General Optimization Criterion Research Articles

An efficient optimality criteria approach to the minimum weight design of elastic structures

This paper is concerned with the optimality criteria approach to the minimum weight design of elastic structures analyzed by finite elements. It is first shown that the classical methods apply the lagrangian multiplier technique to an explicit problem. This one results from high quality, first order approximations of the displacement constraints and cruder, zero order approximations of the stress constraints. A generalized optimality criterion is then proposed as the explicit Kuhn-Tucker conditions of a first order approximate problem. Hence a hybrid optimality criterion is developed by using both zero and first order approximations of the stress constraints, according to their criticality. Efficient solution algorithms of the explicit approximate problem are suggested. Its dual statement generalizes the classical lagrangian approaches. Its primal statement leads to a rigorous definition of the optimality criteria approach, which appears to be closely related to the linearization methods of mathematical programming. Finally some numerical applications clearly illustrate the efficiency of the generalized and hybrid optimality criteria.

A unified approach to structural weight minimization

It is shown that the two classical approaches to structural optimization have now reached a stage where they employ the same basic principles. Indeed, the well-known optimality criteria approach can be viewed as transforming the initial problem in a sequence of simple explicit problems in which the constraints are approximated from virtual work considerations. On the other hand, the mathematical programming approaches have progressively evoluated to a linearization method using the reciprocals of the design variables — this powerful method is proven here to be identical to a generalized optimality criteria approach. Finally, new efficient methods are proposed: (a) a hybrid optimality criterion based on first-order approximations of the most critical stress constraints and zeroth-order approximations of the others and (b) a mixed method which lies between a strict primal mathematical programming method and a pure optimality criteria (or linearization) approach. Simple numerical problems illustrate the concepts established in the paper.

Infinite-Horizon Dynamic Programming Models—A Planning-Horizon Formulation

Two major areas of research in dynamic programming are optimality criteria for infinite-horizon models with divergent total costs and forward algorithm planning-horizon procedures. A fundamental observation for both problems is that the relative cost of two possible initial actions for a given initial state may be quite insensitive to structural information in all but the first few periods of a multiperiod model. Recently Lundin and Morton have developed a unified machinery for the dynamic lot size model that provides a general optimality criterion for the infinite horizon problem and complete planning-horizon procedures. Here those ideas are extended to provide a formal infinite-horizon/planning-horizon framework for a reasonably general form of the dynamic programming problem. Several examples and illustrations are provided. The approach provides a good vehicle for investigating the non-stationary stochastic inventory problem; this work will appear elsewhere.

Design and Evaluation of an Adaptive MTI Filter

The design and evaluation of an adaptive moving target indicator (MTI) filter, the adaptive canceler for extended clutter (ACEC) is dealt with, taking into consideration adaptivity to clutter mean Doppler frequency. This consideration is one of the most important operational requirements in adaptive MTI's and permits a relatively simple hardware implementation as compared to more general optimization and adaptivity criteria (briefly described). The ACEC's algorithm compensates in real time for the clutter mean Doppler frequency. Performances have been obtained by digital computer simulation in various operational conditions.

Linear Combinations of Dependent Meteorological Estimates: A Synopsis

Properties of the optimal combination scheme for several vector estimates are developed for correlated estimates having common ensemble mean. Classic optimality properties of a linear combination of estimates from separate sources are established as corollaries of the more general optimization criterion. simultaneous minimization of variance components.

General Equivalence Theory for Optimum Designs (Approximate Theory)

For general optimality criteria $\Phi$, criteria equivalent to $\Phi$-optimality are obtained under various conditions on $\Phi$. Such equivalent criteria are useful for analytic or machine computation of $\Phi$-optimum designs. The theory includes that previously developed in the case of $D$-optimality (Kiefer-Wolfowitz) and $L$-optimality (Karlin-Studden-Fedorov), as well as $E$-optimality and criteria arising in response surface fitting and minimax extrapolation. Multiresponse settings and models with variable covariance and cost structure are included. Methods for verifying the conditions required on $\Phi$, and for computing the equivalent criteria, are illustrated.

Erratum: "Minimum-Mass Design of a Plate-Like Structure for Specified Fundamental Frequency"

The purpose of this paper is to present a new approach to the problem of the minimum-mass design of two-dimension al continuous structures which are required to satisfy a constraint of a dynamic or aeroelastic nature, expressed in the form of one or more partial differential equations. The minimization of a functional subject to constraints of this form belongs to a wider class of problems, encountered in the theory of optimal control of systems with distributed parameters. Classical methods of optimal control theory are here extended to two dimensions in order to derive the set of necessary conditions for an extremum. They are then applied to the theoretical case of the minimum-mass design of a simply-supported shear plate for a given fundamental frequency of vibration under the structural mass assumption. An equation for the optimal displacement, which is the expression of a general optimality criterion in structural design due to Prager and rendering the necessary conditions also sufficient, is derived and solved uniquely in closed form for any shape of the plate. Results are presented for a square and rectangular shape, and for a circular plate. The case of an inequality constraint applied to the thickness (minimum thickness) is also examined.

Optimality Criteria for Flowshop Schedules

Abstract This article considers the problem of scheduling n jobs on M machines in a flowshop and examines the present formulation of the problem. To understand the true nature of the problem, this article provides economic interpretations of various optimality criteria which are being used for solving the scheduling problem. A general optimization criterion, called minimization of opportunity cost, is proposed for flow-shop scheduling problems and the results of the sensitivity analysis of various optimality criteria are reported which indicate the need to reformulate the scheduling problem.

Optimal plastic design of circular and annular sandwich plates with piecewise constant cross section

Hopkins and Prager (1955) used an intuitive approach based on the concept of competing yield mechanisms to discuss plastic minimum-weight design of a circular plate with piecewise constant cross section. Since this paper was written, the theory of optimal plastic design has progressed considerably, but subsequent papers on optimal plate design were exclusively concerned with plates of continuously varying cross section. In view of the lesser manufacturing cost of plates with piecewise constant cross section, the present paper re-examines the original problem in the light of the modern theory of optimal plastic design. General optimality criteria are established and applied to full circular as well as annular plates. The relation of the designs obtained for annular plates to the singular designs investigated by Mpegarefs (1966, 1967) is discussed.