Showing papers on "Linear programming published in 1979"

Linear Programming for Power-System Network Security Applications

Abstract: A linear programming (LP) method for security dispatch and emergency control calculations on large power systems is presented. The method is reliable, fast, flexible, easy to program, and requires little computer storage. It works directly with the normal power-system variables and limits, and incorporates the usual sparse matrix techniques. An important feature of the method is that it handles multi-segment generator cost curves neatly and efficiently.

Bicriteria transportation problem

Abstract: In a transportation problem, generally, a single criterion of minimizing the total cost is considered. But in certain practical situations two or more objectives are relevant. For example, the objectives may be minimizations of total cost, consumption of certain scarce resources such as energy, total deterioration of goods during transportation, etc. Clearly, this problem can be solved using any of the multiobjective linear programming techniques; but the computational efforts needed would be prohibitive in many cases. The computational complexity in these techniques arises from the fact that each of the methods finds the set of nondominated extreme points in the solution space where such extreme points are, generally, many. Therefore, this paper develops a method of finding the nondominated extreme points in the criteria space. Such extreme points in the criteria space would be generally less and only these are needed while choosing a nondominated solution for implementation. The method involves a parame...

An Efficient SS/TDMA Time Slot Assignment Algorithm

Abstract: This paper presents an efficient time slot assignment algorithm for an SS/TDMA system. The technique utilized in the algorithm is a systematic method of finding distinct representatives from the row sets of a traffic matrix. The assignment efficiency resulting from the algorithm is 100% for any traffic matrix. The number of switching modes generated by the algorithm is bounded by n^{2} - 2n + 2 for an n \times n traffic matrix. The computational procedures are illustrated by an example for the Advanced WESTAR system. Also included in the paper are the computer simulation results on the numbers of required switching modes for various simulated traffic matrices.

A Survey of Lagrangian Techniques for Discrete Optimization.

Abstract: Publisher Summary This chapter proposes Lagrangean techniques for discrete optimization problems A simple method for trying to solve zero–one integer programming (IP) problems is discussed This method is used as a starting point for discussing many of the developments since then The behavior of Lagrangean techniques in analyzing and solving zero–one IP problems is typical of their use on other discrete optimization problems The chapter discusses a number of questions about this method and its relevance for optimizing the original IP problem The goal of Lagrangean techniques is to try to establish sufficient optimality conditions: Lagrangean techniques are useful in computing zero–one solutions to IP problems with soft constraints or in parametric analysis of an IP problem over a family of right hand sides Parametric analysis of discrete optimization problems is also discussed The use of Lagrangean techniques as a distinct approach to discrete optimization has proven theoretically and computationally important for three reasons First, dual problems derived from more complex discrete optimization problems can be represented as linear programming (LP) problems, but ones of immense size, which cannot be explicitly constructed and then solved by the simplex algorithm Second, reason for considering the application of Lagrangean techniques to dual problems, in addition to the simplex algorithm, is that the simplex algorithm is exact and the dual problems are relaxation approximations Lagrangean techniques as a distinct approach to discrete optimization problems emphasize the need they satisfy for exploiting special structures, which arise in various models

Nonlinear perturbation of linear programs

Abstract: The objective function of any solvable linear program can be perturbed by a differentiable, convex or Lipschitz continuous function in such a way that (a) a solution of the original linear program is also a Karush–Kuhn–Tucker point, local or global solution of the perturbed program, or (b) each global solution of the perturbed problem is also a solution of the linear program.

Geometric transforms for fast geometric algorithms

Abstract: Many computational problems are inherently geometrical in nature. For example, cluster analysis involves construction of convex hulls of sets of points, LSI artwork analysis requires a test for intersection of sets of line segments, computer graphics involves hidden line elimination, and even linear programming can be expressed in terms of intersection of half-spaces. As larger geometric problems are solved on the computer, the need grows for faster algorithms to solve them. The topic of this thesis is the use of geometric transforms as algorithmic tools for constructing fast geometric algorithms. We describe several geometric problems whose solutions illustrate the use of geometric transforms. These include fast algorithms for intersecting half-spaces, constructing Voronoi diagrams, and computing the Euclidean diameter of a set of points. For each of the major transforms we include a set of heuristics to enable the reader to use geometric transforms to solve his own problems.

