Showing papers on "Discrete optimization published in 1993"

An Augmented Lagrange Multiplier Based Method for Mixed Integer Discrete Continuous Optimization and Its Applications to Mechanical Design

Abstract: An algorithm for solving nonlinear optimization problems involving discrete, integer, zero-one, and continuous variables is presented The augmented Lagrange multiplier method combined with Powell’s method and Fletcher and Reeves Conjugate Gradient method are used to solve the optimization problem where penalties are imposed on the constraints for integer/discrete violations The use of zero-one variables as a tool for conceptual design optimization is also described with an example Several case studies have been presented to illustrate the practical use of this algorithm The results obtained are compared with those obtained by the Branch and Bound algorithm Also, a comparison is made between the use of Powell’s method (zeroth order) and the Conjugate Gradient method (first order) in the solution of these mixed variable optimization problems

Discrete Applied Mathematics

Abstract: : Significant progress has been made with solution of location problems and in preprocessing and decomposition for discrete optimization. There has also been research on the application of techniques from combinational optimization to nonlinear problems.

Linear Optimization and Extensions: Theory and Algorithms

Abstract: A solution to get the problem off, have you found it? Really? What kind of solution do you resolve the problem? From what sources? Well, there are so many questions that we utter every day. No matter how you will get the solution, it will mean better. You can take the reference from some books. And the linear optimization and extensions theory and algorithms is one book that we really recommend you to read, to get more solutions in solving this problem.

Optimum design of trusses with discrete sizing and shape variables

Abstract: The objective here is to present a method for optimizing truss structures with discrete design variables. The design variables are considered to be sizing variables as well as coordinates of joints. Both types of variables can be discrete simultaneously. Mixed continuous-discrete variables can also be considered. To increase the efficiency of the method, the structural responses, such as forces and displacements are approximated in each design cycle. The approximation of responses is carried out with respect to the design variables or their reciprocals. By substituting these approximate functions of the responses into the original design problem, an explicit high quality approximation is achieved, the solution of which does not require the detailed finite element analysis of the structure in each sub-optimization iteration. First it is assumed that all the design variables are continuous and a continuous variable optimization is performed. With the results of this step, the branch and bound method is employed on the same approximate problem to achieve a discrete solution. The numerical results indicate that the method is efficient and robust in terms of the required number of structural analyses. Several examples are presented to show the efficiency of the method.

A global approach for nonlinear mixed discrete programming in design optimization

Abstract: Most current nonlinear mixed discrete programs can only find locally optimal solutions. This paper proposes an optimization method to find the global solution of a nonlinear mixed discrete program. Based on the fact that: “For a discrete variable xi iff xi ∊{k1, k1, k2…,km } then (xi −k 1) (xi k 2)(xi km =0”, the original mixed discrete program is transformed into a penalty optimization program with continuous variables. This penalty optimization program is then solved to find a local optimum. Utilizing the Multi-Level Single Linkage technique, enough starting points are systematically generated to search for most local optima within the feasible region. A global optimum is then found at a pre-specified sufficiently high confidence level such as 99.5%. Some examples of design optimization in literature are tested, which demonstrate that the proposed method is superior to current methods for finding the global optimum.

A flux observer for induction machines based on a time-variant discrete model

Abstract: An alternative approach to obtaining a discrete-time counterpart to the two-axis continuous model of an induction machine is presented. The discrete time-variant equations are derived from a partial discretization of the continuous state equation. The discrete model can be used with advantage in simulation and real-time control applications. A discrete time-variant reduced-order flux observer based on the discrete model is proposed. Computer simulation results are shown to compare the proposed discrete model with that obtained from the Euler method and the exact continuous model. >

Stochastic quasigradient methods for optimization of discrete event systems

Abstract: In this paper, stochastic programming techniques are adapted and further developed for applications to discrete event systems. We consider cases where the sample path of the system depends discontinuously on control parameters (e.g. modeling of failures, several competing processes), which could make the computation of estimates of the gradient difficult. Methods which use only samples of the performance criterion are developed, in particular finite differences with reduced variance and concurrent approximation and optimization algorithms. Optimization of the stationary behavior is also considered. Results of numerical experiments and convergence results are reported.

Modern mathematical methods of optimization

Abstract: Equilibrium models of mathematical economy numerical optimization methods and software convex programming methods of optimal complexity polynomial algorithms in linear programming decomposition of optimization systems modern apparatus of non-smooth optimization discrete programming models and methods analysis of inconsistent mathematical programming problems multiobjective problems optimization in order scales extremal problems in infinite-dimensional spaces.

Discrete optimization of structures using an improved penalty function method

Abstract: The paper describes an improved penalty function method to solve nonlinear discrete optimization problems. A general method to estimate a suitable initial value of the penalty factor and a technique to avoid repetition of inefficient iterations are suggested here

Visualization of multidimensional image data sets using a neural network

Abstract: This paper describes the application of self-organizing neural networks on the analysis and visualization of multidimensional data sets. First, a mathematical description of cluster analysis, dimensionality reduction, and topological ordering is given taking these methods as problems of discrete optimization. Then, the Kohonen map is introduced, that orders its neurons according to topological features of the data sets to be trained with. For this reason, it can also be called a topology-preserving feature map.

