Showing papers on "Assignment problem published in 1995"
TL;DR: This article shows how the evolution of multi-commodity traffic flows over complex networks can be predicted over time, based on a simple macroscopic computer representation of traffic flow that is consistent with the kinematic wave theory under all traffic conditions.
Abstract: This article shows how the evolution of multi-commodity traffic flows over complex networks can be predicted over time, based on a simple macroscopic computer representation of traffic flow that is consistent with the kinematic wave theory under all traffic conditions. The method does not use ad hoc procedures to treat special situations. After a brief review of the basic model for one link, the article describes how three-legged junctions can be modeled. It then introduces a numerical procedure for networks, assuming that a time-varying origin-destination (O-D) table is given and that the proportion of turns at every junction is known. These assumptions are reasonable for numerical analysis of disaster evacuation plans. The results are then extended to the case where, instead of the turning proportions, the best routes to each destination from every junction are known at all times. For technical reasons explained in the text, the procedure is more complicated in this case, requiring more computer memory and more time for execution. The effort is estimated to be about an order of magnitude greater than for the static traffic assignment problem on a network of the same size. The procedure is ideally suited for parallel computing. It is hoped that the results in the article will lead to more realistic models of freeway flow, disaster evacuations and dynamic traffic assignment for the evening commute.
1,891 citations
TL;DR: This model of the fleet assignment problem is a large multi-commodity flow problem with side constraints defined on a time-expanded network, and the algorithm found solutions with a maximum optimality gap of 0.02% and is more than two orders of magnitude faster than using default options of a standard LP-based branch-and-bound code.
Abstract: Given a flight schedule and set of aircraft, the fleet assignment problem is to determine which type of aircraft should fly each flight segment. This paper describes a basic daily, domestic fleet assignment problem and then presents chronologically the steps taken to solve it efficiently. Our model of the fleet assignment problem is a large multi-commodity flow problem with side constraints defined on a time-expanded network. These problems are often severely degenerate, which leads to poor performance of standard linear programming techniques. Also, the large number of integer variables can make finding optimal integer solutions difficult and time-consuming. The methods used to attack this problem include an interior-point algorithm, dual steepest edge simplex, cost perturbation, model aggregation, branching on set-partitioning constraints and prioritizing the order of branching. The computational results show that the algorithm finds solutions with a maximum optimality gap of 0.02% and is more than two orders of magnitude faster than using default options of a standard LP-based branch-and-bound code.
420 citations
15 Feb 1995
TL;DR: This study is a probabilistic approach to the measurement-to-track assignment problem, where measurements are not assigned to tracks as in traditional multi-hypothesis tracking algorithms; Instead, the probability that each measurement belongs to each track is estimated using a maximum a posteriori (MAP) method.
Abstract: : In a multitarget, multimeasurement environment, knowledge of the measurement-to-track assignments is typically unavailable to the tracking algorithm This study is a probabilistic approach to the measurement-to-track assignment problem Measurements are not assigned to tracks as in traditional multi-hypothesis tracking (MHT) algorithms; Instead, the probability that each measurement belongs to each track is estimated using a maximum a posteriori (MAP) method These measurement-to-track probability estimates are intrinsic to the multitarget tracker called the probabilistic multi-hypothesis tracking (PMHT) algorithm The PMHT algorithm is computationally practical because it requires neither enumeration of measurement-to-track assignments nor pruning The PMHT algorithm is an optimal MAP multitarget tracking algorithm (AN)
284 citations
TL;DR: In this paper, the authors present a rolling horizon framework for addressing the real-time traffic assignment problem, where an ATIS/ATMS controller is assumed to have O-D desires up to the current time interval, and short-term and medium-term forecasts of future O -D desires.
