General Aviation Aircraft (GAA) product family design problem

This problem has nine design variables described in [table_1]. There are three aircraft types (2-seater, 4-seater, and 6-seater), giving a total of 27 design variables. There are 10 objectives [table_2] and one constraint used in this formulation. The code is from https://github.com/matthewjwoodruff/generalaviation and more details about the test problem can be found in [1], [2], [3] and [4].

[table_1]

Design variables
No.	Name	Minimum	Maximum
1	Nominal cruising speed	0.24	0.48
2	Aspect ratio	7	11
3	Wing sweep	0	6
4	Propeller diameter	5.5	5.968
5	Wing loading	19	25
6	Activity factor	85	110
7	Seat width	14	20
8	Tail elonagation	3	3.75
9	Wing taper	0.46	1

[table_2]

Objectives
No.	Objectives	Value	Preference
1	Maximum NOISE	Max (NOISE2, NOISE4 NOISE6)	Minimize
2	Maximum WEMP	Max (WEMP2, WEMP4, WEMP6)	Minimize
3	Maximum DOC	Max (DOC2, DOC4, DOC6)	Minimize
4	Maximum ROUGH	Max (ROUGH2, ROUGH4, ROUGH6)	Minimize
5	Maximum WFUEL	Max (WFUEL2, WFUEL4, WFUEL6)	Minimize
6	Maximum PURCH	Max (PURCH2, PURCH4, PURCH6)	Minimize
7	Minimum RANGE	Min (RANGE2, RANGE4, RANGE6)	Maximize
8	Minimum max LDMAX	Min (LDMAX2, LDMAX4, LDMAX6)	Maximize
9	Minimum max VCMAX	Min (VCMAX2, VCMAX4, VCMAX6)	Maximize
10	PFPF		Minimize

where Product Family Penalty Function (PFPF) [5] penalises the uniqueness within the product family by measuring the percentage variation of the design variables within the product family.

Note that the PFPF value differs a bit from the values in the article [4]. The new version of PFPF that is used here, could explain the difference.

[1]

T. W. Simpson, W. Chen, J. K. Allen, and F. Mistree (1996), “Conceptual design of a family of products through the use of the robust concept exploration method,” in 6th AIAA/USAF/NASA/ ISSMO Symposium on Multidiciplinary Analysis and Optimization, vol. 2, pp. 1535-1545.

[2]

T. W. Simpson, B. S. D’Souza (2004), “Assessing variable levels of platform commonality within a product family using a multiobjective genetic algorithm,” Concurrent Engineering: Research and Applications, vol. 12, no. 2, pp. 119-130.

[3]

R. Shah, P. M. Reed, and T. W. Simpson (2011), “Many-objective evolutionary optimization and visual analytics for product family design,” Multiobjective Evolutionary Optimisation for Product Design and Manufacturing, Springer, London, pp. 137-159.

[4] (1,2)

M. Woodruff, T. W. Simpson, P. M. Reed (2013), “Diagnostic Analysis of Metamodels’ Multivariate Dependencies and their Impacts in Many-Objective Design Optimization,” Proceedings of the ASME 2013 IDETC/CIE Conference, Paper No. DETC2013-13125.

[5]

Messac, A., Martinez, M. P., and Simpson, T. W. (May 16, 2002). “Introduction of a Product Family Penalty Function Using Physical Programming .” ASME. J. Mech. Des. June 2002; 124(2): 164-172. https://doi.org/10.1115/1.1467602