Showing papers on "Assignment problem published in 2000"

A Linear Programming Model for the Single Destination System Optimum Dynamic Traffic Assignment Problem

Abstract: Recently, Daganzo introduced the cell transmission model--a simple approach for modeling highway traffic flow consistent with the hydrodynamic model. In this paper, we use the cell transmission model to formulate the single destination System Optimum Dynamic Traffic Assignment (SO DTA) problem as a Linear Program (LP). We demonstrate that the model can obtain insights into the DTA problem, and we address various related issues, such as the concept of marginal travel time in a dynamic network and system optimum necessary and sufficient conditions. The model is limited to one destination and, although it can account for traffic realities as they are captured by the cell transmission model, it is not presented as an operational model for actual applications. The main objective of the paper is to demonstrate that the DTA problem can be modeled as an LP, which allows the vast existing literature on LP to be used to better understand and compute DTA. A numerical example illustrates the simplicity and applicability of the proposed approach.

Strategyproof assignment by hierarchical exchange

Abstract: We give a characterization of the set of group-strategyproof, Pareto-optimal, and reallocation-proof allocation rules for the assignment problem, where individuals are assigned at most one indivisible object, without any medium of exchange. Although there are no property rights in the model, the rules satisfying the above criteria imitate a trading procedure with individual endowments, in which individuals exchange objects from their hierarchically determined endowment sets in an iterative manner. In particular, these assignment rules generalize Gale's top trading cycle procedure, the classical rule for the model in which each individual owns an indivisible good.

On the power assignment problem in radio networks

Abstract: Given a finite set S of points (i.e. the stations of a radio network) on a d-dimensional Euclidean space and a positive integer 1 ≤ h ≤ |S| - 1, the MIN d D h-RANGE ASSIGNMENT problem consists of assigning transmission ranges to the stations so as to minimize the total power consumption, provided that the transmission ranges of the stations ensure the communication between any pair of stations in at most h hops.Two main issues related to this problem are considered in this paper: the trade-off between the power consumption and the number of hops; the computational complexity of the MIN dD h-RANGE ASSIGNMENT problem.As for the first question, we provide a lower bound on the minimum power consumption of stations on the plane for constant h. The lower bound is a function of |S|, h and the minimum distance over all the pairs of stations in S. Then, we derive a constructive upper bound as a function of |S|, h and the maximum distance over all pairs of stations in S (i.e. the diameter of S). It turns out that when the minimum distance between any two stations is "not too small" (i.e. well spread instances) the upper bound matches the lower bound. Previous results for this problem were known only for very special 1-dimensional configurations (i.e., when points are arranged on a line at unitary distance) [Kirousis, Kranakis, Krizanc and Pelc, 1997].As for the second question, we observe that the tightness of our upper bound implies that MIN 2D h-RANGE ASSIGNMENT restricted to well spread instances admits a polynomial time approximation algorithm. Then, we also show that the same approximation result can be obtained for random instances. On the other hand, we prove that for h=|S|-1 (i.e. the unbounded case) MIN 2D h-RANGE ASSIGNMENT is NP-hard and MIN 3D h-RANGE ASSIGNMENT is APX-complete.

A stochastic transit assignment model considering differences in passengers utility functions

Abstract: The paper presents a framework for public traffic assignment that builds on the probit-based model of Sheffi and Powell [Sheffi, Y., Powell, W.B., 1981. A comparison of stochastic and deterministic traffic assignment over congested networks. Transportation Res. B. 15 (1), 53–64; Sheffi, Y., Powell, W.B., 1982. An algorithm, for the equilibrium assignment problem with random link Times. Networks 12 (2), 191–207.]. Hereby, the problems with overlapping routes that occur in many public transport models can be avoided. The probit-based model with modifications similar to the principles in Nielsen [Nielsen, O.A., 1996. Do stochastic traffic assignment models consider differences in road users utility functions? Twentyfourth European Transport Forum (PTRC Annual Meeting). London, UK, Seminar M.] is used as a starting point. This makes it possible to describe passengers’ different preferences towards different sub-modes and against transfers. This also considers dependencies of choices through chains of sub-modes. The simulation of perceived travel times is extended to describe differences in the distribution of travel- and waiting times for different sub-modes. Parallel lines are frequency aggregated in order to handle waiting times appropriately. Initial tests on a full-scale case show that the methodology can describe route choices in public transport very well. This is both due to the model’s ability to describe overlapping routes and due to the many different coefficients, error components and distributions that make it possible to calibrate the model. In practice, the many parameters might also be the main weakness, since this complicates the calibration. At the end of the paper, proposals to coefficients are presented based on a Danish SP-analysis. This demonstrated the applicability of the method.

