Optimalidad de pareto

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by Károly Jármai

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Source: European Integration Studies (European Integration Studies), issue: 1 / 2003, pages: 91­107, on www.ceeol.com.



European Integration Studies, Miskolc, Volume 1. Number 2. (2002) pp. 91-107DESIGN, FABRICATION AND ECONOMY
KÁROLY JÁRMAI Department of Materials Handling and Logistics, University of Miskolc 3515, Miskolc -Egyetemváros, Hungary altjar@uni-miskolc.hu
[Received November 15, 2002]

1. Introduction Design, fabrication and economy, these are the ‘magic’ words. These three aspects of production are important to be competitive on the market, but to find the connectionbetween them is not always easy. These three aspects are efficiently connected in optimisation. People in everyday life always make optimisation decisions at a conscious or subconscious level ‘to reach the best objective possible with the resources available’. Consciousness makes the act more efficient. There are always targets to reach and constraints to control them. The birth of optimisation methodsas mathematical techniques dates back to the days of Newton, Lagrange and Cauchy. Further development in optimisation became possible through the developments in differential calculus by Newton, Leibnitz, the variational calculus by Bernoulli, Euler, Lagrange and Weierstrass, and the introduction of unknown multipliers by Lagrange. The concept of multi-objective optimisation was formulated onehundred years ago by Pareto in 1896. The first written analytical work published o structural optimisation was made by Maxwell in 1890 n followed by the well-known work of Michell in 1904. These works provided theoretical weight minima of trusses, using highly idealised models, but the analytical solution of the structural optimisation problem can still be used. During the Second World War and inthe late 1940s and the early 1950s the development of optimisation concerned the minimum weight design of aircraft structural components: columns, stiffened panels, subject to compressive loads and buckling. Digital computers appeared in the early 1950s and gave a strong impulse to the application of linear programming techniques. The applications were focused primarily on steel frame structures. Inthe late 1950s and 1960s the application of structural optimisation on lightweight structures concentrated on the aircraft and space industries. New optimisation techniques were developed in works by Rosenbrock, Box and Powell. The great development of this period is that the finite element method, which is a powerful tool for the analysis of complex structures, was invented by Zienkiewich andapplied by many others for structural analysis. Modern structural optimisation dates from the paper by Schmit in 1960, who outlined the role of structural optimisation, the hierarchy of analysis and synthesis, the use of mathematical programming techniques to solve nonlinear inequality constrained problems. The importance of this work is that it proposed a new philosophy of engineering design,structural synthesis, which clarifies the


Károly Jármai

methodology of optimisation. There are several international organisations involved optimisation, probably the largest being the International Society of Structural and Multidisciplinary Optimization (ISSMO), which has its own journal, Structural Optimization (Springer Verlag), and regularly organises conferences. The InternationalInstitute of Welding (IIW) also deals with cost calculations (Journal Welding in the World), and holds an annual assembly each year. There are also a great number of other conferences and courses that have been organized in these two main fields. The University of Miskolc has organised several conferences (Farkas & Jármai (Eds.) 1996, Jármai (Ed.) 1997, Jármai & Farkas (Eds.) 2003), also courses...
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