Richard J. Balling

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.

Execution of Multidisciplinary Design Optimization Approaches on Common Test Problems

A class of synthetic problems for testing multidisciplinary design optimization (MDO) approaches is presented. These test problems are easy to reproduce because all functions are given as closed-form mathematical expressions. They are constructed in such a way that the optimal value of all variables and the objective is unity. The test problems involve three disciplines and allow the user to specify the number of design variables, state variables, coupling functions, design constraints, controlling design constraints, and the strength of coupling. Several MDO approaches were executed on two sample synthetic test problems. These approaches included single-level optimization approaches, collaborative optimization approaches, and concurrent subspace optimization approaches. Execution results are presented, and the robustness and efficiency of these approaches are evaluated for these sample problems.

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.

The maximin fitness function: multi-objective city and regional planning

The maximin fitness function can be used in multi-objective genetic algorithms to obtain a diverse set of non-dominated designs. The maximin fitness function is derived from the definition of dominance, and its properties are explored. The modified maximin fitness function is proposed. Both fitness functions are briefly compared to a state-of-the-art fitness function from the literature. Results from a real-world multi-objective problem are presented. This problem addresses land-use and transportation planning for high-growth cities and metropolitan regions.

Consideration of Worst-Case Manufacturing Tolerances in Design Optimization

The paper discusses the effect of manufacturing tolerances for the design variables on the solution to an optimization problem. Two formulations of the tolerance problem in an optimization context are presented. Linearization is employed to reduce the problems to quadratic and linear programming problems. The formulations and solutions of the two tolerance problems are illustrated with an example application.

A filtered simulated annealing strategy for discrete optimization of 3D steel frameworks

A new strategy is presented for discrete optimization problems. This strategy is called the “filtered simulated annealing strategy”. It includes a filter size which may be adjusted by the user. A coarse filter size results in an unfiltered simulated annealing strategy which is quite robust in obtaining the global optimum provided enough cycles are executed. A fine filter size blocks many candidate designs which are viewed as having little potential, and produces good designs quickly. The strategy is applied to a realistic 3D steel frame test problem. Extensive results are presented and the performance of the strategy is analysed for parameter sensitivity. The performance is also compared to that of the well-known branch and bound strategy.

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.

Collaborative Optimization of Systems Involving Discrete Design at the Discipline Level

The multidisciplinary design optimization technique known as collaborative optimization is applied to two example problems to illustrate the flexibility that the technique extends to disciplinary design teams. In the first problem, disciplinary design variables are discrete-valued representing the cross-sectional dimensions of standardized shapes for structural members in a frame. In the second problem, discrete disciplinary design variables are used to represent the choice between different structural configurations of truss tower. In both problems, disciplinary design was performed by the non-gradient-based strategy, exhaustive search. Nevertheless, system-level optimization was performed by a gradient-based strategy using simple formulas for the necessary gradients.

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

Methods for interfacing analysis software to optimization software

Abstract Three methods are presented for interfacing analysis software to optimization software to create design software. These methods are referred to as the “conventional interface”, the “pro-gramming-free interface”, and the “generalized interface”. The latter two methods introduce new ideas which are attractive from the users standpoint. The programming-free interface simplifies the interface process by eliminating the necessity for tlie user to modify the analysis source code. The generalized interface allows one to create a general-purpose design package from a general-purpose analysis package. Support for the methods has been implemented in a software package named OPTDES.BYU. Use of the methods with this package is illustrated with a simple example.