Traffic equilibrium problem with route-specific costs: Formulation and algorithms

Abstract: Using a new gap function recently proposed by Facchinei and Soares [Facchinei, F., Soares, J., 1995. Testing a new class of algorithms for nonlinear complementarity problems. In: Giannessi, F., Maugeri, A. (Eds.), Variational Inequalities and Network Equilibrium Problems. Plenum Press, New York], we convert the nonlinear complementarity problem (NCP) formulation for the traffic equilibrium problem to an equivalent unconstrained optimization. This equivalent formulation uses both route flows and the minimum origin–destination travel costs as the decision variables. Two unique features of this formulation are that: (i) it can model the traffic assignment problem with a general route cost structure; (ii) it is smooth, unconstrained, and that every stationary point of the minimization corresponds to a global minimum. These properties permit a number of efficient algorithms for its solution. Two solution approaches are developed to solve the proposed formulation. Numerical results using a route-specific cost structure are provided and compared with the classic traffic equilibrium problem, which assumes an additive route cost function.

A Benders Decomposition Approach for the Locomotive and Car Assignment Problem

Abstract: One of the many problems faced by rail transportation companies is to optimize the utilization of the available stock of locomotives and cars. In this paper, we describe a decomposition method for the simultaneous assignment of locomotives and cars in the context of passenger transportation. Given a list of train legs and a fleet composed of several types of equipment, the problem is to determine a set of minimum cost equipment cycles such that every leg is covered using appropriate equipment. Linking constraints, which appear when both locomotives and cars are treated simultaneously, lead to a large integer programming formulation. We propose an exact algorithm, based on the Benders decomposition approach, that exploits the separability of the problem. Computational experiments carried on a number of real-life instances indicate that the method finds optimal solutions within short computing times. It also outperforms other approaches based on Lagrangian relaxation or Dantzig--Wolfe decomposition, as well as a simplex-based branch-and-bound method.

Continuous learning automata solutions to the capacity assignment problem

Abstract: The Capacity Assignment (CA) problem focuses on finding the best possible set of capacities for the links that satisfies the traffic requirements in a prioritized network while minimizing the cost. Most approaches consider a single class of packets flowing through the network, but, in reality, different classes of packets with different packet lengths and priorities are transmitted over the networks. In this paper, we assume that the traffic consists of different classes of packets with different average packet lengths and priorities. We shall look at three different solutions to this problem. K. Marayuma and D.T. Tang (1977) proposed a single algorithm composed of several elementary heuristic procedures. A. Levi and C. Ersoy (1994) introduced a simulated annealing approach that produced substantially better results. In this paper, we introduce a new method which uses continuous learning automata to solve the problem. Our new schemes produce superior results when compared with either of the previous solutions and is, to our knowledge, currently the best known solution.

Robust pole assignment via Sylvester equation based state feedback parametrization

Abstract: By using a Sylvester equation based parametrization, the minimum norm robust pole assignment problem for linear time-invariant systems is formulated as an unconstrained minimization problem for a suitably chosen cost function. The derived explicit expression of the gradient of the cost function allows the efficient solution of the minimization problem by using powerful gradient search based minimization techniques. We also discuss how requirements for a particular Jordan structure of the closed-loop state matrix or for partial pole assignment can be accommodated with the proposed approach.

