Showing papers on "Continuous optimization published in 1975"

Approach to performance and sensitivity multiobjective optimization: The goal attainment method

Abstract: This short paper is concerned with computational methods for solving optimization problems with a vector-valued index function (vector optimization). It uses vector optimization as a tool for analyzing static control problems with performance and parameter sensitivity indices. The first part of this short paper presents a new computational method, the goal attainment method, which overcomes some of the limitations and disadvantages of methods currently available. The second part presents an integrated, multiobjective treatment of performance and sensitivity optimization based on a vector index approach. A numerical example in electric power system control is included, with analysis and results demonstrating the use of the goal attainment method and application of the approach to performance and sensitivity optimization.

Optimal Stratification and Grouping by Dynamic Programming

Abstract: In statistics and their fields of application a number of different problems in respect to stratification and grouping of random variables or their values result in optimization problems of the same structure. By a suitable transformation a global optimal solution of these problems can be determined by dynamic programming. The results are illustrated for discrete and continuous random variables by numerical results.

Minimax optimization of recursive digital filters using recent minimax results

Abstract: The purpose of this paper is to use some recent work by the author on nonlinear minimax optimization to derive an efficient algorithm for the minimax optimization problem. This is followed by the application of the algorithm to the problem of choosing the coefficients of a recursive digital filter to meet arbitrary design specifications on the magnitude or the group delay characteristics.

Reliability Optimization using SLUMT

Abstract: This paper is concerned with the reliability optimization of a spatially redundant system, subject to various constraints, by using nonlinear programming. The constrained optimization problem is converted into a sequence of unconstrained optimization problems by using a penalty function. The new problem is then solved by the conjugate gradient method. The advantages of this method are highlighted.

Optimization Techniques for Computerized Simulation Models.

Abstract: : This paper reports on the state of the art of available optimization techniques which can be associated with computerized simulation models Specifically, the paper focuses on findings from a literature search and contacts with professionals involved in current research on those optimization techniques which can be applied to the identification of an optimum value for a single output performance measure when a family of input variables can assume either continuous or discrete values In addition, the research considers a set of measures of effectiveness which can be used to assess the relative merits of the various optimization techniques encountered without providing a numerical ranking

Multiple-objective optimization for environment development systems

Abstract: This paper deals with multiple-objective optimization problems for the environment development system. The model of the environment development system, which was introduced by Kulikowski, is described by a system of non linear differential equations which include interconnected n exogenous and m endogenous controlled factors or processes. The problem of multiple-objective optimization for the environment development system is formulated. A main difficulty of multiple-objective optimization is that it is no longer clear what one means by an optimal solution. A possible remedy for this situation is to refine the concept of optimal solution by introducing the so-called Pareto-optimal solution set. Then multiple-objective optimization problem boils down to determining the set of Pareto-optimal solutions. The Pareto-optimal solution set is related in a one-to-one manner to a family of auxiliary scalar index problems. For an unconstrained multiple-objective optimization problem for the environment deve...

The Use of the Box Step Method in Discrete Optimization

Abstract: The Boxstep method is used to maximize Lagrangean functions in the context of a branch-and-bound algorithm for the general discrete optimization problem. Results are presented for three applications: facility location, multi-item production scheduling, and single machine scheduling. The performance of the Boxstep method is contrasted with that of the subgradient optimization method.

Optimization in Design by Reliability

Abstract: This paper considers the problem of minimizing the total cost to be spent on controlling the stress and strength parameters for the normal variables subject to the constraint that the component must have a specified reliability. A numerical example is solved to illustrate the optimization technique.

Program structure analysis in a global optimization

Abstract: We described the solution of the analysis problem in the BETA multi-language system. The key moment here is joining the analysis algorithms at the isolated stage of the optimization phase. From our point of view, such a stage is necessary in any well-developed optimizing compiler for finding information and control connections and frequency relations between program objects. This stage can be considered as a result of applying to the optimization phase such an universal optimization algorithm as "unloading of repeated parts".

Optimization Considerations in Design Reliability by Stress-Strength Interference Theory

Abstract: Reliability of a component can be computed if the probability distributions for the stress and strength are known. The factors which determine the parameters of the distributions for stress and strength random variables can be controlled in design problems. This leads to the problem of finding the optimal values of these parameters subject to resource and design constraints. Some optimization models are discussed. The special structure of these models is exploited to develop the optimization techniques which are illustrated by simple design examples.

Optimal design of nonlinear dc transistor circuits without solving network equations

Abstract: A method is described for the optimization of nonlinear dc circuits. A performance index is defined to measure the difference. between the desired and the actual specifications. The novel approach taken here is to treat the network equations as equality constraints on the design parameters. The constrained optimization problem is then converted to an unconstrained one by a penalty function technique. A straightforward method is given for computing all the gradients needed during the optimization, given only the topology of the network and the branch relationships. This makes the algorithm easily amenable to a package program.

A computational method for linear multiple-objective optimization problems

Abstract: An algorithm for finding the set of all Pareto-optimal solutions of a linear multiple-objective optimization problem is presented in this paper. This algorithm is successful in detecting any Pareto-optimal solution and will systematically and efficiently determine the entire set of Pareto-optimal solutions. An example is given to illustrate the algorithm.

Optimization of Structural Elements

Abstract: A numerical method for the solution of structural optimization problems involving ordinary differential equations is presented for a simple situation where the constraint is of an aeroelastic nature. The method is adapted from optimal control theory and has proven successful in a number of structural optimization problems. Its extension to two dimensional structures is outlined ; limitation to situations involving plates, however, is emphasized. It is assumed that the instability exhibited by the optimality condition is related to the fact that plates cannot in general achieve global extrema. Suggestions for further research in this area are presented.

A note on the optimization of constrained design problems

Abstract: This paper describes a new algorithm for solving constrained optimization problems, based on a method proposed by Chattopadhyay. The proposed algorithm replaces the original problem withm constraints,m>1, by a sequence of optimization problems, with one constraint. Here, we modify the algorithm given by Chattopadhyay in order to make it applicable for a larger class of optimization problems and to improve its convergence characteristics.

Performance optimization of nonlinear electrical networks

Abstract: A program suite for the optimization of nonlinear networks is described. This suite provides an interactive automated design aid within a small-machine environment. A unified approach for time-domain design is presented. A generalized form of performance function is used and is based on the development of the adjoint-network from Tellegen's theorem. A suitable set of the adjoint-network excitations is also obtained. The constrained optimization of the performance function is transformed by a change of variables into an unconstrained problem. Powell's algorithm for unconstrained minimization is used. The optimization algorithm requires the value of the performance function and its derivatives which are obtained from analyses of the network and its adjoint. The program is implemented on a small computer with 16k words of (16-bit) core store. The overall structure of the program suite is described and results of the optimization of some simple circuits are given.