Abstract: Existing dynamic traffic assignment formulations predominantly assume the timedependent O-D trip matrix and the time-dependent network configuration to be known a priori for the entire planning horizon. However, there is also a need to provide real-time path information to network users under ATIS/ATMS when unpredicted variations in O-D desires and/or network characteristics (e.g. capacity reduction on certain links due to incidents) occur. This paper presents a rolling horizon framework for addressing the real-time traffic assignment problem, where an ATIS/ATMS controller is assumed to have O-D desires up to the current time interval, and short-term and mediumerm forecasts of future O-D desires. The assignment problem is solved in quasi-real time for a near-term future duration (or stage) to determine an optimal path assignment scheme for users entering the network in real-time for the short-term roll period. The resulting model is intricate due to the intertemporal dependencies characterizing this problem. Two formulations are discussed based on whether a capability to reroute vehicles en route exists. A rolling horizon solution procedure amenable to a quasi-real time implementation of a multiple user classes (MUC) time-dependent traffic assignment solution algorithm developed previously by the authors is described. Implementation issues are discussed from the perspective of ATIS/ATMS applications.
217 citations
TL;DR: This paper presents a novel divide-and-conquer algorithm in which a large global optimization problem is replaced by a sequence of smaller ones, and describes an implementation and some results of its performance on a sample molecule.
Abstract: The molecule problem is that of determining the relative locations of a set of objects in Euclidean space relying only upon a sparse set of pairwise distance measurements. This NP-hard problem has applications in the determination of molecular conformation. The molecule problem can be naturally expressed as a continuous, global optimization problem, but it also has a rich combinatorial structure. This paper investigates how that structure can be exploited to simplify the optimization problem. In particular, we present a novel divide-and-conquer algorithm in which a large global optimization problem is replaced by a sequence of smaller ones. Since the cost of the optimization can grow exponentially with problem size, this approach holds the promise of a substantial improvement in performance. Our algorithmic development relies upon some recently published results in graph theory. We describe an implementation of this algorithm and report some results of its performance on a sample molecule.
192 citations
TL;DR: A general theoretic framework for the solution of the state assignment problem is formulated, and different algorithms trading off computational effort for quality are proposed, resulting in a 16% average reduction in switching activity.
Abstract: We address the problem of reducing the power dissipated by synchronous sequential circuits. We target the reduction of the average switching activity of the input and output state variables by minimizing the number of bit changes during state transitions. Using a probabilistic description of the finite state machines, we propose a state assignment algorithm that minimizes the Boolean distance between the codes of the states with high transition probability. We formulate a general theoretic framework for the solution of the state assignment problem, and propose different algorithms trading off computational effort for quality. We then generalize our model to take into account the estimated area of a multilevel implementation during state assignment, in order to obtain final circuits where the total power dissipation is minimized. A heuristic algorithm has been implemented and applied to standard benchmarks, resulting in a 16% average reduction in switching activity. >
164 citations
TL;DR: This paper applies the cost scaling push-relabel method to the assignment problem and investigates implementations of the method that take advantage of assignment's special structure to show that it is very promising for practical use.
Abstract: The cost scaling push-relabel method has been shown to be efficient for solving minimum-cost flow problems. In this paper we apply the method to the assignment problem and investigate implementations of the method that take advantage of assignment's special structure. The results show that the method is very promising for practical use.
136 citations
TL;DR: A lowest-first, branch-and-bound algorithm for the Asymmetric Traveling Salesman Problem based on the Assignment Problem relaxation and on a tour elimination branching scheme that solves real-world problems with up to 443 movements in less than 6 seconds.
Abstract: A lowest-first, branch-and-bound algorithm for the Asymmetric Traveling Salesman Problem is presented. The method is based on the Assignment Problem relaxation and on a subtour elimination branching scheme. The effectiveness of the algorithm derives from reduction procedures and parametric solution of the relaxed problems associated with the nodes of the branch-decision tree. Large-size, uniformly, randomly generated instances of complete digraphs with up to 2000 vertices are solved on a DECstation 5000/240 computer in less than 3 minutes of CPU time. In addition, we solved on a PC 486/33 no wait flow shop problems with up to 1000 jobs in less than 11 minutes and real-world stacker crane problems with up to 443 movements in less than 6 seconds.
