NDLI: On the analytical derivation of the Pareto-optimal set with applications to structural design

Content Provider	Springer Nature Link
Author	Gobbi, M. Levi, F. Mastinu, G. Previati, G.
Copyright Year	2014
Abstract	The Fritz John conditions for Pareto-optimality have been set in matrix form and used for introducing a procedure for the analytical derivation of the Pareto-optimal set in the design variables domain. Subsequently, the derivation of the Pareto-optimal set in the objective functions domain can be obtained, if possible, by a proper analytical derivation. Both the objective and constraint functions are assumed to be available in analytical form and twice differentiable and convex (or pseudo-convex). The proposed procedure to find the Pareto-optimal set is relatively simple. The computation of the determinant of a matrix is required. A symbolic manipulator can be exploited. If there are two design variables and two objective functions, the Pareto-optimal set can be easily computed by applying a simple formula derived in the paper. If the number of design variables equals the number of objective functions, the Pareto-optimal set in the design variables domain can be found by computing the product of the constraint functions times the determinant of the Jacobian of the objective functions. A number of case studies have been proposed to test the effectiveness of the proposed procedure. The optimal structural design of, respectively, a pair of compressed spheres, a cantilever with rectangular cross section have been faced and solved. Additionally the test problem proposed by Fonseca and Fleming has been addressed and solved analytically. Optimization problems with low dimensionality (2 or 3 design variables and 2 objective functions, 2 or more constraints) have been easily solved. The proposed procedure can be useful in the actual engineering practice at the earliest design stage. In this case the designer can be made aware on the proper design variables setting to obtain the desired tradeoff among conflicting objective functions.
Starting Page	645
Ending Page	657
Page Count	13
File Format	PDF
ISSN	1615147X
Journal	Structural and Multidisciplinary Optimization
Volume Number	51
Issue Number	3
e-ISSN	16151488
Language	English
Publisher	Springer Berlin Heidelberg
Publisher Date	2014-08-21
Publisher Place	Berlin, Heidelberg
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Multi-objective optimization Pareto-optimal set Necessary optimality conditions Analytical solution Beam structures Size optimization Theoretical and Applied Mechanics Computational Mathematics and Numerical Analysis Engineering Design
Content Type	Text
Resource Type	Article
Subject	Control and Optimization Computer Graphics and Computer-Aided Design Control and Systems Engineering Computer Science Applications Software

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