Showing papers on "Discrete optimization published in 1990"

A penalty approach for nonlinear optimization with discrete design variables

Abstract: A penalty approach for the solution of nonlinear discrete optimization problems is proposed. In general, the penalty approach is used for converting a constrained op-timization problem into a sequence of unconstrained problems. The objective function for the unconstrained problem at each step of the sequential optimization includes terms that introduce penalty depending on the degree of constraint violation. In addition to the penalty terms for constraint violation, the proposed approach intro-duces penalty terms to reflect the requirement that the design variables take discrete values. A variable magnitude penalty term in the form of a sine function is introduced and implemented with the extended interior penalty method of the optimization package NEWSUMT-A. The performance of the proposed method is investigated by several numer-ical examples.

Minimax multiobjective optimization in structural design

Abstract: SUMMARY The use of multiobjective optimization techniques, which may be regarded as a systematic sensitivity analysis, for the selection and modification of system parameters is presented. A minimax multiobjective optimization model for structural optimization is proposed. Three typical multiobjective optimization techniques-goal programming, compromise programming and the surrogate worth trade-off method-are used to solve such a problem. The application of multiobjective optimization techniques to the selection of system parameters and large scale structural design optimization problems is the main purpose of this paper.

A new method for discrete optimization problems

Abstract: A generalized optimization system with a discrete decision space, is described, and on an optimization problem is defined which is associated with the system. A new solution method, which is called modular approach (MA), is presented to solve the optimization problem. This method extends the Morin-Marsten hybrid idea to solve troublesome problems of dynamic programming. The present method is also an extension of the branch-and-bound method using breadth-first search.

Discrete mathematics as a precursor to programming

Abstract: Computer programming courses are an option available to many high school and college students. These courses typically teach features of a specific programming language, and students develop programs to solve a variety of problems. Such courses build only slightly on prior mathematics experience, and do not necessarily reinforce mathematics skills. Discrete mathematics, however, provides an important link between mathematics, computing, and problem-solving. When and how should this link be made? What mathematics topics are most appropriate? This paper describes preliminary experiences teaching an innovative discrete mathematics course for a wide range of student populations which include: high school students, college freshman planning to major in computer science, and mathematics education majors. The courses described are designed to address stndent weaknesses in discrete mathematics and problem-solving, and to illustrate the mathematical foundations of computing. They stress general problem-solving techniques and mathematical concepts that aid in the analysis and solution of computer based problems. The concentration is on general problem solving principles, patterns and symmetries, recursive and inductive thinking, algorithmic problem solving, and discrete mathematics concepts including: sets, propositional and predicate logic, proof techniques, relations, graphs and trees, functions, sequences, mathematical induction, language syntax, and algorithms, These concepts are motivated within the context of computer science, and its applications. For example, the principles of logic are used to understand logic programming, and functions are the underlying theory of applicative, or functional programming. To further enhance the learning experience, course material is reinforced through exploratory computer-based laboratory modules.

An interactive algorithm for nonlinear vector optimization

Abstract: In this paper an interactive algorithm for nonlinear vector optimization problems is presented. This algorithm decides, after solving only two optimization problems, whether or not there are efficient points in the feasible set. In the latter case, an efficient point depending on parameters is automatically computed, and (which is much more important) efficient points for each parameter can be calculated by this procedure.

Discrete optimization of geometrically nonlinear truss structures under stability constraints

Abstract: The paper deals with discrete optimization of elastic trusses with geometrical nonlinear behaviour and constraints on stability. The problem consists of minimizing the weight and determining the optimal member distribution so that the external load does not cause a loss of stability of the structure. Member cross-sections are selected from a catalogue of available sections. Element stresses, elment stability and global structural stability constraints are considered. A controlled enumeration method according to the increasing value of the objective function is applied. Shallow space trusses are numerically analysed.

Discrete optimization of trusses with stability constraints

Abstract: The paper deals with discrete optimization of elastic trusses with geometric nonlinear behaviour and constraints on stability. The problem consists of minimizing the weight of the structure and choosing the optimal cross-sectional areas of members so that external loads do not cause a loss of stability. Member cross-sections are selected from a discrete set of available sections. Element stresses, element stability and global structural stability constraints are considered. An enumeration method according to the increasing value of the objective function is applied. The numerical examples concern the optimization of shallow truss structures when snap-through can occur. The discrete optimal solutions have been compared with the results of continuous design variables optimization. The influence of small initial imperfections of geometry on discrete optimal designs has been examined.

Discrete mathematics for computing

Abstract: Logic and sets data representation and manipulation graphs tress functions and databases counting and probability codes.

