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Showing papers on "Assignment problem published in 1997"


Journal ArticleDOI
TL;DR: A collection of electronically available data instances for the Quadratic Assignment Problem are described, indicating whether or not the problem is solved to optimality and the best known bounds for the problem are supplied.
Abstract: A collection of electronically available data instances for the Quadratic Assignment Problem is described. For each instance, we provide detailed information, indicating whether or not the problem is solved to optimality. If not, we supply the best known bounds for the problem. Moreover we survey available software and describe recent dissertations related to the Quadratic Assignment Problem.

826 citations


Journal ArticleDOI
TL;DR: Computational results show that the genetic algorithm heuristic is able to find optimal and near optimal solutions that are on average less than 0.01 % from optimality.

510 citations


Journal ArticleDOI
TL;DR: A new algorithm for the generalized assignment problem is presented that employs both column generation and branch-and-bound to obtain optimal integer solutions to a set partitioning formulation of the problem.
Abstract: The generalized assignment problem examines the maximum profit assignment of jobs to agents such that each job is assigned to precisely one agent subject to capacity restrictions on the agents. A new algorithm for the generalized assignment problem is presented that employs both column generation and branch-and-bound to obtain optimal integer solutions to a set partitioning formulation of the problem.

429 citations


Journal ArticleDOI
TL;DR: An efficient and recursive generalized S-D assignment algorithm (S/spl ges/3) employing a successive Lagrangian relaxation technique is presented, with application to the localization of an unknown number of emitters using multiple high frequency direction finder sensors.
Abstract: We develop a new algorithm to associate measurements from multiple sensors to identify the real targets in a surveillance region, and to estimate their states at any given time. The central problem in a multisensor-multitarget state estimation problem is that of data association-the problem of determining from which target, if any, a particular measurement originated. The data association problem is formulated as a generalized S-dimensional (S-D) assignment problem, which is NP-hard for S/spl ges/3 sensor scans (i.e., measurement lists). We present an efficient and recursive generalized S-D assignment algorithm (S/spl ges/3) employing a successive Lagrangian relaxation technique, with application to the localization of an unknown number of emitters using multiple high frequency direction finder sensors (S=3, 5, and 7).

358 citations


Proceedings ArticleDOI
09 Apr 1997
TL;DR: This work introduces the first unified framework for the study of assignment problems, and presents a unified algorithm for efficient (T/F/C)DMA channel assignments to nodes or to inter-nodal links in a (multihop) wireless network.
Abstract: Channel assignment problems in the time, frequency and code domains have thus far been studied separately. Exploiting the similarity of "constraints" that characterize assignments within and across these domains, we introduce the first unified framework for the study of assignment problems. Our framework identifies eleven atomic constraints underlying most current and potential assignment problems, and characterizes a problem as a combination of these constraints. Based on this framework, we present a unified algorithm for efficient (T/F/C)DMA channel assignments to nodes or to inter-nodal links in a (multihop) wireless network. The algorithm is parametrized to allow for tradeoff-selectable use as three different variants called random (RAND) ordering, minimum neighbors first (MNF), and progressive minimum neighbors first (PMNF). Using theoretical analysis, we show that the worst-case performance guarantee of PMNF is an order of magnitude better than that of the traditional RAND and MNF for most networks. We also experimentally study the relative performance for one node and one link assignment problem. We observe that PMNF performs the best, and that a larger fraction of unidirectional links degrades the performance in general.

226 citations


Proceedings ArticleDOI
08 Jun 1997
TL;DR: A new algorithm for the dynamic centralized wavelength assignment problem in fixed-routing WDM networks without wavelength conversion is proposed and an earlier analytical model for predicting the blocking probability with and without wavelength Conversion to dense multi-fiber networks is extended.
Abstract: We propose a new algorithm for the dynamic centralized wavelength assignment problem in fixed-routing WDM networks without wavelength conversion. The blocking performance of our algorithm is better in many cases (and no worse in tire cases we studied) than other previously proposed algorithms. The performance improvement of our algorithm over other algorithms is high for multi-fiber ring networks with a moderate number of fibers per link. In a multi-fiber mesh-torus network, the difference in performance is not as significant, but the blocking probabilities for all algorithms approach those achievable by wavelength conversion as the number of fibers per link increases. We also extend an earlier analytical model for predicting the blocking probability with and without wavelength conversion to dense multi-fiber networks. Finally, our simulation results on multi-fiber rings and mesh-tori reveal surprising results about the benefits of wavelength conversion as the number of fibers per link increases.

