J. Sobieszczanski-Sobieski

OPTIMIZATION OF COUPLED SYSTEMS: A CRITICAL OVERVIEW OF APPROACHES

A unified overview is given of problem formulation approaches for the optimization of multidisciplinary coupled systems. The overview includes six fundamental approaches upon which a large number of variations may be made. Consistent approach names and a compact approach notation are given. The approaches are formulated to apply to general nonhierarchic systems. The approaches are compared both from a computational viewpoint and a managerial viewpoint. Opportunities for parallelism of both computation and manpower resources are discussed. Recommendations regarding the need for future research are advanced.

AN ALGORITHM FOR SOLVING THE SYSTEM-LEVEL PROBLEM IN MULTILEVEL OPTIMIZATION

A multilevel optimization approach applicable to nonhierarchic coupled systems is presented. The approach includes a general treatment of design (or behaviour) constraints and coupling constraints at the discipline level through the use of norms. Three different types of norms are examined - the max norm, the Kreisselmeier-Steinhauser (KS) norm, and theℓp norm. The max norm is recommended. The approach is demonstrated on a class of hub frame structures that simulate multidisciplinary systems. The max norm is shown to produce system-level constraint functions which are nonsmooth. A cutting-plane algorithm is presented, which adequately deals with the resulting corners in the constraint functions. The algorithm is tested on hub frames with an increasing number of members (which simulate disciplines), and the results are summarized.

On options for interdisciplinary analysis and design optimization

The interdisciplinary optimization of engineering systems is discussed from the standpoint of the computational alternatives available to the designer. The analysis of such systems typically requires the solution of coupled systems of nonlinear algebraic equations. The solution procedure is necessarily iterative in nature. It is shown that the system can be solved by fixed point iteration, by Newtons method, or by a combination of the two. However, the need for sensitivity analysis may affect the choice of analysis solution method. Similarly, the optimization of the system can be formulated in several ways that are discussed in the paper. It is shown that the effect of the topology of the interaction between disciplines is a key factor in the choice of analysis, sensitivity and optimization methods. Several examples are presented to illustrate the discussion.

New optimality criteria methods - Forcing uniqueness of the adjoint strains by corner-rounding at constraint intersections

In new, iterative continuum-based optimality criteria (COC) methods, the strain in the adjoint structure becomes non-unique if the number of active local constraints is greater than the number of design variables for an element. This brief note discusses the use of smooth envelope functions (SEFs) in overcoming economically computational problems caused by the above non-uniqueness.

An algorithm for solving the system-level problem in multilevel optimization

A multilevel optimization approachwhich is applicableto nonhierarchiccoupledsystems is presented.The approachincludesa generaltreatment of design(or behavior) constraints and coupling constraints at the discipline level through the useof norms. Three different types of normsareexamined-themax norm, the Kreisselmeier-Steinhauser (KS) norm, and the lp norm. The max norm is recommended.The approachis demonstratedon a classof hub frame structures which simulatemultidisciplinary systems.The max norm is shownto producesystem-levelconstraint functions which arenon-smooth. A cutting-plane algorithm is presentedwhich adequatelydealswith the resulting cornersin the constraint functions. The algorithm is testedon hub frameswith increasingnumberof members(which simulate disciplines), and the resultsare summarized. *Thisresearch wassupportedbytheNational Aeronautics andSpaceAdministration underNASAContract No. NASl-19480 while the first author was in residence at the Institute for Computer Applications in Science and Engineering (ICASE), NASA Langley Research Center, Hampton, VA 23681-0001.

Optimization of coupled systems - A critical overview of approaches

The paper identified six fundamental approaches, named by three part names referring to decomposition into levels and treatment of the variables: Single level vs multilevel optimization, System level simultaneous analysis and design vs analysis nested in optimization, discipline level simultaneous analysis and design vs analysis nested in optimization. A compact notation was introduced for these approaches to define concisely the multitude of variations that may be developed by mixing, sequencing, and composing the approaches

BELL-CURVE BASED EVOLUTIONARY OPTIMIZATION ALGORITHM

The paper presents an optimization algorithm that falls in the category of genetic, or evolutionary algorithms. While the bit exchange is the basis of most of the Genetic Algorithms (GA) in research and applications in America, some alternatives, also in the category of evolutionary algorithms, but using a direct, geometrical approach have gained popularity in Europe and Asia. The Bell-Curve Based Evolutionary Algorithm (BCB) is in this alternative category and is distinguished by the use of a combination ofn-dimensional geometry and the normal distribution, the bell-curve, in the generation of the offspring. The tool for creating a child is a geometrical construct comprising a line connecting two parents and a weighted point on that line. The point that defines the child deviates from the weighted point in two directions: parallel and orthogonal to the connecting line, the deviation in each direction obeying a probabilistic distribution. Tests showed satisfactory performance of BCB. The principal advantage of BCB is its controllability via the normal distribution parameters and the geometrical construct variables.