Design optimization: Difference between revisions

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'''Design optimization''' is an engineering design '''methodology''' using a mathematical formulation of a design problem to support selection of the optimal design among many alternatives. Design optimization involves the following stages:
<ref name="pyp2017edo2021">{{Cite book|url=http://principlesofoptimaldesignflowlab.orggroups.et.byu.net/mdobook.pdf|title=Principles of OptimalEngineering Design: Modeling and ComputationOptimization|lastlast1=PapalambrosMartins|firstfirst1=PanosJoaquim YR. R. A.|last2=WildeNing|first2=Douglass J.Andrew|date=20172021-10-01-31|publisher=Cambridge University Press|year=|isbn=9781316867457|___location=|pages=978-1108833417|language=en}}</ref>:

<ref name="pyp2017">{{Cite book|url=http://principlesofoptimaldesign.org/|title=Principles of Optimal Design: Modeling and Computation|last1=Papalambros|first1=Panos Y.|last2=Wilde|first2=Douglass J.|date=2017-01-31|publisher=Cambridge University Press|isbn=9781316867457|language=en}}</ref>

# [[Variable (mathematics)|Variables]]: Describe the design alternatives

# Objective: Elected functional combination of variables (to be maximized or minimized)

# Constraints: Combination of Variables expressed as equalities or inequalities that must be satisfied for any acceptable design alternative

# Feasibility: Values for set of variables that satisfies all constraints and minimizes/maximizes Objective.

== Design optimization problem ==

{{Main|Optimization problem}}

The formal mathematical ([[Canonical form|standard form]]) statement of the design optimization problem is <ref>{{Cite book|url=https://web.stanford.edu/~boyd/cvxbook/bv_cvxbook.pdf|title=Convex Optimization|lastlast1=Boyd|firstfirst1=Stephen|last2=Boyd|first2=Stephen P.|last3=California)|first3=Stephen (Stanford University Boyd|last4=Vandenberghe|first4=Lieven|last5=Angeles)|first5=Lieven (University of California Vandenberghe, Los|date=2004-03-08|publisher=Cambridge University Press|year=|isbn=9780521833783|___location=|pages=|language=en}}</ref> 

<math>\begin{align}

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* <math>h_i(x)</math> are <math>m_1</math>'''equality constraints'''

* <math>g_j(x)</math> are <math>m_2</math> '''inequality constraints'''

* <math>X</math> is a set constraint that includes additional restrictions on <math>x</math> besides those implied by the equality and inequality constraints.  

The problem formulation stated above is a convention called the ''negative null form'', since all constraint function are expressed as equalities and negative inequalities with zero on the right-hand side. This convention is used so that numerical algorithms developed to solve design optimization problems can assume a standard expression of the mathematical problem.  

We can introduce the vector-valued functions

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\end{align}

</math> ''  ''

to rewrite the above statement in the compact expression  

<math>\begin{align}

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\end{align}</math>

We call <math>h, g</math> the ''set'' or ''system of'' (''functional'') ''constraints'' and <math>X</math> the ''set constraint''.  

== Application ==

Design optimization applies the methods of [[mathematical optimization]] to design problem formulations and it is sometimes used interchangeably with the term [[engineering optimization]].  When the objective function ''f'' is a [[Vector-valued function|vector]] rather than a [[Scalar field|scalar]], the problem becomes a [[multi-objective optimization]] one. If the design optimization problem has more than one mathematical solutions the methods of [[global optimization]] are used to identified the global optimum. 

'''Optimization Checklist''' <ref name="pyp2017" />

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A detailed and rigorous description of the stages and practical applications with examples can be found in the book [http://www.cambridge.org/gh/academic/subjects/engineering/control-systems-and-optimization/principles-optimal-design-modeling-and-computation-3rd-edition?format=HB&isbn=9781107132672#C3r6r6aLRe2bUoef.97 Principles of Optimal Design].

Practical design optimization problems are typically solved numerically and many [[:Category:Mathematical optimization software|optimization software]] exist in academic and commercial forms.<ref>{{Cite book|url=https://books.google.com/books?hl=en&lr=&id=wy5hBwAAQBAJ&oi=fnd&pg=PR17&dqq=design+optimization+with+matlab+achille+messac&otspg=n9WXaRte_T&sig=DVBwayB-6W1b2YyruSz6O2fMKAM#v=onepage&q=design%20optimization%20with%20matlab%20achille%20messac&f=falsePR17|title=Optimization in Practice with MATLAB®: For Engineering Students and Professionals|last=Messac|first=Achille|author-link1=Achille Messac|date=2015-03-19|publisher=Cambridge University Press|isbn=9781316381373|language=en}}</ref>. There are several ___domain-specific applications of design optimization posing their own specific challenges in formulating and solving the resulting problems; these include, [[shape optimization]], [[wing-shape optimization]], [[topology optimization]], [[architectural design optimization]], [[Power optimization (EDA)|power optimization]]. Several books, articles and journal publications are listed below for reference.