126 citations
TL;DR: An optimal on-line algorithm is presented for the following optimization problem, which constitutes the special case of the k-track assignment problem with identical time windows, and performs as well as the optimal greedy k-coloring algorithm due to Faigle and Nawijn and, independently, to Carlisle and Lloyd for the same problem under full a priori information.
85 citations
TL;DR: A deterministic queueing assignment model which seeks to reduce total travel delays in a road traffic network by routeing drivers according to the total delay caused on each link (the local marginal delay) is described.
Abstract: We describe a deterministic queueing assignment model which seeks to reduce total travel delays in a road traffic network by routeing drivers according to the total delay caused on each link (the local marginal delay). The model is approximate and is applicable to networks with many origin-destination pairs and many bottlenecks. Optimality of the solution determined by the model is discussed. It is particularly shown that, unlike in the steady state (Dafermos and Sparrow, 1969), reducing total travel times by using the local marginal delay will not generally result in an optimal solution. Results are provided for two networks.
84 citations
Posted Content•
TL;DR: In this article, a hierarchical decomposition of the planning problem is proposed to solve the feeder rack assignment problem, which takes into account as much as possible the individual board type characteristics as well as the machine characteristics.
Abstract: In this paper a typical situation arising in the assembly of printed circuit boards is investigated. The planning problem we face is how to assemble boards of different types using a single line of placement machines. From a practical viewpoint, the multiplicity of board types adds significantly to the complexity of the problem, which is already very hard to solve in the case of a single board type. In addition, relatively few studies deal with the multiple board type case. We propose a solution procedure based on a hierarchical decomposition of the planning problem. An important subproblem in this decomposition is the so-called feeder rack assignment problem. By taking into account as much as possible the individual board type characteristics (as well as the machine characteristics) we heuristically solve this problem. The remaining subproblems are solved using constructive heuristics and local search methods. The solution procedure is tested on real-life instances. It turns out that, in terms of the makespan, we can substantially improve the current solutions. Keywords: heuristics, PCB-assembly, feeder rack assignment problem.
01 Feb 1995
TL;DR: Recent developments such as parameter uncertainty robustness and hybrid eigenstructure assignment/H∞ control are examined in the recent literature, together with some suggestions for future research.
Abstract: This paper surveys the field of eigenstructure assignment literature from the early 1960s to the present. The eigenstructure assignment problem is first defined as the assignment of eigenvectors within an eigenspace associated with each eigenvalue. Four broad approaches to eigenstructure assignment are identified: the protection method, the parametric method, the projection method and the orthogonal eigenvector method. The major papers for each method are described in a common nomenclature and the techniques discussed. Recent developments such as parameter uncertainty robustness and hybrid eigenstructure assignment/H∞ control are examined in the recent literature, together with some suggestions for future research. The survey includes over 140 important references.
01 Jan 1995
TL;DR: In this article, the authors address the problem faced by a central controller seeking to optimize overall network performance through the provision of real-time routing information to suitably equipped motorists, and propose a dynamic assignment formulation for electronic route guidance systems.
Abstract: This paper addresses the problem faced by a central controller seeking to optimize overall network performance through the provision of real-time routing information to suitably equipped motorists. Conceptual and mathematical formulations are presented for various scenarios that arise based on the amount of information available to the controller. Principal elements of a dynamic assignment formulation for electronic route guidance systems are discussed, and the associated difficulties for solution methodologies are illustrated. The ideal case of known time-dependent origin-destination flows over the whole planning horizon is formulated as a dynamic system-optimal assignment problem. Extensions and variants of the basic formulation are discussed for incomplete information availability to the central controller.
