Showing papers on "Assignment problem published in 1985"

A Graph Matching Approach to Optimal Task Assignment in Distributed Computing Systems Using a Minimax Criterion

Abstract: A graph matching approach is proposed in this paper for solving the task assignment problem encountered in distributed computing systems. A cost function defined in terms of a single unit, time, is proposed for evaluating the effectiveness of task assignment. This cost function represents the maximum time for a task to complete module execution and communication in all the processors. A new optimization criterion, called the minimax criterion, is also proposed, based on which both minimization of interprocessor communication and balance of processor loading can be achieved. The proposed approach allows various system constraints to be included for consideration. With the proposed cost function and the minimax criterion, optimal task assignment is defined. Graphs are then used to represent the module relationship of a given task and the processor structure of a distributed computing system. Module assignment to system processors is transformed into a type of graph matching, called weak homomorphism. The search of optimal weak homomorphism corresponding to optimal task assignment is next formulated as a state-space search problem. It is then solved by the well-known A* algorithm in artificial intelligence after proper heuristic information for speeding up the search is suggested. An illustrative example and some experimental results are also included to show the effectiveness of the heuristic search.

Optimizing Gate Assignments at Airport Terminals

Abstract: The airport flight-to-gate assignment problem is solved using two methods: (1) a linear programming relaxation of an integer program formulation and (2) a heuristic. The objective is to minimize passenger walking distances within the airport terminal area through a judicious gate assignment policy. An actual flight schedule for an average day at Toronto International Airport is used to compare existing walking distances, obtained from the original assignment, with results from the two methods. The results indicated that the original assignment had a 32% higher average per passenger walking distance than the minimum possible distance given by the LP solution. The heuristic’s performance was near optimal; it gave an average walking distance which was only 3.9% greater than the minimum. Computation times for the heuristic are 3.4 CPU seconds per run, while the linear program consumes 386 seconds per run on an IBM 370/168. In addition, if the heuristic is solved first and its solution is used as an initial fe...

Signature Methods for the Assignment Problem

Abstract: The "signature" of a dual feasible basis of the assignment problem is an n-vector whose ith component is the number of nonbasic activities of type i, j. This paper uses signatures to describe a method for finding optimal assignments that terminates in at most n-1n-2/2 pivot steps and takes at most On3 work.

A new algorithm for solving variational inequalities with application to the traffic assignment problem

Abstract: The variational inequality problem in Euclidian space is formulated as a nonconvex, nondifferentiable optimization problem. We show that any stationary point is optimal, and we propose a solution algorithm that decreases the nondifferential objective monotonically. Application to the asymmetric traffic assignment problem is considered.

On the simplex algorithm for networks and generalized networks

Abstract: We consider the simplex algorithm as applied to minimum cost network flows on a directed graph, G=(V, E). First we consider the strongly convergent pivot rule of Elam, Glover, and Klingman as applied to generalized networks. We show that this pivot rule is equivalent to Dantzig’s lexicographical rule in its choice of the variable to leave the basis. We also show the following monotonicity property that is satisfied by each basis B of a generalized network flow problem. If b′≤b≤b * and if l≤B −1 b′, B −1 b *≤u, then l≤B −1 b≤u; i.e., if a basis is feasible for b′ and b * then it is feasible for b. Next we consider Dantzig’s pivot rule of selecting the entering variable whose reduced cost is minimum and using lexicography to avoid cycling. We show that the maximum number of pivots using Dantzig’s pivot rule is O(|V|2|E| log |V|) when applied to either the assignment problem or the shortest path problem. Moreover, the maximum number of consecutive degenerate pivots for the minimum cost network flow problem is O(|V|2|E|log|V|).

A distributed asynchronous relaxation algorithm for the assignment problem

Abstract: Relaxation methods for optimal network flow problems resemble classical coordinate descent, Jacobi, and Gauss-Seidel methods for solving unconstrained non-linear optimization problems or systems of nonlinear equations. In their pure form they modify the dual variables (node prices) one at a time using only local node information while aiming to improve the dual cost. They are particularly well suited for distributed implementation on massively parallel machine. For problems with strictly convex arc costs they can be shown to converge even if relaxation at each node is carried out asynchronously with out-of-date price information from neighboring nodes [1]. For problems with linear arc costs relaxation methods have outperformed by a substantial margin the classical primal simplex and primal-dual methods on standard benchmark problems [2], [3]. However in these particular methods it is necessary to change sometimes the prices of several nodes as a group in addition to carrying out pure relaxation steps. As a result global node price information is needed occasionally, and distributed implementation becomes somewhat complicated. In this paper we describe a distributed algorithm for solving the classical linear cost assignment problem. It employs exclusively pure relaxation steps whereby the prices of sources and sinks are changed individually on the basis of only local (neighbor) node price information. The algorithm can be implemented in an asynchronous (chaotic) manner, and seems quite efficient for problems with a small arc cost range. It has an interesting interpretation as an auction where economic agents compete for resources by making successively higher bids.