A revised simplex algorithm for the absolute deviation curve fitting problem

Abstract: (1979). A revised simplex algorithm for the absolute deviation curve fitting problem. Communications in Statistics - Simulation and Computation: Vol. 8, No. 2, pp. 175-190.

Review Of Linear Programming Applied To Power System Rescheduling

Abstract: Linear and related programming methods have application in transmission planning, security dispatch and emergency control of power systems. With a large still-growing body of literature on the subject, this paper offers a short review of the available LP approaches, techniques and formulations, with due emphasis on state-of-the-art versions. The differences between primal and dual methods and sparse and nonsparse formulations are exposed, and various important techniques such as relaxation, upper bounding and separable programming are dealt with. Thus the paper attempts to provide some clarification of the main fundamental analytical and computational, issues involved in the design of an LP-based method for the rescheduling of power-system operation.

Covering, Packing and Knapsack Problems

Abstract: We survey some of the recent results that have been obtained in connection with covering, packing, and knapsack problems formulated as linear programming problems in zero-one variables.

Computational methods for solving two-stage stochastic linear programming problems

Abstract: Approximating a given continuous probability distribution of the data of a linear program by a discrete one yields solution methods for the stochastic linear programming problem with complete fixed recourse. For a procedure along the lines of [8], the reduction of the computational amount of work compared to the usual revised simplex method is figured out. Furthermore, an alternative method is proposed, where by refining particular discrete distributions the optimal value is approximated.

Enhancements of Spanning Tree Labeling Procedures for Network Optimization.

Abstract: : New labeling techniques are provided for accelerating the basis exchange step of specialized linear programming methods for network problems. Computational results are presented which show that these techniques substantially reduce the amount of computation involved in updating operations. (Author)

An introduction to linear programming and game theory

Abstract: Introduction to Linear Programming and Game Theory, Third Edition includes various additions as well as improvements that have been developed over the last decade, and the most significant addition to the text involves technology. It features an introduction, discussion, and utilization of Solver, a spreadsheet software package that solves mathematical programming problems. PRT Simplex, a computer application for learning the simplex method, has been developed by co-author Gerard Keough and was designed to be used with this book.

Algorithms for worst-case tolerance optimization

Abstract: New algorithms are presented for the solution of optimum tolerance assignment problems. The problems considered are defined mathematically as a worst-case problem (WCP), a fixed tolerance problem (FTP), and a variable tolerance problem (VTP). The basic optimization problem without tolerances is denoted the zero tolerance problem (ZTP). For solution of the WCP we suggest application of interval arithmetic and also alternative methods. For solution of the FTP an algorithm is suggested which is conceptually similar to algorithms previously developed by the authors for the ZTP. Finally, the VTP is solved by a double-iterative algorithm in which the inner iteration is performed by the FTP- algorithm. The application of the algorithm is demonstrated by means of relatively simple numerical examples. Basic properties, such as convergence properties, are displayed based on the examples.

Systems of Linear Inequalities

Abstract: This volume describes the relationship between systems of linear inequalities and the geometry of convex polygons, examines solution sets for systems of linear inequalities in two and three unknowns (extension of the processes introduced to systems in any number of unknowns is quite simple), and examines questions of the consistency or inconsistency of such systems. Finally, it discusses the field of linear programming, one of the principal applications of the theory of systems of linear inequalities. A proof of the duality theorem of linear programming is presented in the last section.

Optimal stopping, exponential utility, and linear programming

Abstract: This paper uses linear programming to compute an optimal policy for a stopping problem whose utility function is exponential. This is done by transforming the problem into an equivalent one having additive utility and nonnegative (not necessarily substochastic) transition matrices.

Computer Codes for Problems of Integer Programming

Abstract: Publisher Summary This chapter presents computer codes for the problems of integer programming. The term “integer programming” covers a wide spectrum of models, which can be characterized by mixed integer programming (MIP) at one end and combinatorial programming at the other end. The interest of those working in commercial organizations is currently focused at the MIP end of the spectrum—indeed on problems, which are basically large linear programming (LP) systems with relatively few integer variables. The chapter presents a “consumer research” report on the different products and also the methods for solving pure integer problems—frequently with special combinatorial structures. Thus, in a consumer report, one has to bear in mind, which consumers are intended for each code. The code should be capable of obtaining a guaranteed optimum solution. A large and complex problem may not be capable of yielding an optimum integer solution within feasible cost and time limits on any code so that the user has in fact to be content with a significant solution obtained by heuristic methods.

