A gradientbased transformation method in multidisciplinary design optimization
 Po Ting Lin,
 Hae Chang Gea
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Multidisciplinary design optimization (MDO) has become essential for solving the complex engineering design problems. The most common approach is to “divide and conquer” the MDO problem, that is, to decompose the complex problem into several subproblems and to collect the local solutions to give a new design point for the original problem. In 1990s, researchers have developed some decomposition strategies to find or synthesize the optimal model of the optimization structure in order to evenly distribute the computational workloads to multiple processors. Several MDO methods, such as Collaborative Optimization (CO) and Analytical Target Cascading (ATC), were then developed to solve the decomposed subproblems and coordinate the coupling variables among them to find the optimal solution. However, both the synthesis of the decomposition structure and the coordination of the coupling variables require additional function evaluations, in terms of evaluating the functional dependency between each subproblem and determining the proper weighting coefficients between each coupling functions respectively. In this paper, a new divideandconquer strategy, Gradientbased Transformation Method (GTM), is proposed to overcome the challenges in structure synthesis and variable coordination. The proposed method first decomposes the MDO problem into several subsystems and distributes one constraint from the original problem to each subsystem without evaluating the dependency between each subsystem. Each subsystem is then transformed to the singlevariate coordinate along the gradient direction of the constraint. The total function evaluations equal the number of constraints times the number of variables plus one in every iteration. Due to the monotonicity characteristics of the transformed subproblems, they are efficiently solved by Monotonicity Analyses without any additional function evaluations. Two coordination principles are proposed to determine the significances of the responses based on the feasibility and activity conditions of every subproblem and to find the new design point at the average point of the most significant responses. The coordination principles are capable of finding the optimal solution in the convex feasible space bounded by the linearized subsystem constraints without additional function evaluations. The optimization processes continue until the convergence criterion is satisfied. The numerical examples show that the proposed methodology is capable of effectively and efficiently finding the optimal solutions of MDO problems.
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 Title
 A gradientbased transformation method in multidisciplinary design optimization
 Journal

Structural and Multidisciplinary Optimization
Volume 47, Issue 5 , pp 715733
 Cover Date
 20130501
 DOI
 10.1007/s001580120852y
 Print ISSN
 1615147X
 Online ISSN
 16151488
 Publisher
 SpringerVerlag
 Additional Links
 Topics
 Keywords

 Multidisciplinary design optimization
 Gradientbased transformation method
 Monotonicity analysis
 Coordination principles
 Industry Sectors
 Authors

 Po Ting Lin ^{(1)}
 Hae Chang Gea ^{(2)}
 Author Affiliations

 1. Department of Mechanical Engineering, Research and Development Center for Microsystem Reliability, Chung Yuan Christian University, 200 Chungpei Road, Chungli City, Taoyuan County, 32023, Taiwan
 2. Department of Mechanical and Aerospace Engineering, Rutgers, The State University of New Jersey, 98 Brett Road, Piscataway, NJ, 08854, USA