Two-film brachytherapy reconstruction algorithm.

Abstract: We have developed a new isocentric two‐film reconstruction algorithm for brachytherapy seed and needle implants. The algorithm has no requirements that the two films be orthogonal, symmetric, or even be taken in a transverse plane. In addition, there is no requirement that the two films even have the same number of images. We have found removal of these usual constraints useful for head and neck implants where images are often obscured by patient anatomy. The inherent image matching ambiguities associated with traditional two‐film techniques are minimized by considering the image end points, rather than just the image centroids. For two films, the new algorithm, which considers all image combinations at o n e time, matches all the end‐point images on one film with those on the other, and then reconstructs the end‐point positions of the seeds. The algorithm minimizes the difference between the actual images and the projected images from the reconstructed seeds. The new two‐film image matching problem is shown to be equivalent to the well‐known assignment problem. For an implant of N seeds, this equivalence allows the two‐film problem to be solved by an algorithm (ACM algorithm 548) that scales with a polynomial power of N, rather than N! as is usually assumed. An implant of N seeds can be matched and reconstructed in approximately (N/20)2 s on a VAX 11/780.

The shortest augmenting path method for solving assignment problems — Motivation and computational experience

Abstract: In this paper we discuss the shortest augmenting path method for solving assignment problems in the following respect: we introduce this basic concept using matching theory we present several efficient labeling techniques for constructing shortest augmenting paths we show the relationship of this approach to several classical assignment algorithms we present extensive computational experience for complete problems, and we show how postoptimal analysis can be performed using this approach and naturally leads to a new, highly efficient hybrid approach for solving large-scale dense assignment problems

Accelerating convergence of the Frank-Wolfe algorithm☆

Abstract: We consider the Frank-Wolfe algorithm in the context of the traffic assignment problem. The slow-convergence characteristics close to the optimum solution of this popular approach are well known. Several proposals have improved on the original method by modifying the search direction. We propose modifying the step size, which leads to very significant improvements in efficiency.

Decision Making, Models and Algorithms: A First Course

Abstract: Partial table of contents: A FRAMEWORK FOR DECISION MAKING. Decision Making. The Decision Framework. THE LINEAR-PROGRAMMING MODEL: APPLICATIONS. What's for Breakfast?: The Diet Problem. You're in the Army Now: The Personnel-Assignment Problem. SOLVING LINEAR-PROGRAMMING PROBLEMS: THE MODEL AND ITS ALGORITHM. A Manufacturing Problem. The Simplex Algorithm. NETWORK AND RELATED COMBINATORIAL PROBLEMS. Network-Flow Problems. The Transportation and Assignment Problem Algorithms. GAMES, TREES AND DECISION. The Theory of Games. The Analytic Hierarchy Process. Combined References. Index.

Time-slot assignment for TDMA-systems

Abstract: In satellite communication as in other technical systems using the TDMA-technique (time division multiple access) the problem arises to decompose a given (n×n)-matrix in a weighted sum of permutation matrices such that the sum of the weights becomes minimal. We show at first that an optimal solution of this problem can be obtained inO(n 4)-time using at mostO(n 2) different permutation matrices. Thereafter we discuss shortly the decomposition inO(n) different matrices which turns out to be NP-hard. Moreover it is shown that an optimal decomposition using a class of 2n permutation matrices which are fixed in advance can be obtained by solving a classical assignment problem. This latter problem can be generalized by taking arbitrary Boolean matrices. The corresponding decomposition problem can be transformed to a special max flow min cost network flow problem, and is thus soluble by a genuinely polynomial algorithm.

The three dimensional bottleneck assignment problem and its variants

Abstract: The three dimensional bottleneck assignment problem and some of its variants are studied in the present paper. A procedure is developed for each of these bottleneck assignment problems.

The dual of the traffic assignment problem with elastic demands

Abstract: This article is concerned with the dual of the traffic assignment problem, and of the combined generation, distribution, and assignment problem. The duals, and duality relations, for the arc-chain and node-arc formulations of the problem are derived using only the Kuhn-Tucker conditions for convex programs. This has the advantage of being more familiar to most readers than the conjugate function presentation which has been used elsewhere.