214 citations


Journal ArticleDOI
TL;DR: In this article, the eigenvectors of a symmetric matrix can be chosen to form an orthogonal set with respect to the identity and to the matrix itself, and the same can be said of the symmetric definite quadratic pencil.

175 citations


Journal ArticleDOI
TL;DR: A new nonlinear integer programming representation of the static channel assignment (SCA) problem is formulated and a new self-organizing neural network is proposed which is able to solve the SCA problem and many other practical optimization problems due to its generalizing ability.
Abstract: We examine the problem of assigning calls in a cellular mobile network to channels in the frequency domain. Such assignments must be made so that interference between calls is minimized, while demands for channels are satisfied. A new nonlinear integer programming representation of the static channel assignment (SCA) problem is formulated. We then propose two different neural networks for solving this problem. The first is an improved Hopfield (1982) neural network which resolves the issues of infeasibility and poor solution quality which have plagued the reputation of the Hopfield network. The second approach is a new self-organizing neural network which is able to solve the SCA problem and many other practical optimization problems due to its generalizing ability. A variety of test problems are used to compare the performance of the neural techniques against more traditional heuristic approaches. Finally, extensions to the dynamic channel assignment problem are considered.

141 citations


Proceedings ArticleDOI
09 Apr 1997
TL;DR: Numerical results illustrate that the heuristic algorithm is efficient and can give near-optimal solutions for spare capacity allocation and flow assignment in the design of self-healing ATM networks using path based restoration.
Abstract: This paper studies the capacity and flow assignment problem arising in the design of self-healing ATM networks using the virtual path (VP) concept The problem is formulated as a linear programming problem which is solved using standard methods The objective is to minimize the spare capacity cost for the given restoration requirement The spare cost depends on the restoration strategies used in the network We compare several restoration strategies, notably, global versus failure-oriented reconfiguration, path versus link based restoration and state-dependent versus state-independent restoration, quantitatively in terms of spare cost The advantages and disadvanages of various restoration strategies are also highlighted Such comparisons provide useful guidance for real network design Further, a new heuristic algorithm is developed for the design of large self-healing ATM networks using path based restoration Numerical results illustrate that the heuristic algorithm is efficient and can give near-optimal solutions for spare capacity allocation and flow assignment

114 citations


Journal ArticleDOI
TL;DR: FASoft as discussed by the authors is a system for discrete channel frequency assignment that incorporates state-of-the-art heuristics, sequential assignment algorithms, and a maximal clique algorithm to aid in the assignment process.
Abstract: This paper describes a system, FASoft, for discrete channel frequency assignment. In practice, the assignment of frequencies in a network of compatible equipment is often done manually or by the use of a single computational technique. FASoft incorporates state-of-the-art heuristics, sequential assignment algorithms, and a maximal clique algorithm to aid in the assignment process. Lower bounding procedures are included into the system to assess the performance of the assignment techniques and to provide an assessment of how close a particular assignment is to the optimal. The results show that FASoft produces optimal solutions to several practical examples.

112 citations


Journal ArticleDOI
TL;DR: The aim of this paper is to evaluate the effectiveness of a branch-and-cut algorithm exploiting ATSP-specific facet-defining cuts to be used to attack hard instances that cannot be solved by the AP-based procedures from the literature.
Abstract: Several branch-and-bound algorithms for the exact solution of the asymmetric traveling salesman problem ATSP, based on the assignment problem AP relaxation, have been proposed in the literature. These algorithms perform very well for some instances e.g., those with uniformly random integer costs, but very poorly for others. The aim of this paper is to evaluate the effectiveness of a branch-and-cut algorithm exploiting ATSP-specific facet-defining cuts, to be used to attack hard instances that cannot be solved by the AP-based procedures from the literature. We present new separation algorithms for some classes of facet-defining cuts, and a new variable-pricing technique for dealing with highly degenerate primal LP problems. A branch-and-cut algorithm based on these new results is designed and evaluated through computational analysis on several classes of both random and real-world instances. The outcome of the research is that, on hard instances, the branch-and-cut algorithm clearly outperforms the best AP-based algorithms from the literature.

Journal ArticleDOI
TL;DR: Since the task assignment problem is NP-hard, three novel heuristic algorithms are presented that have been tested for solving it and compared to the well-known greedy heuristic.

Journal ArticleDOI
TL;DR: A solution procedure based on a hierarchical decomposition of the planning problem of the assembly of printed circuit boards, taking into account as much as possible the individual board type characteristics (as well as the machine characteristics) is proposed.