Characterizing distributions of discrete bivariate random variables for simulation and evaluation of solution methods

Abstract: Results are presented from empirical evaluations of the performance of solution procedures on random binary knapsack and weighted set covering problems in which correlation is induced between the objective function and constraint coefficients. The performance of the solution procedures degrades as the correlation induced among the test problem parameters is increased, and test problems with structured dependence should be used for many empirical evaluations of solution methods. Since structured dependence in discrete optimization test problems is desirable, ways to characterize the joint distribution of a discrete bivariate random variable for any feasible correlation are needed. The problem of finding a characterization with the maximum value of the smallest probability for any possible point is formulated as a linear program. An efficient algorithm based on the northwest corner rule and a simple probability reallocation scheme are presented. >

Rule-based expert systems and discrete optimization

Abstract: Making inference efficient and intelligent is essential in developing expert systems. Inference in a rule-based expert system has intrinsic connection to quantitative approaches of optimization. This thesis presents a linear programming representation for a subset of propositional logic, Horn clauses, which have simple forms but are widely used in expert systems. The inverse of a basis matrix of the associated linear program provides a comprehensive proof structure for inference. In particular, the basis matrix inverse tells how each assertion determines the others, and is itself determined by the others. This tabularized proof structure provides a convenient way of making inference transparent and flexible. The linear program associated with a Horn clause system belongs to the class of Leontief flow problems. This thesis proves that the Leontief flow problem enjoys the same strong integrality property as the network flow problem. In particular, all extreme points of the polyhedron of a Leontief flow problem with integral data are integral. A log-linear time algorithm is developed for a class of Leontief flow problems. This algorithm leads to an efficient procedure for selecting a question to ask the user when more information is needed. For general propositional logic, a list processing procedure is developed and tested. This procedure combines the branch and bound method for integer programming with the symbolic inference process. Computational experiments show the improvement in inference efficiency.

Discrete optimal design of trusses with stress and frequency constraints

Abstract: The problem of structural optimization of trusses subject to stress and frequency constraints is considered from a practical viewpoint. Assuming that the choice of members has to be from a discrete set of available sections, the solution is attempted using a mathematical programming approach and an approximate two‐step procedure involving a continuous variable optimization followed by a discrete programming algorithm. The latter approach is highly promising for problems involving stress and frequency constraints. Detailed results are presented using several benchmark problems.

System Modelling and Optimization: Proceedings of the 14th Ifip-Conference Leipzig, Gdr, July 3-7, 1989

Abstract: Models and optimal control of robotic systems.- New approaches in optimization techniques.- Deterministic control of uncertain systems via a constructive use of Lyapunov stability theory.- A mathematical model for structural analysis of dynamical systems.- An interactive procedure based on the inscribed ellipsoid method.- On the absolute center of a set in an edge.- On parallel programming environments and multilevel optimization.- Primal-dual decomposition of separable nonconvex optimization problems with constraints.- Automatic and parallel generation of gradient and Hessian matrix.- Solving non-cooperative games by continuous subgradient projection methods.- Extended Fibonacci search for proper sinusoidal functions.- Grid optimization in the finite- element- method.- An algorithm for large-scale linearly constrained nondifferentiable convex minimization.- Superlinearly convergent optimization methods without solving QF.- Multilevel dichotomy algorithm in global optimization.- Discrete approximation of extremum problems with operator constraints.- On the methods of nonsmooth optimization.- 1-Determinacy of feasible sets.- Symbolic generation of an optimal Karmarkar's projective algorithm for sparse linear programs.- Relations between the Karush-Kuhn-Tucker points of a nonlinear optimization problem and of a generalized Lagrange dual problem.- The relief indicator method as a new approach to constrained global optimization.- Comparison of six types of separating functionals.- On differential estimations for marginal functions in mathematical programming problems with inclusion constraints.- Methods of centers in nonlinear programming.- On the control of neutron density subject to a transport equation and a reflection law.- The maximum principle and relativity theory.- Upper semicontinuity of solutions of singularly perturbed differential inclusions.- Optimal control of two point boundary value problems.- Guaranteed cost control of linear polytope systems.- Time-optimal control in nonlinear evolution equations.- Necessary and sufficient dynamic programming conditions for optimal control problem with state constraints.- Extensions of Pontryagin's maximum principle.- Optimal guidance of dynamic systems.- Planar robot motion with an obstacle: -Synthesis of time-optimal control.- The problem of time-optimal control with the search of the goal point.- Solving some optimal control problems using the barrier penalty function method.- Second-order conditions in a time-optimal control problem for linear system.- Optimal control problems under disturbances.- Impulsive control problems.- Global solutions in optimal control via silp.- Approximate controllability with positive controls for linear retarded systems : A discrete-time approach.- Applications of analytic centers for the numerical solution of semiinfinite, convex programs arising in control theory.- Semigroup methods and approximation of nonlinear parabolic boundary control problems.- Two-level systems of mathematical physics with cross connections.- New results on No-Wait Flow Shop scheduling.- New exact and feuristic algorithms for the Crew Scheduling problem.- The job - shop problem - modelling by latin rectangles, exact and heuristic solution.- Maximal displacement of discrete loaded strings.- Succesively decomposed networks and their application in discrete programming.- Ficets of the scheduling polytope.- Solution of a class of interval scheduling problems using network flows.- A fuzzy algorithm for constructing cyclic schedules.- Min-sum and min-max single-machine scheduling with stochastic tree-like precedence constraints: Complexity and algorithms.- The PLA-folding problem: Simulated annealing and iterative improvement approaches.- On finding sets of alternatives for the discrete multiobjective problems.- Recent results on the Discrete Lotsizing and Scheduling Problem.- Structural net systems optimization.- Inverse optimization problems and methods for their solution.- Approximate modeling of dynamic systems.- Model building and simulation of a reactor for coal pyrolysis.- Parametrization for curve interpolation in technical applications.- Optimal control of the arrival and service processes in an M/G/1 queue.- Control of nonlinear systems described by QuasiLinear Fuzzy Models.- Decomposition of objective function in stochastic combinatorial optimization.- Polynomial design of the stochastic optimal, minimal complication system.- Economic development, learning and stopping rules.- Invariance, parameter estimations, sensitivity analysis and other help functions in computer aided desigh by GI/GI/c - Queueing models.- Numerical analysis of suboptimal stochastic control systems of a diffusion type.- Complete ideal observability of some classes of dynamic systems with unknown nonlinear inputs.- Laser propagation in atmospheric turbulence, stochastic models and simulation Robert Patton Leland.- Optimal inspection under semimarkovian deterioration: Extensions.- On some selection problem.- Stochastic programs with complete recourse: Stability and an application to power dispatch.- The estimation of the magnitude response of a linear system from the restored covariance function.- An approximation method for queueing network with a common buffer and blocking.- Technological change and policy in MRIO models.- Mathematical modelling of sedimentation processes in a centrifuge.- Modelling the relation between foreign currencies.- An account of uncertainty factor in models of discrete optimization of electric power supply systems.- Mathematical description of the synaptic transmission and its entropy production.- Synthesis of control strategies in flexible manufacturing.- On the solution of a class of quadratic programs using a differentiable exact penalty function.- Energy and cost optimization in industrial models.- Placement heuristics for generation of FMS layouts.- A model for electricity demand forecasting in a communal electric utility.- An optimization technique with neural networks and its application to a ferry routing.- Real-time simulation and control system for the continuous casting process.- Transmission range control for packet radio networks or why magic numbers are distance dependent.- A model for antibiotic therapy: Tecidual kinetics implications.- System modelling of functional processes in living organisms.- Optimization of real nonrecursive processors implemented in floating point arithmetic.- PROTOS: Towards better production planning systems.- Optimal control of integrated communication system.- Reliability-based optimization of parallel systems.- Optimization-based nycely nonlinear modelling.- Computer aided design of optimal regulators and filters with constraints.- Modelling of an expert system tool for configuration problems.- Turboprop engine behaviour modelling based on optimization approach.- Optimal local flow control of a general multiple data link with limited buffers.- Heuristic reasoning in mathematical programming.- Parallel global optimization algorithms in optimal design.