On the selection of primary paths for a communication-network

Abstract: This paper deals with a non-bifurcated flow assignment problem in communication networks in which communication paths are limited to a set of pre-selected paths for each node pair. This problem is formulated as a mixed 0–1 linear model with multiple-choice constraints. A heuristic algorithm is presented, which takes a straightforward iterative approach, conceptually similar to that of the Simplex method, for finding the characterized local optimal solution. Several subprocedures which exploit the special structure of the model are included to make the algorithm computationally efficient. The relaxed linear programming model is used for the analysis of the algorithm, and its solution is found to be a tight lower bound. Applications of the algorithm to problems with other performance criteria are also suggested. Computational experience obtained thus far indicates that the algorithm almost always guarantees a quick convergence to a good suboptimal solution.

Asymptotic Approximations of the Assignment Model with Stochastic Heterogeneity in the Matching Utilities

Abstract: A large-scale linear assignment problem is considered under the assumption that the coefficients of the objective function are imperfectly known but have a probability distribution. Asymptotic approximations are derived by using the statistical theory of extremes. It is shown how the resulting approximate problem has an easily computable form, provides a closed-form solution which has the structure of a logit model, and is embedded by a mathematical program whose objective function is related to entropy.

Improving Christofides' lower bound for the traveling salesman problem

Abstract: In 1972 Christofides introduced a lower bound for the Traveling Salesman Problem (TSP). The bound is based on solving repeatedly a Linear Assignment Problem. We relate the bound to the Complete Cycle Problem; as a consequence the correctness of the bound is easier to prove. Further we give improvements for the bound in the symmetric case and we deal with the influence of the triangle equation together with the identification of non-optimal edges for the TSP. The improvements are illustrated by examples and computational results for large problems.

An Optimal Road Network Design Model with Traffic Congestion and its Application

Abstract: An optimal road network design model is formulated as a two level planning problem. It is interpretted as a two-person, planner and user of road, non-cooperative non-zero sum game. Master problem decides continuous link capacities so as to minimize the sum of total transportation cost and total link construction cost subject to link capacity constraints. Sub problem is user equilibrium traffic assignment problem, in which traffic congestion is explicitly involved. A heuristic solution procedure is proposed which is effective for convex performance function and link construction cost function. In the case of BPR-type performance function and linear cost function, model application is executed for the actual size of road network planning problem.

A decomposition algorithm for linear relaxation of the weighted r-covering problem

Abstract: In this paper the linear relaxation of the weightedr-covering problem (r-LCP) is considered. The dual problem (c-LMP) is the linear relaxation of the well-knownc-matching problem and hence can be solved in polynomial time. However, we describe a simple, but nonpolynomial algorithm in which ther-LCP is decomposed into a sequence of 1-LCP’s and its optimal solution is obtained by adding the optimal solutions of these 1-LCP’s. An 1-LCP can be solved in polynomial time by solving its dual as a max-flow problem on a bipartite graph. An accelerated algorithm based on this decomposition scheme to solve ar-LCP is also developed and its average case behaviour is studied.

Truck lane needs methodology: a heuristic approach to solve a five option discrete network design problem. interim report

Abstract: Special truck lanes have been proposed as a measure to deal with the increasing traffic of larger and heavier trucks on the Texas highway system. This report describes a procedure for the selection of an optimal subset of truck-related link improvements in the highway network. This procedure is a component of an integrated network modelling methodology for the study of truck lane needs in the Texas highway network. The link improvement selection problem is cast as a discrete network design problem with multiple improvement types per link. One of the principal features of this procedure is the definition of link improvement in terms of both capacity expansion (lane addition) and operational scheme (exclusive use by cars or trucks of both existing and added lanes). Another is the consideration of the interaction of cars and trucks in the traffic stream in solving the network equilibrium assignment problem embedded in the network design problem. A branch and bound integer programming approach is adapted and tested for this problem and the particular features introduced by truck-related link improvement measures.

Eigenvalue assignment procedure for delayed interconnected system by expansion

Abstract: A procedure for constructing the decentralized and the hierarchical control that achieves precise eigenvalue assignment for dynamically interconnected system is presented. Delays in signals transmitted through the interconnecting channels is taken into consideration. It will be shown that the problem can be solved by reformulating it also as an assignment problem for an independent of delay augmented system. Emphasis is made on the manner in which eigenvectors interact to achieve desired spectrum by coordinating subsystem-interconnections solutions.