Journal ArticleDOI
TL;DR: Original preprocessing techniques for finding optimal solutions in which g ⩽ k rows are assigned, for determining rows and columns which must be assigned in an optimal solution and for reducing the cost matrix are introduced.

Journal ArticleDOI
TL;DR: A modeling technique is developed that transforms the assignment problem in an array or tree into a minimum-cut maximum-flow problem, which is then solved for a generalarray or tree network in polynomial time.
Abstract: This paper considers the problem of assigning the tasks of a distributed application to the processors of a distributed system such that the sum of execution and communication costs is minimized. Previous work has shown this problem to be tractable for a system of two processors or a linear array of N processors, and for distributed programs of serial parallel structures. Here we focus on the assignment problem on a homogeneous network, which is composed of N functionally-identical processors, each with its own memory. Some processors in the network may have unique resources, such as data files or certain peripheral devices. Certain tasks may have to use these unique resources; they are called attached tasks. The tasks of a distributed program should therefore be assigned so as to make use of specific resources located at certain processors in the network while minimizing the amount of interprocessor communication. The assignment problem in such a homogeneous network is known to be NP-hard even for N=3, thus making it intractable for a network with a medium to large number of processors. We therefore focus on task assignment in general array networks, such as linear arrays, meshes, hypercubes, and trees. We first develop a modeling technique that transforms the assignment problem in an array or tree into a minimum-cut maximum-flow problem. The assignment problem is then solved for a general array or tree network in polynomial time.

Journal ArticleDOI
TL;DR: In this paper, a genetic algorithm for the generalised assignment problem is described, where instead of genetically improving a set of feasible solutions, the algorithm tries to restore feasibility to the set of near-optimal ones.
Abstract: A new algorithm for the generalised assignment problem is described in this paper. The algorithm is adapted from a genetic algorithm which has been successfully used on set covering problems, but instead of genetically improving a set of feasible solutions it tries to genetically restore feasibility to a set of near-optimal ones. Thus it may be regarded as operating in a dual sense to the more familiar genetic approach. The algorithm has been tested on generalised assignment problems of substantial size and compared to an exact integer programming approach and a well-established heuristic approach.

Journal ArticleDOI
TL;DR: Experimental results using Murty's algorithm suggest that a solution to the real-time data association problem is now feasible and the relationship between the two algorithms is shown and how Danchick and Newnam's algorithm can be very easily modified to MurTY's algorithm.
Abstract: Recently, it has become clear that determining a ranked set of assignments allows computation of very good approximations to the data association problem. Several algorithms have been proposed but only two return the k-best assignments in reasonable time. One is Danchick and Newnams' [1993] algorithm, which is based on the recognition that determining the best assignment is a classical assignment problem and that determining a ranked set of assignments may be accomplished by solving a series of modified copies of the initial assignment problem. The other algorithm is originally due to Murty [1968] and was most recently described within the context of multitarget tracking. We evaluate the two algorithm using randomly generated data and data obtained from an electrooptical sensor simulation in which 90 missiles are launched. These evaluations show that Murty's algorithm perform significantly better in all scenarios. We show the relationship between the two algorithms and how Danchick and Newnam's algorithm can be very easily modified to Murty's algorithm. Experimental results using Murty's algorithm suggest that a solution to the real-time data association problem is now feasible.

Journal ArticleDOI
TL;DR: This paper presents two recurrent neural networks for solving the assignment problem, called primal and dual assignment, which are guaranteed to make optimal assignment and even simpler in architecture than the primal network.
Abstract: This paper presents two recurrent neural networks for solving the assignment problem. Simplifying the architecture of a recurrent neural network based on the primal assignment problem, the first recurrent neural network, called the primal assignment network, has less complex connectivity than its predecessor. The second recurrent neural network, called the dual assignment network, based on the dual assignment problem, is even simpler in architecture than the primal assignment network. The primal and dual assignment networks are guaranteed to make optimal assignment. The applications of the primal and dual assignment networks for sorting and shortest-path routing are discussed. The performance and operating characteristics of the dual assignment network are demonstrated by means of illustrative examples.

Proceedings ArticleDOI
01 Apr 1997
TL;DR: Applications of heuristic techniques for solving the terminal assignment (TA) problem are investigated and the different heuristics used include greedy-based algorithms, genetic algorithms, and grouping genetic algorithms (GGA).
Abstract: In this paper, applications of heuristic techniques for solving the terminal assignment (TA) problem are investigated. The task here is to assign terminals to concentrators in such a way that each terminal is assigned to one (and only one) concentrator and the aggregate capacity of all terminals assigned to any concentrator does not overload that concentrator, i.e., is within the concentrator's capacity. Under these two hard constraints, an assignment with the lowest possible cost is sought. The proposed cost is taken to be the distance between a terminal and a concentrator. The heuristic techniques we investigate in this article include greedy-based algorithms, genetic algorithms (GA), and grouping genetic algorithms (GGA) [4]. We elaborate on the different heuristics we use, and compare the solutions yielded by them.

