Showing papers on "Assignment problem published in 1978"

Optimality Conditions for a Dynamic Traffic Assignment Model

Abstract: We consider a dynamic traffic assignment model formulated as a nonlinear and noneonvex mathematical program. Necessary optimality conditions require equalization of certain marginal costs for all the paths that are being used, and these optimality conditions are shown to be a generalization of the optimality conditions of a conventional static traffic assignment problem. We also examine the behavior of the dynamic model under static demand conditions and show that in this case our model is a generalized version of a standard static model. Our model suggests a promising refinement of the objective function for the static case.

Some Matching Problems for Bipartite Graphs

Abstract: Certam apphcatlons require finding a perfect matching in a bipartite graph that satisfies some additional properties For one such type of restncUon the problem is proven to be NP-complete. If for a single subset of edges no more than r edges may be included m the matching then an O(ne) algorithm is given An efficient algorithm for finding all perfect matchmgs is presented It requires O(e) time per matching and a total of O(e) space This algorithm may be used to calculate the permanent of a matrix Finally, the algorithm ts generahzed to find all maximum matchmgs

An augmenting path method for solving Linear Bottleneck Assignment problems

Abstract: An efficient method for solving Linear Bottleneck Assignment problems is described. The method starts with a heuristically determined partial assignment. Then shortest augmenting paths are constructed with the aid of a modification of the algorithm of Dijkstra. Comprehensive numerical investigations are reported and discussed. A FORTRAN IV subroutine can be found in the appendix.

Pin Assignment on a Printed Circuit Board

Abstract: The design of a Printed Circuit Board is complete when the board is routed. All effort prior to activating the router is aimed at insuring successful routing, often involving the following steps: 1) Assigning elements to packages (this is known as the assignment problem). 2) Placing the packages on the board (the placement problem). 3) Assigning the connections of the nets to specific pins on the packages (the pin assignment problem). Each of these steps is designed to help produce a routable board. This paper describes a method of solving the pin assignment problem that achieves routability of the board by reducing prospective wire crossings. Routability is improved by ordering the nets to be assigned to a specific set of pins according to their location relative to this set of pins, and then assigning them, in this order, to the nearest available pin.

Colouring criteria for adjacency on 0–1-polyhedra

Abstract: The adjacency of two vertices on an arbitrary 0–1-polyhedron P is characterized by certain criteria involving the (prime) implicants of P, which are generalizations of the circuits of an independence system. These criteria can be checked by straightforward “colouring algorithms”. They are sufficient for all 0–1-polyhedra and necessary for at least three classes containing the polyhedra of many well-known discrete optimization problems, e.g. the vertex packing problem, set packing problem, vertex covering problem, matching problem, assignment problem, partitioning problem, linear ordering problem, partial ordering problem.

A practical algorithm for the Menger-type generalization of the independent assignment problem

Abstract: It is shown that the primal-dual algorithm for the ordinary assignment problem and for its Menger-type generalization can be extended in a natural manner to the case where both the entrance vertex set and the exit vertex set of the underlying graph are endowed with respective matroidal structures. The generalization of a Menger theorem is proved on the basis of the algorithm.

An algorithm for the state assignment of synchronous sequential circuits

Abstract: A systematic procedure for finding solutions to the state assignment problem in synchronous sequential circuits is described. It is based on two-block partition and is designed for use with D flip-flop memory elements.

The solution of algebraic assignment and transportation problems

Abstract: In this paper solution methods for the algebraic transportation problem (ATP) are considered. The ATP covers besides the Hitchcock and the time transportation problem several other types of transportation problems of practical relevance. The solution methods are based on (weakly) admissible transformations which can be determined by maximal flow resp. by shortest path algorithms. Numerical results for these and primal methods applied to sum and bottleneck assignment resp. transportation problems are mentioned.

Design and Control of a Three-Stage Switch Matrix in the Presence of Fan-Out

Abstract: Recent advancements in high-speed sold-state switching technology have created considerable interest in automatic switching of computation modules within analog computers under the control of digital computers. In this description of work done in "autopatching" of analog computers, relationships are derived among the parameters of a 3-stage asymmetrical connection network which will minimize the number of switches required and yet leave the network rearrangeable or effectively nonblocking. The problem of routing connections through a 3-stage network in presence of fan-out is also considered. The assignment problem is viewed as a mapping of the input terminal set onto the output terminal set. An algorithm is presented which employs mapping operations to resolve blocking conflicts systematically as they are encountered.

On Solving Symmetric Assignment and Perfect Matching Problems with Algebraic Objectives

Abstract: In this paper the algebraic symmetric assignment problem and the algebraic perfect matching problem are introduced. The equivalence of these two problems is stated and a method for their solution is outlined.