A Chance Constrained Optimization Model for reservoir design and operation

Abstract: A chance constrained linear programing model which employs multiple linear decision rules is developed. The model incorporates explicitly the stochastic nature of the streamflow process, can be used in design and/or management situations, does not significantly restrict the operating policy prior to solution, and is economically and computationally feasible. A portion of the Yakima River system is modeled to demonstrate the use of the multiple linear decision rules.

Reliability Optimization by Generalized Lagrangian-Function and Reduced-Gradient Methods

Abstract: Nonlinear optimization problems for reliability of a complex system are solved using the generalized Lagrangian function (GLF) method and the generalized reduced gradient (GRG) method GLF is twice continuously differentiable and closely related to the generalized penalty function which includes the interior and exterior penalty functions as a special case GRG generalizes the Wolfe reduced gradient method and has been coded in FORTRAN title ``GREG'' by Abadie et al Two system reliability optimization problems are solved The first maximizes complex-system reliability with a tangent cost-function; the second minimizes the cost, with a minimum system reliability The results are compared with those using the Sequential Unconstrained Minimization Technique (SUMT) and the direct search approach by Luus and Jaakola (LJ) Many algorithms have been proposed for solving the general nonlinear programming problem Only a few have been demonstrated to be effective when applied to large-scale nonlinear programming problems, and none has proved to be so superior that it can be classified as a universal algorithm Both GLF and GRG methods presented here have been successfully used in solving a number of general nonlinear programming problems in a variety of engineering applications and are better methods among the many algorithms

Parametric integer programming

Abstract: : A parametric integer linear program (PILP) may be defined as a family of closely related integer linear programs (ILP). Within this definition the author incorporates not only continuous scalar parameterizations but also finite parameterizations. These may include an ILP with a finite number of objective functions or right hand sides or constraint matrices or any combination of these. A general framework for PILP is presented. It begins by outlining the need for PILP algorithms. Basic solution methodologies are explained and two rudimentary approaches for the PILP are stated. Theoretical properties for special parameterizations are proved, and techniques for improving algorithmic efficiency are discussed. The framework concludes with an examination of underlying factors which intimately relate to the scheduling of solution priorities in a PILP algorithm.

Integer Programming Post-Optimal Analysis with Cutting Planes

Abstract: Sufficient conditions have been developed for testing the optimality of solutions to all-integer and mixed-integer linear programming problems after coefficient changes in the right hand side and the objective function, or after introduction of new variables. The same conditions can be used as necessary conditions for coefficient changes to alter an optimal solution. The tests are based on cutting-plane theory, and the application of the tests requires solution of the original integer problem with a cutting-plane algorithm.

A polynomial time algorithm for solving systems of linear inequalities with two variables per inequality

Abstract: We present a constructive algorithm for solving systems of linear inequalities (LI) with at most two variables per inequality. The algorithm is polynomial in the size of the input. The LI problem is of importance in complexity theory since it is polynomial time (Turing) equivalent to linear programming. The subclass of LI treated in this paper is also of practical interest in mechanical verification systems, and we believe that the ideas presented can be extended to the general LI problem.

Application of mathematical programming to metal cutting

Abstract: In this paper, a general problem involving the single-pass, single-point turning operation is introduced. Different mathematical models and solution approaches for solving various single objective problems are described. The mathematical properties of the minimization of cost and maximization of production rate solutions are discussed in detail. The solution approaches used are differential calculus, linear programming, and geometric programming. Finally, a multiple criteria machining problem is formulated and solved using goal programming techniques.

Least-Index Resolution of Degeneracy in Linear Complementarity Problems.

Abstract: : This study centers on the circling phenomenon associated with degeneracy in linear complementarity problems and presents an easily implemented technique for resolving it. With certain exceptions, the device is to use the least-index for selecting the variable to leave the basic set. The results of this report pertain only to linear complementarity problems involving P-matrices or positive semi-definite matrices. With this restriction, it is shown that inclusion of the least-index pivot selection rule insures finiteness for the principal pivoting method of Dantzig and Cottle, Lemke's algorithm, and Cottle's parametric principal pivoting method. It is shown that for circling to occur in the principal pivoting method, the matrix must have order at least four, and for Lemke's algorithm it must be at least three. Examples are given showing that these bounds are sharp. Finally, Murty's version of Bard's method is extended from P-matrices to the positive semi-definite case. (Author)