TL;DR: Algorithms for thek-Matroid Intersection Problem and for the Matroidk-Parity Problem when the matroids are represented over the field of rational numbers andk > 2.
Abstract: We present algorithms for the k-Matroid Intersection Problem and for the Matroid k-Pafity Problem when the matroids are represented over the field of rational numbers and k > 2. The computational complexity of the algorithms is linear in the cardinality and singly exponential in the rank of the matroids. As an application, we describe new polynomially solvable cases of the k-Dimensional Assignment Problem and of the k-Dimensional Matching Problem. The algorithms use some new identities in mululinear algebra including the generalized Binet-Cauchy formula and its analogue for the Pfaffian. These techniques extend known methods developed earlier for k=2.
TL;DR: The proposed analog sorting neural network is shown to be capable of monotonic and bitonic sorting and suitable for hardware implementation and design principles and an op-amp based circuit realization of the analog neural network are delineated.
Abstract: An analog sorting neural network is presented. First, existing order representations are discussed and a generalized order representation is introduced. The sorting problem is then formulated as the assignment problem. Based on the assignment problem formulation, the neural network architecture is described. Design principles and an op-amp based circuit realization of the analog neural network are delineated. Three illustrative examples are also discussed to demonstrate the capability and performance of the analog neural network. The proposed analog neural network is shown to be capable of monotonic and bitonic sorting and suitable for hardware implementation. >
01 Jan 1995
TL;DR: A novel selection mechanism is introduced, and suitable genetic operators for crossover and mutation, are constructed, and a canonical form for a solution is defined to significantly reduce the search space and number of local minima.
Abstract: Finding the best state assignment for implementing a synchronous sequential circuit is important for reducing silicon area or chip count in many digital designs. This state assignment problem (SAP) belongs to a broader class of combinatorial optimization problems than the well studied traveling salesman problem, which can be formulated as a special case of SAP. The search for a good solution is considerably involved for the SAP due to a large number of equivalent solutions, and no effective heuristic has been found so far to cater to all types of circuits. In this paper, a matrix representation is used as the genotype for a genetic algorithm (GA) approach to this problem. A novel selection mechanism is introduced, and suitable genetic operators for crossover and mutation, are constructed. The properties of each of these elements of the GA are discussed and an analysis of parameters that influence the algorithm is given. A canonical form for a solution is defined to significantly reduce the search space and number of local minima. Experiments with several examples show that the GA approach yields results that are often comparable to, or better than those obtained using established heuristics that embody extensive domain knowledge. >
Journal Article•
TL;DR: The introduction of side constraints are considered to describe those flow relationships that have more natural interpretations as flow restrictions than as additional travel costs and to lead to more reliable traffic models than that using the traditional refinement strategy only.
Abstract: In order to refine the basic model of traffic assignment to capture supplementary flow relationships, the traditional modelling strategy is to modify the travel cost mapping. This strategy is well suited for capturing relationships such as interactions among vehicles on different road links and turning priorities in junctions, and it usually results in nonseparable and asymmetric travel cost functions. It is, however, not the proper approach for incorporating traffic flow restrictions such as those imposed by joint capacities on two-way streets or in junctions, or the presence of a traffic control policy. We consider the introduction of side constraints to describe those flow relationships that have more natural interpretations as flow restrictions than as additional travel costs. Such a refinement should be easier to construct and calibrate as well as lead to more reliable traffic models than that using the traditional refinement strategy only. The utilization of the appropriate combination of these two modelling strategies results, in general, in a variational inequality model of the traffic assignment problem augmented with a set of side constraints. We establish characterizations of its solutions as Wardrop and queueing delay equilibria in terms of well-defined and natural generalized travel costs, and derive stability results for the model. The results obtained may, for example, be applied to derive link tolls for achieving traffic management goals without using centralized traffic control.
TL;DR: The problem of optimally assigning highway trailers to railcar hitches in intermodal transportation is studied and an integer-linear programming formulation is constructed, which finds the optimal solution to all of the problem instances furnished over a two year period.
