shipping logistic planning for a hub-and-spoke network with given discrete intershipment times

INTERNATIONAL TRANSACTIONS IN OPERATIONAL RESEARCH, Issue 1 2006
Libby Chong
Abstract This paper proposes a heuristic procedure to solve the problem of scheduling and routing shipments in a hybrid hub-and-spoke network, when a given set of feasible discrete intershipment times is given. The heuristic procedure may be used to assist in the cooperative operational planning of a physical goods network between shippers and logistics service provider, or to assist shippers in making logistics outsourcing decisions. The objective is to minimise the transportation and inventory holding costs. It is shown through a set of problem instances that this heuristic procedure provides better solutions than existing economic order quantity-based approaches. Computational results are presented and discussed. [source]

Approximate algorithms for the container loading problem

INTERNATIONAL TRANSACTIONS IN OPERATIONAL RESEARCH, Issue 6 2002
M. Hifi
In this paper we develop several algorithms for solving three,dimensional cutting/packing problems. We begin by proposing an adaptation of the approach proposed in Hifi and Ouafi (1997) for solving two,staged unconstrained two,dimensional cutting problems. We show how the algorithm can be polynomially solved for producing a constant approximation ratio. We then extend this algorithm for developing better approximate algorithms. By using hill,climbing strategies, we construct some heuristics which produce a good trade,off between the computational time and the solution quality. The performance of the proposed algorithms is evaluated on different problem instances of the literature, with different sizes and densities (a total of 144 problem instances). [source]

A generalization of the weighted set covering problem

NAVAL RESEARCH LOGISTICS: AN INTERNATIONAL JOURNAL, Issue 2 2005
Jian Yang
Abstract We study a generalization of the weighted set covering problem where every element needs to be covered multiple times. When no set contains more than two elements, we can solve the problem in polynomial time by solving a corresponding weighted perfect b -matching problem. In general, we may use a polynomial-time greedy heuristic similar to the one for the classical weighted set covering problem studied by D.S. Johnson [Approximation algorithms for combinatorial problems, J Comput Syst Sci 9 (1974), 256,278], L. Lovasz [On the ratio of optimal integral and fractional covers, Discrete Math 13 (1975), 383,390], and V. Chvatal [A greedy heuristic for the set-covering problem, Math Oper Res 4(3) (1979), 233,235] to get an approximate solution for the problem. We find a worst-case bound for the heuristic similar to that for the classical problem. In addition, we introduce a general type of probability distribution for the population of the problem instances and prove that the greedy heuristic is asymptotically optimal for instances drawn from such a distribution. We also conduct computational studies to compare solutions resulting from running the heuristic and from running the commercial integer programming solver CPLEX on problem instances drawn from a more specific type of distribution. The results clearly exemplify benefits of using the greedy heuristic when problem instances are large. © 2003 Wiley Periodicals, Inc. Naval Research Logistics, 2005 [source]

Upper bounds for single-source uncapacitated concave minimum-cost network flow problems

NETWORKS: AN INTERNATIONAL JOURNAL, Issue 4 2003
Dalila B. M. M. Fontes
Abstract In this paper, we describe a heuristic algorithm based on local search for the Single-Source Uncapacitated (SSU) concave Minimum-Cost Network Flow Problem (MCNFP). We present a new technique for creating different and informed initial solutions to restart the local search, thereby improving the quality of the resulting feasible solutions (upper bounds). Computational results on different classes of test problems indicate the effectiveness of the proposed method in generating basic feasible solutions for the SSU concave MCNFP very near to a global optimum. A maximum upper bound percentage error of 0.07% is reported for all problem instances for which an optimal solution has been found by a branch-and-bound method. © 2003 Wiley Periodicals, Inc. [source]

Network flow models for designing diameter-constrained minimum-spanning and Steiner trees

NETWORKS: AN INTERNATIONAL JOURNAL, Issue 3 2003
Luis Gouveia
Abstract We formulate and computationally test several models for the Diameter-Constrained Minimum Spanning and Steiner Tree Problems, which seek a least-cost spanning or Steiner tree subject to a (diameter) bound imposed on the number of edges in the tree between any node pair. A traditional multicommodity flow model with a commodity for every pair of nodes was unable to solve a 20-node and 100-edge spanning tree problem after 1 week of computation. In contrast, the new models were able to optimality solve this problem in less than 1 second and larger problem instances with up to 100 nodes and 1000 edges. The largest model contains more than 250,000 integer variables and more than 125,000 constraints. The new models simultaneously find a directed tree with a central node or a central edge that serve as a source for the commodities in a multicommodity flow model with hop constraints. Our results demonstrate the power of using single-sourcing combined with other reformulation techniques: directing the model and using hop-indexed formulations. Enhancements improve the models when the diameter bound is odd (these situations are more difficult to solve). The linear programming relaxation of the best formulations discussed in this paper always give an optimal integer solution for two special, polynomially solvable cases of the problem. © 2003 Wiley Periodicals, Inc. [source]