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Research Papers: Design Automation

A Novel Decomposition-Based Evolutionary Algorithm for Engineering Design Optimization

[+] Author and Article Information
Kalyan Shankar Bhattacharjee

School of Engineering and Information
Technology,
The University of New South Wales,
Canberra 2600, Australia
e-mail: k.bhattacharjee@student.adfa.edu.au

Hemant Kumar Singh

School of Engineering and Information
Technology,
The University of New South Wales,
Canberra 2600, Australia
e-mail: h.singh@adfa.edu.au

Tapabrata Ray

School of Engineering and Information
Technology,
The University of New South Wales,
Canberra 2600, Australia
e-mail: t.ray@adfa.edu.au

1Corresponding author.

Contributed by the Design Automation Committee of ASME for publication in the JOURNAL OF MECHANICAL DESIGN. Manuscript received July 25, 2016; final manuscript received January 16, 2017; published online February 23, 2017. Assoc. Editor: Harrison M. Kim.

J. Mech. Des 139(4), 041403 (Feb 23, 2017) (11 pages) Paper No: MD-16-1531; doi: 10.1115/1.4035862 History: Received July 25, 2016; Revised January 16, 2017

In recent years, evolutionary algorithms based on the concept of “decomposition” have gained significant attention for solving multi-objective optimization problems. They have been particularly instrumental in solving problems with four or more objectives, which are further classified as many-objective optimization problems. In this paper, we first review the cause-effect relationships introduced by commonly adopted schemes in such algorithms. Thereafter, we introduce a decomposition-based evolutionary algorithm with a novel assignment scheme. The scheme eliminates the need for any additional replacement scheme, while ensuring diversity among the population of candidate solutions. Furthermore, to deal with constrained optimization problems efficiently, marginally infeasible solutions are preserved to aid search in promising regions of interest. The performance of the algorithm is objectively evaluated using a number of benchmark and practical problems, and compared with a number of recent algorithms. Finally, we also formulate a practical many-objective problem related to wind-farm layout optimization and illustrate the performance of the proposed approach on it. The numerical experiments clearly highlight the ability of the proposed algorithm to deliver the competitive results across a wide range of multi-/many-objective design optimization problems.

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References

Figures

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Fig. 1

Final distribution using I-DBEA: (a) MOP1 and (b) C1DTLZ3

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Fig. 2

Structured two-layered set of reference points with M = 3, H1 = 1, H2 = 1. The filled circles represent the reference points generated on the boundary/outside layer, while the hollow circles represent those generated on the inside layer.

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Fig. 4

Assignment strategy

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Fig. 5

Nondominated solutions for the runs with the lowest IGD values for unconstrained problems obtained using A-DBEA: (a) DTLZ1, (b) DTLZ2, (c) MOP1, and (d) MOP2

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Fig. 6

Nondominated solutions for the run with the lowest IGD value for three-objective C1DTLZ3 obtained using A-DBEA

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Fig. 7

Wind farm layouts corresponding to the best value in each objective

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