Multiob jective Optimization of Trusses using Genetic Algorithms
Carlos A. Co ello Co ello
y
Alan D. Christiansen
z
y
Engineering Design Centre, University of Plymouth, Plymouth, PL4 8AA, UK
z
Department of Computer Science, Tulane University, New Orleans, LA 70118, USA
Abstract:
In this paper we propose the use of the genetic algorithm (GA) as a tool to solve multiobjective
optimization problems in structures. Using the concept of min-max optimum, a new GA-based multiobjective
optimization technique is proposed and two truss design problems are solved using it. The results produced by
this new approach are compared to those produced by other mathematical programming techniques and GA-based
approaches, proving that this technique generates better trade-os and that the genetic algorithm can be used as a
reliable numerical optimization tool.
Keywords
:
genetic algorithms, multiob jective optimization, vector optimization, multicriteria optimization,
structural optimization, truss optimization
1 Intro duction
In most real-world problems, several goals must b e satised simultaneously in order to obtain an optimal
solution. The multiple ob jectives are typically conicting and non-commensurable, and must b e satised simul-
taneously. For example, we might want to b e able to minimize the total weight of a truss while minimizing
its maximum deection and maximizing its maximum allowable stress. The common approach in this sort of
problem is to cho ose one ob jective (for example, the weight of the structure) and incorp orate the other ob jectives
as constraints. This approach has the disadvantage of limiting the choices available to the designer, making the
optimization pro cess a rather dicult task.
Another common approach is the combination of all the ob jectives into a single ob jective function. This
technique has the drawback of mo delling the original problem in an inadequate manner, generating solutions that
will require a further sensitivity analysis to b ecome reasonably useful to the designer.
A more appropriate approach to deal with multiple ob jectives is to use techniques that were originally designed
for that purpose in the eld of Op erations Research. Work in that area started a century ago, and many approaches
have b een rened and commonly applied in economics and control theory.
This paper addresses the imp ortance of multiob jective structural optimization and reviews some of the basic
concepts and part of the most relevant work in this area. Also, we discuss the suitability of a heuristic technique
inspired by the mechanics of natural selection (the genetic algorithm, or GA) to solve multiob jective optimization
problems. We also intro duce a new metho d, based on the concept of min-max optimum. The new metho d
is compared with other GA-based multiob jective optimization metho ds and some mathematical programming
techniques. We show that the new metho d is capable of nding b etter trade-os among the comp eting ob jectives.
Our approach is tested on two well-known truss optimization problems. We p erform these tests with a computer
program called MOSES, which was develop ed by the authors to exp eriment with new and existing multiob jective
optimization algorithms.
This work was done while the author was at Tulane University.
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