Showing papers on "Discrete optimization published in 1987"

Optimization of Chemical Processes

Abstract: I Problem Formulation 1 The Nature and Organization of Optimization Problems 2 Developing Models for Optimization 3 Formulation of the Objective Function II Optimization Theory and Methods 4 Basic Concepts of Optimization 5 Optimization for Unconstrained Functions: One- Dimensional Search 6 Unconstrained Multivariable Optimization 7 Linear Programming and Applications 8 Nonlinear Programming with Constraints 9 Mixed-Integer Programming 10 Global Optimization for Problems Containing Continuous and Discrete Variables IIIApplications of Optimization 11 Heat Transfer and Energy Conservation 12 Separation Processes 13 Fluid Flow Systems 14 Chemical Reactor Design and Operation 15 Optimization in Large-Scale Plant Design and Operations 16 Integrated Planning, Scheduling, and Control in the Process Industries Appendixes

Configuring a Kanban system using a discrete optimization of multiple stochastic responses

Abstract: This paper investigates the development of a production control strategy for a custom door manufacturer. A Kanban system is developed for the production environment. Simulation and discrete optimization techniques are applied to configure the system. The paper demonstrates that a Kanban approach can be applied to a production environment which neither represents a pure flow shop nor contains balanced production processes. It also highlights the difficulties that can arise in performing a discrete optimization upon conflicting multiple stochastic responses.

Roof duality for polynomial 0-1 optimization

Abstract: The purpose of this note is to generalize the roof duality theory of Hammer, Hansen and Simeone to the case of polynomial 0---1 optimization (0-1PP). By reformulating 0-1PP and expanding some of their definitions, we show that most of the results for quadratic 0---1 problem (0-1QP) can be extended to the general polynomial case.

Testing strategies for simulation optimization

Abstract: There is increasing interest in science and industry in the optimization of computer simulation models. Often these models are not Monte-Carlo simulations, but consist of systems of differential equations, or other mathematical models. These models can present special problems to numerical optimization methods. First, derivatives are often unavailable. Second, function evaluations can be extremely expensive (e.g. 1 hour on an IBM 3090). Third, the numerical accuracy of each function value may depend on a complicated chain of calculations, and so be impractical to pre-specify. This last point makes it difficult to calibrate optimization routines that use finite difference approximations for gradients. This paper presents a strategy for comparing optimization techniques for these problems, and reviews several interesting findings for quasi-Newton methods, simplex search, and others.

A Class of Discrete Time Models for a Continuous Time System

Abstract: An equivalence class, called the T-equivalence class in this study, is introduced for discrete time models of a continuous time system such that any member of this class has the same input-output characteristics when the discrete time interval approaches zero. This concept provides a systematic way of viewing the various discrete time models including those already proposed in the literature.

A discrete optimization method for high-order FIR filters with finite wordlength coefficients

Abstract: A transfer function is Constructed in a cascade form, using a low-order error free function and a high-order function. The high-order function is discretely optimized so that its error spectrum is suppressed by the error-free function. In order to save computing time, the error spectrum is equivalently evaluated in a time domain, and the coefficients are divided into small groups in a discrete optimization procedure.

Application of a simulation optimization system for a continuous review inventory model

Abstract: The system described here is a combination of a simulation generator, output analysis techniques, and optimization procedures. The simulation generator translates the description of a continuous review inventory control system into a SIMAN simulation model. The output analysis techniques estimate the mean and variance of the observations generated by the simulation program. The optimization techniques systematically generate the alternative scenarios and identify the optimal scenario. The simulation results are validated using the analytical solution to the problem.

Effective method for physical mapping the DNA molecule

Abstract: The method of DNA molecules physical mapping based on the algorithms of discrete optimization and graph theory was proposed. The input information consisted of the sizes of single and double restrictions fragments and the level of their measurement errors. The method presents possibilities for optimal planning of experiments and step by step construction of physical maps. Efficiency of the method and examples of its application are discussed.

An application of gomory cuts in number theory

Abstract: Frobenius has stated the following problem. Suppose thata1, a2, ⋯, an are given positive integers and g.c.d. (a1, ⋯ , an) = 1. The problem is to determine the greatest positive integerg so that the equation $$\sum\limits_{i = 1}^n {a_i x_i = g} $$ has no nonnegative integer solution. Showing the interrelation of the original problem and discrete optimization we give lower bounds for this number using Gomory cuts which are tools for solving discrete programming problems.

Discrete optimization of digital filters using Gaussian adaptation and quadratic function minimization

Abstract: In this paper, a new strategy for discrete optimization of a function F(x) is presented. Let A be the region in the n -dimensional parameter space, where F(x) is less than some constant. First, A is located and characterized by a Gaussian search process, called Gaussian adaptation. This makes it possible to approximate the behavior of F(x) . over A by a quadratic function Q(x) . Q(x) is then optimized for the N best discrete solutions using a branch and bound technique. Finally, these points are evaluated for the best F(x) points. By various digital filter examples it will be demonstrated that the new method is more capable of finding good solutions than methods presented so far.

