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Research Papers: Design Automation

A Novel Sequential Multi-Objective Optimization Using Anchor Points in the Design Space of Global Variables

[+] Author and Article Information
Jianhua Zhou, Min Xu

National Engineering Laboratory for the
Automotive Electronic Control Technology,
Shanghai Jiao Tong University,
Shanghai 200240, China

Mian Li

National Engineering Laboratory for the
Automotive Electronic Control Technology,
Shanghai Jiao Tong University,
Shanghai 200240, China;
University of Michigan-Shanghai Jiao Tong
University Joint Institute,
Shanghai Jiao Tong University,
Shanghai 200240, China
e-mail: mianli@sjtu.edu.cn

1Corresponding author.

Contributed by the Design Automation Committee of ASME for publication in the JOURNAL OF MECHANICAL DESIGN. Manuscript received February 1, 2016; final manuscript received August 24, 2016; published online October 3, 2016. Assoc. Editor: Harrison M. Kim.

J. Mech. Des 138(12), 121406 (Oct 03, 2016) (11 pages) Paper No: MD-16-1092; doi: 10.1115/1.4034671 History: Received February 01, 2016; Revised August 24, 2016

Multi-objective problems are encountered in many engineering applications and multi-objective optimization (MOO) approaches have been proposed to search for Pareto solutions. Due to the nature of searching for multiple optimal solutions, the computational efforts of MOO can be a serious concern. To improve the computational efficiency, a novel efficient sequential MOO (S-MOO) approach is proposed in this work, in which anchor points in the design space for global variables are fully utilized and a data set for global solutions is generated to guide the search for Pareto solutions. Global variables refer to those shared by more than one objective or constraint, while local variables appear only in one objective and corresponding constraints. As a matter of fact, it is the existence of global variables that leads to couplings among the multiple objectives. The proposed S-MOO breaks the couplings among multiple objectives (and constraints) by distinguishing the global variables, and thus all objectives are optimized in a sequential manner within each iteration while all iterations can be processed in parallel. The computational cost per produced Pareto point is reduced and a well-spread Pareto front is obtained. Six numerical and engineering examples including two three-objective problems are tested to demonstrate the applicability and efficiency of the proposed approach.

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Figures

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Fig. 2

Hyperarea and overall spread

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Fig. 1

Multi-objective solutions

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Fig. 3

Monotonicity of objective and domination relationship

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Fig. 4

Set Z for a five-objective problem with two global variables

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Fig. 8

Pareto fronts of example 1 (a) results of WS, (b) results of NNC, and (c) results of S-MOO

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Fig. 9

Pareto fronts of example 2 (a) results of WS, (b) results of NNC, and (c) results of S-MOO

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Fig. 5

Observations with one global and local variable(s)

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Observation with two global variables

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Fig. 10

Pareto fronts of example 3 (a) results of WS, (b) results of NNC, and (c) results of S-MOO

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Fig. 14

Pareto fronts for four-bar truss (a) results of WS, (b) results of NNC, and (c) results of S-MOO

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Fig. 11

Pareto fronts of speed reducer (a) results of WS, (b) results of NNC, (c) results of S-MOO before inserting more points, and (d) results of S-MOO after inserting more points

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Fig. 12

Pareto fronts for three-objective example (a) results of NNC and (b) results of S-MOO

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Fig. 13

Illustration of the four-bar truss problem

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