Traffic engineering using multiple multipoint-to-point LSPs

Abstract: Traffic engineering aims to optimize the utilization of existing network resources for load balance and failure recovery, and these are to be accomplished in a scalable fashion. This paper proposes a traffic engineering scheme using multiple multipoint-to-point (m-t-p) label switched paths (LSP) which can reduce the number of LSP and required labels in links. The scheme consists of m-t-p LSP creation and flow assignment. Routes are first selected, and m-t-p LSP are designed to include them. The m-t-p LSP design problem is formulated as a 0-1 integer programming problem. The flow assignment problem is formulated as a mixed integer programming problem in which maximum link load, i.e., maximum congestion, is minimized. Numerical comparisons with the conventional point-to-point LSP approach show that the m-t-p LSP approach can reduce the number of required LSP and labels. Moreover, numerical comparisons with conventional shortest path fast-based flow assignment show that our flow assignment scheme can reduce maximum link load.

Nonlinear assignment problems : algorithms and applications

Abstract: List of Figures. List of Tables. Preface. Contributing Authors. Introduction P. Pardalos, L. Pitsoulis. 1. Multi Index Assignment Problems: Complexity, Approximation, Applications F.C.R. Spieksma. 2. MD Assignment of Data Association A.B. Poore. 3. Target-Based Weapon Target Assignment Problems R.A. Murphey. 4. The Nonlinear Assignment Problem in Experimental High Energy Physics J.-F. Pusztaszeri. 5. Three Index Assignment Problem L. Qi, D. Sun. 6. Polyhedral Methods for the QAP V. Kaibel. 7. Semidefinite Programming Approaches to the Quadratic Assignment Problem H. Wolkowicz. 8. Heuristics for Nonlinear Assignment Problems S. Voss. 9. Symbolic Scheduling of Parameterized Task Graphs on Parallel Machines M. Cosnard, et al. 10. Decomposition Algorithms for Communication Minimization in Parallel Computing I.T. Christou, R.R. Meyer.

Performance of the MOSA Method for the Bicriteria Assignment Problem

Abstract: The classical linear Assignment problem is considered with two objectives. The aim is to generate the set of efficient solutions. An exact method is first developed based on the two-phase approach. In the second phase a new upper bound is proposed so that larger instances can be solved exactly. The so-called MOSA (Multi-Objective Simulated Annealing) is then recalleds its efficiency is improved by initialization with a greedy approach. Its results are compared to those obtained with the exact method. Extensive numerical experiments have been realized to measure the performance of the MOSA method.

Robust and minimum norm pole assignment with periodic state feedback

Abstract: A computational approach is proposed to solve the minimum norm or robust pole assignment problem for linear periodic discrete-time systems. The proposed approach uses a periodic Sylvester-equation-based parametrization of the periodic pole assignment problem and exploits the nonuniqueness of the problem by imposing conditions on the norm of the resulting periodic state feedback or on the condition numbers of the periodic eigenvector matrices of the closed-loop system. The solution method relies on using gradient search methods on suitably defined cost functions. Explicit expressions of the gradients of cost functions are derived, and the efficient evaluation of the cost functions and gradients is discussed. Numerical examples illustrate the effectiveness of the proposed approach.

A New Heuristic for the Traveling Salesman Problem with Time Windows

Abstract: The aim of this paper is to present a new heuristic method for the Traveling Salesman Problem with Time Windows, based on the solution of an auxiliary problem. The idea is to solve an assignment problem with an ad hoc objective function to obtain a solution close enough to a feasible solution of the original problem. Given this solution, made by a long main tour containing the depot and few small subtours, it is easy to insert all the subtours into the main path using a greedy insertion procedure. The algorithm described applies the proposed constructive scheme and then uses a local search procedure to improve the initial solution. The computational results show the effectiveness of this approach.

On the wavelength assignment problem in multifiber WDM star and ring networks

Abstract: This paper studies the off-line wavelength assignment problem in star and ring networks that deploy multiple fibers between nodes and use wavelength division multiplexing (WDM) for transmission. The results in this paper show that the ability to switch between fibers increases wavelength utilization. In particular, sharper per-fiber bounds on the number of required wavelengths are derived for the multifiber version of the assignment problem in star and ring networks. Additionally, the complexity of the problem is studied and several constrained versions of the problem are also considered for star and ring networks. A summary of contributions is provided in the first section.