Abstract: The problem of optimally assigning highway trailers to railcar hitches in intermodal transportation is studied. An integer-linear programming formulation is constructed. The problem is formulated using set covering. The resulting formulation is very small, and possesses in practice a tight linear programming relaxation. This allows it to be solved effectively by a general purpose branch-and-bound code. This formulation also provided the basis for the development of a Greedy Randomized Adaptive Search Procedure (GRASP). This heuristic is observed to be extremely fast. Empirically, it finds the optimal solution to all of the problem instances furnished over a two year period by Consolidated Rail Corporation.
TL;DR: In this article, the core of the assignment problem coincides with the set of competitive allocations of the economy, and the characterization theorems also give axiomatic characterizations of the competitive allocations.
Abstract: This paper presents axiomatic characterizations of the core of assignment problems. In the main axiomatization theorem we use six axioms including the consistency (CONS) and the weak pairwise-monotonicity (W.P.MON) which are firstly proposed and defined for this setup in the present paper. Since an assignment problem may be converted into a model of a private ownership economy with indivisible goods and the core of the assignment problem coincides with the set of the competitive allocations of the economy, our characterization theorems also give axiomatic characterizations of the set of competitive allocations. Because the consistency is a desirable property of resource allocation mechanisms, our main result gives a new normative implication of competitive equilibria.
TL;DR: The algorithm developed in this paper is also based on the parametric approach, but it is combined with the approximate binary search method, and provides with a better time bound than the above algorithm.
TL;DR: A technique based on the problem-space genetic algorithm (PSGA) for the static task assignment problem in both homogeneous and heterogeneous distributed computing systems to reduce the task turnaround time and to increase the throughput of the system by properly balancing the load and reducing the interprocessor communication time among processors.
Abstract: The task assignment problem is one of assigning tasks of a parallel program among the processors of a distributed computing system in order to reduce the job turnaround time and to increase the throughput of the system. Since the task assignment problem is known to be NP-complete except in a few special situations, satisfactory suboptimal solutions obtainable in a reasonable amount of computation time are generally sought. In the paper we introduce a technique based on the problem-space genetic algorithm (PSGA) for the static task assignment problem in both homogeneous and heterogeneous distributed computing systems to reduce the task turnaround time and to increase the throughput of the system by properly balancing the load and reducing the interprocessor communication time among processors. The PSGA based approach combines the power of genetic algorithms, a global search method, with a simple and fast problem-specific heuristic to search a large solution space efficiently and effectively to find the best possible solution in an acceptable CPU time. Experimental results on test examples from the literature show considerable improvements in both the assignment cost and the CPU times over the previous work. The proposed scheme is also applied to a digital signal processing (DSP) system consisting of 119 tasks to illustrate its balancing properties and computational advantage on a large system. The proposed scheme offers 12–30% improvement in the assignment cost as compared to the previous best known results for the DSP example.
01 Mar 1995
TL;DR: A heuristic is presented for edge crossing minimization in bipartite graphs, which works by reducing the problem to an assignment problem, and it is shown that the idea underlying the assignment heuristic can be effectively applied in other cases requiring edge crossings minimization.
Abstract: Several applications use algorithms for drawing k-layered networks and, in particular, 2-layered networks (i.e. bipartite graphs). Bipartite graphs are commonly drawn in the plane so that all vertices lie on two parallel vertical lines, and an important requirement in drawing such graphs is to minimize edge crossings. Such a problem is NP-complete even when the position of the vertices on one layer is held fixed. This paper presents a heuristic, called the assignment heuristic, for edge crossing minimization in bipartite graphs, which works by reducing the problem to an assignment problem. The main idea of the assignment heuristic is to position simultaneously all the vertices of one layer, so that the mutual interaction of the position of all the vertices can be taken into account. We also show that the idea underlying the assignment heuristic can be effectively applied in other cases requiring edge crossing minimization. >
TL;DR: This paper describes several heuristics for BiQAPs, in particular pair exchange algorithms (improvement methods) and variants of simulated annealing and taboo search, implemented as C codes and analyzed.