Design of discrete coefficient FIR digital filters with arbitrary amplitude and phase responses

Abstract: The design of FIR digital filters with discrete coefficients in the complex frequency domain is considered. A design method based on a recently developed weighted-least-squares (WLS) algorithm is presented. First, FIR filters with continuous coefficients are designed, using the WLS algorithm to meet the desired frequency response specifications in the minimax sense. To avoid the effect of a nonuniformly distributed coefficient grid due to discretization of filter coefficients, a procedure is then performed to obtain an optimal filter gain factor. Finally, utilizing the error weighting function obtained by the WLS algorithm, an efficient discrete optimization process is performed to obtain a discrete solution in the minimax sense. The efficiency of the method is illustrated by the design of discrete-coefficient FIR filters with constant group delay and filter length greater than 60. >

Discrete Optimal Design Using a Genetic Algorithm

Abstract: A genetic algorithm is applied for the optimal design of skeletal building structures accounting for discrete sizing, geometrical and topological variables. An approximate fitness evaluation technique is developed that requires very few structural reanalyses to account for performance constraints during the genetic search. A simple example illustrate the principles involved.

An Interactive Genetic Algorithm for Controller Parameter Optimization

Abstract: Genetic algorithms are stochastic search algorithms inspired by biological phenomena of genetic recombination and natural selection. They simulate the evolution of string individuals encoding candidate solutions to a given problem. Genetic algorithms proved robust and efficient in finding near-optimal solutions in complex problem spaces. They are usually exploited as an optimization method, suitable for both continuous and discrete optimization tasks.

Optimization-a powerful tool for analysis and design

Abstract: An introduction to the theory and application of optimization as a general-purpose problem-solving tool is presented. The use of optimization is greatly enhanced through the development of a general problem-formulation structure which is applicable to a wide range of problems. The work describes the use of various optimization strategies, and includes several examples of the use of optimization to obtain least-squares solutions for circuit and system designs using curve matching, nonlinear equation solving, and complex-plane optimization. >

Efficient Optimum Design of Structures with Discrete Design Variables

Abstract: A method is presented for optimum design of structures, where some or all design variables can be chosen from a set of prescribed values. The main idea is to reduce the number of structural analyse...

What is Optimization

Abstract: Basic concepts of optimization are described using design of a plate girder as an example. First, a way to formulate the problem as an optimization problem is presented. Then basic terminologies and concepts are presented using the graphical optimization procedure. Optimality conditions are explained and basic ideas of iterative optimization methods are presented. It is shown that once the optimization problem is formulated, numerical methods are available to solve the problem and study the effects of variations in various parameters and conditions. This way, the optimization methodology is viewed as a basic framework facilitating computerization of the design process.

Multicriteria discrete optimization of large scale truss systems

Abstract: The paper discusses optimization problems in civil engineering structural design. The following questions are discussed: continuous or discrete optimization, single- or multicriteria optimization, one- or multi-level optimization. The paper is illustrated with examples of the multi-criteria discrete optimization of large scale truss systems. The cross-sectional areas of truss bars are taken as design variables. Minimization of mass, labour cost and displacements are chosen as optimization criteria. Optimization constraints concern stresses, displacements and stability, as well as technological and computational requirements. The results of single- and multicriteria optimization of hall structures are presented in the form of diagrams and tables.

Method and apparatus for real-time constraint solution

Abstract: A circuit and method for executing real time constraint solution permits real time control of computational tasks using analog very large scale integrated (VLSI) circuits. The constraints of a computation or task are first defined as a function or set of functions. The function(s) are used to produce an error measure function which described how well the constraint(s) is/are stisfied. Analog gradient descent techniques are then used to minimize the error measure function and produce an improved output of the task and optionally adjust the performance of the task. As this is performed in analog VLSI, the constraint solution can be performed continuously and continually in real time, without the limitations of discrete optimization as implemented using digital processing.

Adaptive hierarchical multi-objective fuzzy optimization for circuit design

Abstract: The outline of a methodology for adaptive hierarchical multiobjective function optimization in a fuzzy sense is presented, suitable for circuit optimization and able to mimic to some extent the designer's interactive circuit design process. It is an effort to generalize and go beyond the Taguchi methodology of variability-then-target optimization with the addition of automated selection of optimization variables. The methodology allows for the simultaneous and/or sequential optimization of an arbitrary number of statistical measures of an arbitrary number of circuit performances. >

Comparison schemes for discrete optimization with estimation algorithms

Abstract: Consider a discrete optimization problem where the objective function is the mean of a random variable and only samples of the random variable are available. A fundamental issue in such a problem is how to compare objective functions through the samples. Ideally, the chosen comparison scheme should lead to an algorithm whose output converges rapidly to the optimum value. In this paper the authors give some general conditions for convergence and then consider several algorithms having different comparison schemes. >

A modeling framework for hybrid systems

Abstract: We present a modeling framework for hybrid system. In this paper, a hybrid system is a physical plant together with its hybrid control system. The physical plant is described with an hybrid model. The hybrid control system includes a discrete time controller, a discrete event controller and the necessary interface between the two. The proposed modeling framework is applicated to a tank-conveyer system. >

Channel ranking in passive microwave wet-path delay measurements

Abstract: Discrete optimization by channel ranking is used to study the utility of various radiometric channel combinations near the 22235-GHz water vapor line for use in spaceborne wet path delay measurements The study is based on brightness data from a combined statistical geophysical and radiative transfer model Retrieval simulations show that most of the available information on wet path delay can be obtained from a pair of closely spaced channels located on one of the two wings of the 22235 water vapor line The results of the optimization study provide a quantitative basis for assessing performance and cost tradeoffs in spaceborne hardware design >

Explicit Stochastic Optimization

Abstract: The paper includes the theory behind mathematical models (linear and dynamic programming) with explicit consideration of the stochasticity of river flows into a reservoir system. Three examples of application are presented in increasing order of complexity.