The Minimum Range Assignment Problem on Linear Radio Networks

Abstract: Given a set S of radio stations located on a line and an integer h (1 ≤ h ≤ |S| - 1), the Min Assignment problem is to find a range assignment of minimum power consumption provided that any pair of stations can communicate in at most h hops. Previous positive results for this problem were known only when h = |S| - 1 (i.e. the unbounded case) or when the stations are equally spaced (i.e. the uniform chain). In particular, Kirousis, Kranakis, Krizanc and Pelc (1997) provided an efficient exact solution for the unbounded case and efficient approximated solutions for the uniform chain, respectively. This paper presents the first polynomial time, approximation algorithm for the Min Assignment problem. The algorithm guarantees an approximation ratio of 2 and runs in time O(hn3). We also prove that, for constant h and for "well spread" instances (a broad generalization of the uniform chain case), we can find a solution in time O(hn3) whose cost is at most an (1 + Ɛ(n)) factor from the optimum, where Ɛ(n) = o(1) and n is the number of stations. This result significantly improves the approximability result by Kirousis et al on uniform chains. Both of our approximation results are obtained by new algorithms that exactly solves two natural variants of the Min Assignment problem that might have independent interest: the All-To-One problem (in which every station must reach a fixed one in at most h hops) and the Base Location problem (in which the goal is to select a set of Basis among the stations and all the other stations must reach one of them in at most h -1 hops). Finally, we show that for h = 2 the Min Assignment problem can be solved in O(n3)-time.

A generalized assignment problem with special ordered sets: a polyhedral approach

Abstract: We study a generalized assignment problem that arises in production scheduling in which special ordered sets of type II appear naturally in the formulation. We derive three families of facet-defining valid inequalities, and we show that they cut off all infeasible vertices of the LP relaxation. We also give the complete facetial description for a particular case. We then use the inequalities as cuts in a branch-and-cut scheme, and we report computational results that demonstrate the superiority of branch-and-cut over branch-and-bound on this class of problems.

Adaptive Labeling Algorithms for the Dynamic Assignment Problem

Abstract: We consider the problem of dynamically routing a driver to cover a sequence of tasks (with no consolidation), using a complex set of driver attributes and operational rules Our motivating application is dynamic routing and scheduling problems, which require fast response times, the ability to handle a wide range of operational concerns, and the ability to output multiple recommendations for a particular driver A mathematical formulation is introduced that easily handles real-world operational complexities Two new optimization-based heuristics are described, one giving faster performance and the second providing somewhat higher solution quality Comparisons to optimal solutions are provided, which measure the quality of the solutions that our algorithms provide Experimental tests show that our algorithms provide high quality solutions, and are fast enough to be run in real-time applications

Scheduling multirate sessions in time division multiplexed wavelength-routing networks

Abstract: We consider multiwavelength wavelength-routing networks operating in circuit-switched mode. Wavelength utilization is poor in such networks if sessions require only a fraction of a wavelength's capacity. An all-optical approach to improve wavelength utilization is to use time division multiplexing (TDM) on each wavelength, and switch time slots and wavelengths. In this paper, we address the off-line multirate session scheduling problem, i.e., the problem of assigning time slots and wavelengths to a given static set of multirate sessions, in ring topologies. Given a set of sessions and their relative rates, our objective is to maximize network throughput. This objective translates to the problem of minimizing the maximum length of a TDM frame over all wavelengths. We first show that the off-line single-rate session scheduling problem is equivalent to the off-line wavelength assignment problem, and hence obtain bounds on frame length. We then present scheduling algorithms with provable worst-case bounds on frame length for multirate session scheduling.