New evidence favoring multilevel decomposition and optimization

Abstract: A new multilevel optimization technique based on a global sensitivity matrix which uses behavior variables in addition to design variables and constraints to decompose the problem is proposed. The technique simplifies the decomposition of the design problem and the programming task and improves the convergence speed of multilevel optimization compared to conventional optimization. The technique is particularly well suited to problems with large numbers of design variables and with computationally expensive constraints.

Discrete Optimization (R. Gary Parker and Ronald L. Rardin)

Abstract: The field of morphological image processing is relatively new and was initiated in the late 1960s mainly by the work ofGeorges Matheron [1 ]. The literature on mathematical morphology is not exactly full of easy-toread texts. Probably the best-known and most comprehensive work in this area is the book Image Analysis and Mathematical Morphology by J. Serra [2]. However, find this book difficult to read, and apparently from anecdotal evidence, so do others. Now, barely one year after their text Image Processing--Continuous to Discrete [3], Giardina and Dougherty have written this new text complete with homework problems and references. While am not an expert in this field, my first reaction is: If you have ever wanted to teach a course in this subject or want to learn the field yourself, this is probably the text of choice (at least for the moment). The book is clearly written and totally devoid of the ruminations, philosophical detours, and awkward vocabulary characteristic of the book by Serra. First, what is morphological image processing? Morphology refers to the study of forms, and morphological image processing is the study of image forms largely based on Minkowski algebra. Two key Minkowski operations are addition and subtraction defined, respectively, for any two sets A, B as A B LJb. A + b and A @ B CIb. A + b. Using these operations we can \"erode\" (shrink) or \"dilate\" (expand) an image. These operations are useful in checking the connectivity of conducting strips on printed circuit boards, to give but one example. The book is organized into six chapters: 1. \"Morphology in the Euclidean Plane\"; 2. \"Digital Morphology\"; 3. \"Morphological Features\"; 4. \"Topological Processing\"; 5. \"Morphological Filters for Two-Valued Images\"; and 6. \"Gray-Scale Morphology.\" Readers ignorant of morphological methods but familiar with classical digital image processing may not find this material easy to absorb at first. Morphological operators do not look like Wiener filters or least-squares estimators. But, as the authors have demonstrated in their well-executed book, morphological methods are mathematically elegant and directly implementable on computers.