Analysis of discrete dynamic robot models

Abstract: The discrete shift-transformation matrix of general orthogonal polynomials is introduced. The discrete shift-transformation matrix is employed to transform the difference equations, which describe the discrete dynamic robot model, into algebraic equations. Several lemmas are introduced which, together with the discrete shift-transformation matrix, solve for the joint positions and velocities of discrete dynamic robot models via discrete orthogonal polynomials approximations. The initial numerical experiment with a cylindrical coordinate robot shows the feasibility and applicability of discrete orthogonal polynomials approximations.

A statistical approach to computer performance modeling

Abstract: Models of discrete systems are often utilized to assist in computer engineering and procurement. The tools for modeling have been traditionally developed using either analytic methods or discrete event simulation. The research presented here explores the use of statistical techniques to augment and assist this basic set of tools.

Expression optimization using high-level knowledge

Abstract: Combining symbolic algebra with numerical computation has become an effective way of solving many scientific and engineering problems. One of the difficulties in practice is producing concise, efficient, stable code from the large expressions generated in symbolic algebra. Most of the existing optimization techniques are applied after an operation or algorithm has been performed. We introduce techniques using high-level knowledge which are to be applied while the output expressions are generated.

A discrete optimization model for joint communication network design and facility engineering

Abstract: Optimal network design and facility engineering constructs network topologies that minimize total network cost while selecting facility types, allocating capacity, and routing traffic to accommodate demand and performance requirements. Such problems are characterized by large dimensionality even when relatively small networks are considered. This paper describes a data network design model based on a Mixed Integer/Linear Programming (MILP) formulation that does not, as do most other approaches, separate link capacity and facility selection from routing and topological design but fully integrates these processes in order to capture the very important couplings that exist between them. The performance constraints are incorporated into the model in such a way that they are linear but lead to the same grade of service as nonlinear average network delay constraints. Even the basic single-facility network design problem is NP-complete, and no exact solution can be obtained for large-scale networks. The multifacility problem adds even more computational complexity. We present a fast link reduction algorithm that efficiently designs single-facility or multifacility networks and yields robust local extrema. This algorithm is based on a special-purpose greedy drop procedure. In the absence of capacity allocation constraints, the capacity and flow assignment problem is solved optimally and efficiently as part of the overall design process. Numerical results are provided to demonstrate the computational efficiency of the algorithm. A dual relaxation procedure for the computation of a lower bound on network cost is also suggested. In addition, the properties of optimal multifacility, networks are discussed by comparing single-facility and multifacility assignment policies under various network traffic scenarios.

Optimization Aspects of Logical Formulas

Abstract: We consider logical formulas and we are interested in the question whether a clause γ is a consequence of a given formula α. We investigate the problem whether efficiency of an algorithm deciding deducibility α ⊨ γ for some clause γ can be improved by learning from queries γ' having been answered by the algorithm before. Thus, instead of α we consider a formula α' being equivalent to α. In the first part of this paper we show a connection of this kind of optimization problem to the P=NP-problem. Afterwards we consider Prolog programs and the Prolog inference strategy under these aspects of optimization presenting various possibilities of optimizing propositional Prolog programs.

An optimal planning method of plants based on mixed-discrete variable nonlinear programming.

Abstract: An optimal planning method based on a nonlinear programming approach is proposed for the initial design of plants. The optimal constitution and operational policy of equipment are investigated so as to minimize the tota1 annual cost of the plant. This planning problem is formulated as a mixed-discrete variable programming problem, in which discrete and zero-one integer variables are adopted to indicate respectively the scales and on/off status of operation together with continuous variables indicating the operational level. The generalized reduced gradient algorithm is adopted in order to take account of nonlinear equations representing performance characteristics and other properties of each piece of equipment, and is combined effectively with the branch and bound algorithm. The application of the proposed method is illustrated with the planning problem of an energy supply plant of an LNG carrier, and it is shown that this approach is an effective tool for designing plants.

A discrete optimization method for high-order FIR filters with finite wordlength coefficients

Abstract: This paper suggests a discrete optimization method which can solve high order FIR filter problems within a practically reasonable computing time The error spectrum caused by rounding off the coefficients is shaped through the discrete optimization so to be effectively cancelled, in the L 2 norm sense, by other factors connected in cascade In order to save computing time, the error spectrum is evaluated in a time domain, and parameters are divided into small groups during searching for the optimum solution LPF and BPF design examples, with 200 lengths, show the proposed approach can reduce coefficient wordlengths by 2 or 3 bits, compared with results obtained by only rounding off The execution time on the general purpose computer, ACOS System 900, is 97 seconds

Knowledge gathering for heuristic programming in design optimization

Abstract: Presented is an approach to optimization which uses performance criteria from tests conducted on a large variety of different classes of nonlinearly constrained design problems, to improve the design optimization process. The knowledge gathering methods and evaluation techniques are discussed along with how heuristic procedures are integrated to enhance the program's optimization capabilities.