Wavelength Assignment Problem on All-Optical Networks with k Fibres per Link

Abstract: Given a (possibly directed) network, the wavelength assignment problem is to minimize the number of wavelengths that must be assigned to communication paths so that paths sharing an edge are assigned different wavelengths. Our generalization to multigraphs with k parallel edges for each link (k fibres per link, with switches at nodes) may be of practical interest. While the wavelength assignment problem is NP-hard, even for a single fibre, and even in the case of simple network topologies such as rings and trees, the new model suggests many nice combinatorial problems, some of which we solve. For example, we show that for many network topologies, such as rings, stars, and specific trees, the number of wavelengths needed in the k-fibre model is less than 1/k fraction of the number required for a single fibre. We also study the existence and behavior of a gap between the minimum number of wavelengths and the natural lower bound of network congestion, the maximum number of communication paths sharing an edge. For optical stars (any size) while there is a 3/2 gap in the single fibre model, we show that with 2 fibres the gap is 0, and present a polynomial time algorithm that finds an optimal assignment. In contrast, we show that there is no fixed constant k such that for every ring and every set of communication paths the gap can be eliminated. A similar statement holds for trees. However, for rings, the gap can be made arbitrarily small, given enough fibres. The gap can even be eliminated, if the length of communication paths is bounded by a constant. We show the existence of anomalies: increasing the number of fibres may increase the gap.

Low-power state assignment techniques for finite state machines

Abstract: The problem of minimizing the power consumption in synchronous sequential circuits is explored in this paper. We present a general theoretical framework to solve the state assignment problem for Finite State Machines (FSMs). In this framework, the problem has been separated in two different tasks. First, we define heuristic techniques to visit the State Transition Graph (STG) and thus to assign a priority to the symbolic states. Second, we define encoding techniques to assign binary codes to the symbolic states to reduce the switching activity of state registers. Based on this approach, we propose five power-oriented state assignment algorithms. These techniques have been applied to MCNC benchmark circuits and the experimental results have shown an average reduction in transition activity (power) of 8.56% (5.35%) over well-known low-power state encoding schemes.

High fidelity interval assignment

Abstract: Quadrilateral meshing algorithms impose certain constraints on the number of intervals or mesh edges of the curves bounding a surface. When constructing a conformal mesh of a collection of adjoining surfaces, the constraints for all of the surfaces must be simultaneously satisfied. These constraints can be formulated as an integer linear program. Not all solutions to this problem are equally desirable, however. The user typically indicates a goal (soft-set) or required (hard-set) number of intervals for each curve. The hard-sets constrain the problem further, while the soft-sets influence the objective function. This paper describes an algorithm for solving this interval assignment problem. In a good solution, for each curve the positive or negative difference between its goal and assigned number of intervals is small relative to its number of goal intervals. The algorithm solves a series of linear programs, and comes close to minimizing the maximum lexicographic vector of these weighted differences. Then the algorithm solves a nearby mixed-integer linear program to satisfy certain "sum-even" constraints. The algorithm reliably produces numbers of intervals that are very close to the user's desires and is easily extendible to new constraints. Earlier versions of the algorithm1 were slower than alternative algorithms, but this is no longer a significant issue; in practice, the running time is a minor fraction of the time to mesh, even in models composed of thousands of curves.

Approximation and complexity in numerical optimization : continuous and discrete problems

