Research Papers: Design Automation

Multiple Surrogate-Assisted Many-Objective Optimization for Computationally Expensive Engineering Design

[+] Author and Article Information
Kalyan Shankar Bhattacharjee

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

Hemant Kumar Singh

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

Tapabrata Ray

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

Contributed by the Design Automation Committee of ASME for publication in the JOURNAL OF MECHANICAL DESIGN. Manuscript received September 11, 2017; final manuscript received February 15, 2018; published online March 23, 2018. Assoc. Editor: Mian Li.

J. Mech. Des 140(5), 051403 (Mar 23, 2018) (10 pages) Paper No: MD-17-1624; doi: 10.1115/1.4039450 History: Received September 11, 2017; Revised February 15, 2018

Engineering design often involves problems with multiple conflicting performance criteria, commonly referred to as multi-objective optimization problems (MOP). MOPs are known to be particularly challenging if the number of objectives is more than three. This has motivated recent attempts to solve MOPs with more than three objectives, which are now more specifically referred to as “many-objective” optimization problems (MaOPs). Evolutionary algorithms (EAs) used to solve such problems require numerous design evaluations prior to convergence. This is not practical for engineering applications involving computationally expensive evaluations such as computational fluid dynamics and finite element analysis. While the use of surrogates has been commonly studied for single-objective optimization, there is scarce literature on its use for MOPs/MaOPs. This paper attempts to bridge this research gap by introducing a surrogate-assisted optimization algorithm for solving MOP/MaOP within a limited computing budget. The algorithm relies on principles of decomposition and adaptation of reference vectors for effective search. The flexibility of function representation is offered through the use of multiple types of surrogate models. Furthermore, to efficiently deal with constrained MaOPs, marginally infeasible solutions are promoted during initial phases of the search. The performance of the proposed algorithm is benchmarked with the state-of-the-art approaches using a range of problems with up to ten objective problems. Thereafter, a case study involving vehicle design is presented to demonstrate the utility of the approach.

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Grahic Jump Location
Fig. 1

(a) Uniform reference vectors and (b) distance measures

Grahic Jump Location
Fig. 2

Schematic comparison of ASF and ED measures

Grahic Jump Location
Fig. 4

Vehicle modules: (a) side view and (b) top view

Grahic Jump Location
Fig. 5

Comparison of MaO and SaMaOASF-ED over function evaluations based on the median run: (a) fraction of nondominated solutions and (b) HV

Grahic Jump Location
Fig. 3

Local search behavior for ASF and ED measures



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