Journal ArticleDOI
TL;DR: The problem of generating a matrix A with specified eigenvalues, which maps a given set of vectors of another given set, is presented and an existence theorem is given and proved.

Journal ArticleDOI
TL;DR: In this article, the problem of assigning classes to professors, in such a way that the average number of distinct subjects assigned to each professor is minimized, is formulated as a mixed integer program.

Proceedings ArticleDOI
13 Nov 1997
TL;DR: A minimum cost circulation approach is used to efficiently generate high performance addressing code in polynomial time and results show that memory layout has a small effect on code size and performance when optimal addressing is used.
Abstract: This paper presents a new approach to solving the DSP address assignment problem. A minimum cost circulation approach is used to efficiently generate high performance addressing code in polynomial time. Addressing code size improvements of up to 7 times are obtained, accounting for up to 1.6 times improvement in code size and performance of compiler-generated DSP code. Results also show that memory layout has a small effect on code size and performance when optimal addressing is used. This research is important for industry since this value-added technique can improve code size, power dissipation and performance, without increasing cost.

Journal ArticleDOI
R.A. Leese1
TL;DR: The main aim is to investigate the interplay between the cochannel and adjacent channel separations without restricting the assignments unnecessarily, and to develop an algorithm which assigns channels on any cochannel lattice so that the adjacent channel separation is maximized.
Abstract: In radio systems, quality of service is achieved by assigning channels with reference to a set of protection ratios, which in a simplified setting may be replaced with frequency-distance bounds. This paper considers the assignment problem on a lattice of hexagonal cells, with the allowed assignments generated by regular tilings of a single polyhex. The main aim is to investigate the interplay between the cochannel and adjacent channel separations without restricting the assignments unnecessarily. The outcome is a unified framework in which all previous results appear as particular cases. The possible cochannel lattices are carefully classified, and then an algorithm is developed, which assigns channels on any cochannel lattice so that the adjacent channel separation is maximized. In this way, a library of the best assignments can be compiled. The results are of relevance to a range of applications, including both broadcast and mobile systems.

Journal ArticleDOI
TL;DR: A Heuristic Algorithm for the Vehicle Routing Problem with Backhauls and Hybrid Genetic Algorithms for Bus Driver Scheduling are presented.
Abstract: O-D Demand Adjustment Problem with Congestion: Part I. Model Analysis and Optimality Conditions.- Generating Highway Travel Times with a Large-Scale, Asymmetric User Equilibrium Assignment Model.- An Efficient Algorithm for a Bicriterion Traffic Assignment Problem.- A Stochastic User Equilibrium (SUE) Path Flow Estimator for the Dedale Database in Lyon.- Modelling and Performance Analysis of Urban Transportation Networks.- Zone Planning in Public Transportation Systems.- Multicriteria Evaluation Model of Public Transport Networks.- Multi-Objective Approach for Designing Transit Routes with Frequencies.- Relationship between Parking Location and Traffic Flows in Urban Areas.- A DSS Prototype for Urban Intermodal Path Planning with Parking Management.- Structure of a Dynamic Network Loading Model for the Evaluation of Control Strategies.- Dynamic Traffic Assignment in Congested Networks.- A System Optimal Traffic Assignment Model with Distributed Parameters.- Stochastic Assignment Models for Transit Low Frequency Services: Some Theoretical and Operative Aspects.- A Parallel Approach to Large-Scale Nonlinear Network Optimization.- Data Management of Large-Scale Transportation Networks.- Why Regulate Prices in Freight Transportation Markets?.- Optimal Freight Transport Pricing and the Freight Network Equilibrium Problem.- The Impact of Predictive Information on Guidance Efficiency: An Analytical Approach.- Dynamic Traffic Prediction for Motorway Networks.- A Parking Simulation Model for Evaluating Availability Information Service.- Flexible Dispatching Control Tools in Public Transport.- Queuing Optimization of Signalized Intersections.- A Model for Real-Time Traffic Coordination Using Simulation Based Optimization.- An Approximate Labelling Algorithm for the Dynamic Assignment Problem.- A Heuristic Algorithm for the Vehicle Routing Problem with Backhauls.- Hybrid Genetic Algorithms for Bus Driver Scheduling.