Optimization techniques : proceedings of the 8th IFIP Conference on Optimization Techniques, Würzburg, September, 5-9, 1977

Abstract: Semi-infinite programming: Conditions of optimality and applications.- On equiwellset minimum problems.- Second-order necessary and sufficient optimality conditions for infinite-dimensional programming problems.- An underrelaxed gauss-newton method for equality constrained nonlinear least squares problems.- A modification of Robinson's algorithm for general nonlinear programming problems requiring only approximate solutions of subproblems with linear equality constraints.- On a minimization problem in structural mechanics.- Non-linear least squares inversion of an integral equation using free-knot cubic splines.- On the convergence of the modified tui algorithm for minimizing a concave function on a bounded convex polyhedron.- A class of algorithms for the determination of a solution of a system of nonlinear equations.- Stochastic linear programs with random data having stable distributions.- Methods of feasible directions with increased gradient memory.- The continuous method of steepest descent and its discretizations.- Convergence rate results for a penalty function method.- A combined variable metric - Conjugate Gradient algorithm for a class of large scale unconstrained minimization problems.- Simplex method for dynamic linear program solution.- An adaptive precision method for the numerical solution of constrained optimization problems applied to a time-optimal heating process.- Generalized inverses and a new stable secant type minimization algorithm.- A conjugate directions method and its application.- The development of an efficient optimal control package.- An accuracy selection algorithm for the modified gradient projection method in minimax problems.- Single-iterative saddle-point algorithms for solving constrained optimization problems via augmented Lagrangians.- Improved lower bounds to 0/1 problems via lagrangean relaxation.- A unified approach to reshipment, overshipment and post-optimization problems.- Solving an integer programming problem.- Worst-case analysis for a class of combinatorial optimization algorithms.- An improved method of successive optima for the assignment problem.- Accelerated greedy algorithms for maximizing submodular set functions.- Resource allocation in a set of networks under multiple objectives.- An algorithm for solving the generalized transportation problem.- An efficient algorithm for solving a stochastic, integer programming problem arising in radio navigation.- Using pseudoboolean programming in decomposition method.- Solving the general project scheduling problem with multiple constrained resources by mathematical programming.- Threshold methods for boolean optimization problems with separable objectives.- Comparison of some educational planning models.- Mathematical programming in health-care planning.- A model of housing developing costs related to location.- An optimum surveillance and control system for synchronized traffic signals.- Regional classification problem and weaver's method.- A mathematical model for decision making in public service planning.- Optimal control of regional economic growth.- System modeling for interconnected dynamic economy and the decentralized optimal control.- Economic consequences of a change in demographic patterns: A linear programming model.- The multiple covering problem and its application to the dimensioning of a large scale seismic network.- A remark on econometric modelling, optimization and decision making.- Formulation and solution of the sequencing problem with parallel machines.- Stochastic model of resource allocation to R & D activities under cost value uncertainty.- Scheduling of trains - An optimization approach.- Optimal portfolios where proceeds are a function of the current asset price.- An algorithm for optimal sequencing of aircraft in the near terminal area.- A mathematical model of traffic in communication networks.- Partitioning a computer network into subnetworks and allocation of distributed data bases.- Effective file allocation method onto disc devices.- Optimal file allocation problem and relational distributed data bases.- General purpose nonlinear programming package.

Gateless synchronous counters with D flip-flops

Abstract: A new approach to the state assignment problem for the synthesis of sequential switching circuits is applied to solve completely the synthesis problem of gateless counters. The necessary and sufficient condition that assures that the counter may be synthesised without gates is found. A method is developed to determine a priori if a given state table corresponds to a circuit that may be synthesised without gates.

Mathematical programming techniques in majorization

Abstract: In this paper, we are concerned with mathematical programs which construct nonmajorizing vectors for several specific majorization applications. In particular, we develop a linear integer program and two integer goal programs which solve the assignment majorization problem. We also develop a quadratic program for solving majorization problems which arise in probability and statistics. In the appendix, we present a general goal-programming algorithm for these, as well as others, goal programs.

algorithms and computer programs in deterministic network optimization applied to public systems

Abstract: this book reports on the state of the art in application of deterministic network optimization to public systems. after general remarks on problems of applying mathematical methods to decision problems in public systems in chapter 1, the fundamental definitions for graphs and networks are presented in chapter 2. in chapter 3 the network flow problems are discussed: after presenting algorithms for the well known shortest path and maximum flow problem, the traffic assignment problem is discussed. in case of constant arc costs a minimum cost flow algorithm is presented. for the general case of arc costs, depending on the arc flow together with multiple origin-destination flow, a new algorithmic approach is presented that is based onklein's minimum cost flow algorithm. the relationships between descriptive and normative assignment are shown. chapter 4 deals with algorithms to find optimal subnetwork on a given network for the following problems: optimal waste water canal systemand optimal filter plant location to minimize construction and operating costs optimal location of emergency service facilities to minimize number of locations; optimal routes for airplanes to maximize number of people who fly non-stop from their origin to their destination; optimal spanning tree for an offshore oil-pipeline system to minimize construction and operating costs; optimal investment into a rail network to maximize transportation time reduction and optimal investment into a road network. knowing the optimal network, it might also be of interest how this network should be constructed sequentially. in chapter 5 an algorithm for finding the optimal construction sequence of a waste water canal network is presented which maximizes the amount of purified water during construction period. the similar problem in case of a railway network is treated too. chapter 6 deals with the problem of finding routes with minimum length that either pass through all arcs (chinese postman problem) or pass through all vertices (travelling salesman problem). in case the routes may not exceed a given length different heuristic algorithms are proposed. the applications to street cleaning, garbage collection as well as school bus routing are discussed. in the final chapter 7 the problem of computing optimal routes for an urban public transportation system is discussed in detail, stating a new algorithm for solving it . to most of the presented algorithms computer programs are listed which are able to solve small up to medium sized problems.;