TL;DR: A linear speed-up in the number of processors is reached on a shared memory multiprocessor, the Cray 2 and the optimality of solutions for famous problems of size less than 20 is proved by this program.
28 Mar 1995
TL;DR: It is conjecture that the algorithm correctly computes a maximum flow even in networks that contain cycles, as this paper presents a distributed self-stabilizing algorithm for the maximum flow problem.
Abstract: The maximum flow problem is a fundamental problem in graph theory and combinatorial optimization with a variety of important applications. Known distributed algorithms for this problem do not tolerate faults or adjust to dynamic changes in network topology. This paper presents the first distributed self-stabilizing algorithm for the maximum flow problem. Starting from an arbitrary state, the algorithm computes the maximum flow in a acyclic network in finitely many steps. Since the algorithm is self-stabilizing, it is inherently tolerant to transient faults and can automatically adjust to topology changes and to changes in other parameters of the problem. A slight modification of the original algorithm is also presented and it is conjectured that the new algorithm computes a maximum flow in arbitrary networks. >
TL;DR: This work considers such a resource-constrained assignment problem and presents a tabu search heuristic to solve it, which establishes the superiority of the proposed algorithm over the existing algorithms.
Abstract: Efficient algorithms are availabe to solve the unconstrained assignment problem. However, when resource or budgetary restrictions are imposed, the problem becomes difficult to solve. We consider such a resource-constrained assignment problem and present a tabu search heuristic to solve it. Extensive computational results are presented which establish the superiority of the proposed algorithm over the existing algorithms. Our adaptation of tabu search uses strategic oscillation, randomized short-term memory and multiple start as a means of search diversification.
TL;DR: This paper considers the index assignment problem and adopts a minimax design criterion instead of the usual mean squared error (MSE) measure, finding the problem to be NP-hard, and an effective, heuristic, polynomial-time algorithm is presented for computing approximate solutions.
Abstract: The distortion of a message due to channel noise can be alleviated significantly without redundant error control bits by judicious assignment of binary indices to message symbols. The nonredundant coding gain relies only on a notion of distance between symbols. In this paper, we consider the index assignment problem and adopt a minimax design criterion instead of the usual mean squared error (MSE) measure. The problem is found to be NP-hard, and an effective, heuristic, polynomial-time algorithm is presented for computing approximate solutions. The minimax criterion yields greatly improved worst case performance while maintaining good average performance. In addition, the familiar MSE criterion is shown likewise to yield an NP-hard index assignment task. The MSE problem is a special case of the classical quadratic assignment problem, for which computationally and theoretically useful results are available from the discrete mathematics literature. >
TL;DR: An explicit construction algorithm is obtained that generates a non-empty set C of output matrices such that for any member C of this set, the corresponding system characterized by the triple has the prescribed finite- and infinite-zero structures.
TL;DR: The Fortran code CDT, implementing an algorithm for theasymmetric traveling salesman problem, based on the Assignment Problem relaxation and on a tour elimination branching scheme, is presented.
Abstract: The Fortran code CDT, implementing an algorithm for the asymmetric traveling salesman problem, is presented. The method is based on the Assignment Problem relaxation and on a subtour elimination branching scheme. The effectiveness of the implementation derives from reduction procedures and parametric solution of the relaxed problems associated with the nodes of the branch-decision tree.
TL;DR: The study involves determining the relevant parameter constraints, and provides a comparison of the performance of the Hopfield model with that of a conventional approach.
Abstract: The Hopfield neural network is proposed as a method for solving the Quadratic Assignment Problem. The study involves determining the relevant parameter constraints, and provides a comparison of the performance of the Hopfield model with that of a conventional approach.