Journal ArticleDOI
TL;DR: A framework for discussing how to adjust load in order to handle periodic processes whose timing parameters vary with time is provided and an approximation algorithm for the period assignment problem is presented.
Abstract: We provide a framework for discussing how to adjust load in order to handle periodic processes whose timing parameters vary with time. The schedulability of adjustable periodic processes by a preemptive fixed priority scheduler is formulated in terms of a configuration selection problem for which a PTIME solution is shown. When the list of allowable configurations is implicitly given by a set of scalable periodic processes, the corresponding period assignment problem is shown to be NP-Complete. We present an approximation algorithm for the period assignment problem for which we show some encouraging experimental results.

Proceedings ArticleDOI
01 Apr 1997
TL;DR: This research proposes a number of algorithms based around the A* technique, a best-first search technique from the area of artificial intelligence, which guarantees an optimal solution but is not feasible for problems of practically large sizes due to its high time and space complexity.
Abstract: Distributed systems comprising networked heterogeneous workstations are now considered to be a viable choice for high-performance computing. For achieving a fast response time from such systems, an efficient assignment of the application tasks to the processors is imperative. The general assignment problem is known to be NP-hard, except in a few special cases with strict assumptions. While a large number of heuristic techniques have been suggested in the literature that can yield sub-optimal solutions in a reasonable amount of time, we aim to develop techniques for optimal solutions under relaxed assumptions. The basis of our research is a best-first search technique known as the A* algorithm from the area of artificial intelligence. The original search technique guarantees an optimal solution but is not feasible for problems of practically large sizes due to its high time and space complexity. We propose a number of algorithms based around the A* technique. The proposed algorithms also yield optimal solutions but are considerably faster. The first algorithm solves the assignment problem by using parallel processing. Parallelizing the assignment algorithm is a natural way to lower the time complexity, and we believe our algorithm to be novel in this regard. The second algorithm is based on a clustering based pre-processing technique that merges the high affinity tasks. Clustering reduces the problem size, which in turn reduces the state-space for the assignment algorithm. We also propose three heuristics which do not guarantee optimal solutions but provide near-optimal solutions and are considerably faster. By using our parallel formulation, the proposed clustering technique and the heuristics can also be parallelized to further improve their time complexity.

Journal ArticleDOI
TL;DR: This dissertation addresses several problems in the area of routing and capacity assignment in backbone communication networks and efficient solution procedures based on Lagrangean relaxations of the problems are developed.

Book ChapterDOI
20 Aug 1997
TL;DR: A model for small scale examination scheduling that is able to generate schedules that satisfy student as well as university expectations and the application of the model to a real world situation is presented.
Abstract: In this paper we develop a model for small scale examination scheduling. We formulate a quadratic assignment problem and then transform it into a quadratic semi assignment problem. The objective of our model is to maximize student’s study time as opposed to minimizing some cost function as suggested in other QAP approaches. We use simulated annealing to demonstrate the model’s ability to generate schedules that satisfy student as well as university expectations. Furthermore the application of the model to a real world situation is presented.

Journal ArticleDOI
TL;DR: It is shown that in the context of the bipartite matching and assignment problems, global updates yield a theoretical improvement as well.
Abstract: Periodic global updates of dual variables have been shown to yield a substantial speed advantage in implementations of push-relabel algorithms for the maximum flow and minimum cost flow problems. In this paper, we show that in the context of the bipartite matching and assignment problems, global updates yield a theoretical improvement as well. For bipartite matching, a push-relabel algorithm that uses global updates runs in $O\big(\sqrt n m\frac{\log(n^2/m)}{\log n}\big)$ time (matching the best bound known) and performs worse by a factor of $\sqrt n$ without the updates. A similar result holds for the assignment problem, for which an algorithm that assumes integer costs in the range $[\,-C,\ldots, C\,]$ and that runs in time $O(\sqrt n m\log(nC))$ (matching the best cost-scaling bound known) is presented.

Journal ArticleDOI
TL;DR: It is shown that the static deterministic single machine scheduling problem with a common due window can be formulated as an assignment problem and thus can be solved with well-known algorithms.
Abstract: A static deterministic single machine scheduling problem with a common due window is considered. Job processing times are controllable to the extent that they can be reduced, up to a certain limit, at a cost proportional to the reduction. The window location and size, along with the associated job schedule that minimizes a certain cost function, are to be determined. This function is made up of costs associated with the window location, its size, processing time reduction as well as job earliness and tardiness. We show that the problem can be formulated as an assignment problem and thus can be solved with well-known algorithms.