Abstract: Preface. Navigating Graph Surfaces J. Abello, S. Krishnan. The Steiner Ratio of Lp-planes J. Albrecht, D. Cieslik. Hamiltonian Cycle Problem via Markov Chains and Min-type Approaches M. Andramonov, et al. Solving Large Scale Uncapacitated Facility Location Problems F. Barahona, F. Chudak. A Branch - and - Bound Procedure for the Largest Clique in a Graph E.R. Barnes. A New 'Annealed' Heuristic for the Maximum Clique Problem I.M. Bomze, et al. Inapproximability of some Geometric and Quadratic Optimization Problems A. Brieden, et al. Convergence Rate of the P-Algorithm for Optimization of Continious Functions J.M. Calvin. Application of Semidefinite Programming to Circuit Partitioning C.C. Choi, Y. Ye. Combinatorial Problems Arising in Deregulated Electrical Power Industry: Survey and Future Directions D. Cook, et al. On Approximating a Scheduling Problem P. Crescenzi, et al. Models and Solution for On-Demand Data Delivery Problems M.C. Ferris, R.R. Meyer. Complexity and Experimental Evaluation of Primal-Dual Shortest Path Tree Algorithms P. Festa, et al. Machine Partitioning and Scheduling under Fault-Tolerance Constraints D.A. Fotakis, P.G. Spirakis. Finding Optimal Boolean Classifiers J. Franco. Tighter Bounds on the Performance of First Fit Bin Packing M. Furer. Block Exchange in Graph Partitioning W.W. Hager, et al. On the Efficient Approximability of 'HARD' Problems A Survey H.B. Hunt III, et al. Exceptional Family of Elements, Feasibility, Solvability and Continuous Paths of epsilon-Solutions for Nonlinear Complementarity Problems G. Isac. Linear Time Approximation Schemes for Shop Scheduling Problems K. Jansen, et al. On Complexity and Optimization in EmergentComputation V. Korotkich. Beyond Interval Systems: What Is Feasible and What Is Algorithmically Solvable? V. Kreinovich. A Lagrangian Relaxation of the Capacitated Multi-Item Lot Sizing Problem Solved with an Interior Point Cutting Plante Algorithm O. du Merle, et al. An Approximate Algorithm For a Weapon Target Assignment Stochastic Program R.A. Murphey. Continuous-based Heuristics for Graph and Tree Isomorphisms, with Application to Computer Vision M. Pelillo, et al. Geometric Optimization Problems for Steiner Minimal Trees in E3 J. MacGregor Smith. Optimization of a Simplified Assignment Problem with Metaheuristics: Simulated Annealing and GRASP D. Sosnowska. Towards Implementations of Successive Convex Relaxation Methods for Nonconvex Quadratic Optimization Problems A. Takeda, et al. Piecewise Concavity and Discrete Approaches to Continuous Minimax Problems F. Tardella. The MCCNF Problem with a Fixed Number of Nonlinear Arc Costs: Complexity and Approximation H. Tuy. A New Parametrization Algorithm for the Linear Complementarity Problem S. Verma, et al. Obtaining an Approximate Solution for Quadratic Maximization Problems Y. Yajima.

Genetic algorithm in uncertain environments for solving stochastic programming problem

Abstract: Many real problems with uncertainties may often be formulated as Stochastic Programming Problem. In this study, Genetic Algorithm (GA) which has been recently used for solving mathematical programming problem is expanded for use in uncertain environments. The modified GA is referred as GA in uncertain environments (GAUCE). In the method, the objective function and/or the constraint are fluctuated according to the distribution functions of their stochastic variables. Firstly, the individual with highest frequency through all generations is nominated as the individual associated with the solution presenting the best expected value of objective function. The individual with highest frequency is associated with the solution by GAUCE. The proposed method is applied to Stochastic Optimal Assignment Problem, Stochastic Knapsack Problem and newly formulated Stochastic Image Compression Problem. Then, it has been proved that the solution by GAUCE has excellent agreement with the solution presenting the best expected value of objective function, in cases of both Stochastic Optimal Assignment Problem and Stochastic Knapsack Problem. GAUCE is also successfully applied to Stochastic Image Compression Problem where the coefficients of discrete cosine transformation are treated as stochastic variables.

Analysis, eigenstructure assignment and H/sub 2/ multichannel synthesis with enhanced LMI characterizations

Abstract: This paper describes a new framework for the analysis and synthesis of control systems, which constitutes a genuine continuous-time extension of results that are only available in discrete time. In contrast to earlier results the proposed methods involve a specific transformation on the Lyapunov variables and a reciprocal variant of the projection lemma, in addition to the classical linearizing transformations on the controller data. For a wide range of problems including robust analysis and synthesis, multichannel H/sub 2/ stateand output-feedback syntheses, the approach leads to potentially less conservative LMI characterizations. This comes from the fact that the technical restriction of using a single Lyapunov function is to some extent ruled out in this new approach. Moreover, the approach offers new potentials for problems that cannot be handled using earlier techniques. As an instance, the eigenstructure assignment problem blended with Lyapunov-type constraints is given a simple and tractable formulation.