One modern application of design optimization is structural design optimization (SDO) is in building and construction sector. SDO emphasizes automating and optimizing structural designs and dimensions to satisfy a variety of performance objectives. These advancements aim to optimize the configuration and dimensions of structures to optimize augmenting strength, minimize material usage, reduce costs, enhance energy efficiency, improve sustainability, and optimize several other performance criteria. Concurrently, structural design automation endeavors to streamline the design process, mitigate human errors, and enhance productivity through computer-based tools and optimization algorithms. Prominent practices and technologies in this ___domain include the parametric design, generative design, building information modelling (BIM) technology, machine learning (ML), and artificial intelligence (AI), as well as integrating finite element analysis (FEA) with simulation tools.<ref>Towards BIM-Based Sustainable Structural Design Optimization: A Systematic Review and Industry Perspective. Sustainability 2023, 15, 15117. https://doi.org/10.3390/su152015117</ref>

== Journals ==

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* [http://mechanicaldesign.asmedigitalcollection.asme.org/journal.aspx Journal of Mechanical Design]

* [http://mechanicaldesign.asmedigitalcollection.asme.org/issue.aspx?journalid=126&issueid=28068 Journal of Mechanisms, Transmissions, and Automation in Design]

* Design Optimization

* [https://www.cambridge.org/core/journals/design-science Design Science]

* [https://www.tandfonline.com/toc/geno20/current Engineering Optimization]

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* [[Journal of Product Innovation Management]]

* [[International Journal of Research in Marketing]]

== References ==

<references />

== See also ==

* [https://wiki.ece.cmu.edu/ddl/index.php/Main_Page Design Decisions Wiki (DDWiki)] : Established by the Design Decisions Laboratory at Carnegie Mellon University in 2006 as a central resource for sharing information and tools to analyze and support decision-making

== References ==

<references />

== Further reading ==

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* ''Foundations of structural optimization : a unified approach''. Morris, A. J. Chichester [West Sussex]: Wiley. 1982. {{ISBN|0471102008}}. [[OCLC]]&nbsp;8031383.

* N., Siddall, James (1982). ''Optimal engineering design : principles and applications''. New York: M. Dekker. {{ISBN|0824716337}}. [[OCLC]]&nbsp;8389250.

* 1944-, Ravindran, A., (2006). ''Engineering optimization : methods and applications''. Reklaitis, G. V., 1942-, Ragsdell, K. M. (2nd ed ed.). Hoboken, N.J.: John Wiley & Sons. {{ISBN|0471558141}}. [[OCLC]]&nbsp;61463772.

* N.,, Vanderplaats, Garret (1984). ''Numerical optimization techniques for engineering design : with applications''. New York: McGraw-Hill. {{ISBN|0070669643}}. [[OCLC]]&nbsp;9785595.

* T., Haftka, Raphael (1990). ''Elements of Structural Optimization''. Gürdal, Zafer., Kamat, Manohar P. (Second rev. edition ed.). Dordrecht: Springer Netherlands. {{ISBN|9789401578622}}. [[OCLC]]&nbsp;851381183.

* S., Arora, Jasbir (2011). ''Introduction to optimum design'' (3rd ed ed.). Boston, MA: Academic Press. {{ISBN|9780123813756}}. [[OCLC]]&nbsp;760173076.

* S.,, Janna, William. ''Design of fluid thermal systems'' (SI edition ; fourth edition ed.). Stamford, Connecticut. {{ISBN|9781285859651}}. [[OCLC]]&nbsp;881509017.

* ''Structural optimization : status and promise''. Kamat, Manohar P. Washington, DC: American Institute of Aeronautics and Astronautics. 1993. {{ISBN|156347056X}}. [[OCLC]]&nbsp;27918651.

* ''Mathematical programming for industrial engineers''. Avriel, M., Golany, B. New York: Marcel Dekker. 1996. {{ISBN|0824796209}}. [[OCLC]]&nbsp;34474279.

* Hans., Eschenauer, (1997). ''Applied structural mechanics : fundamentals of elasticity, load-bearing structures, structural optimization : including exercises''. Olhoff, Niels., Schnell, W. Berlin: Springer. {{ISBN|3540612327}}. [[OCLC]]&nbsp;35184040.

* 1956-, Belegundu, Ashok D., (2011). ''Optimization concepts and applications in engineering''. Chandrupatla, Tirupathi R., 1944- (2nd ed ed.). New York: Cambridge University Press. {{ISBN|9781139037808}}. [[OCLC]]&nbsp;746750296.

* Okechi., Onwubiko, Chinyere (2000). ''Introduction to engineering design optimization''. Upper Saddle River, NJ: Prentice-Hall. {{ISBN|0201476738}}. [[OCLC]]&nbsp;41368373.

* ''Optimization in action : proceedings of the Conference on Optimization in Action held at the University of Bristol in January 1975''. Dixon, L. C. W. (Laurence Charles Ward), 1935-, Institute of Mathematics and Its Applications. London: Academic Press. 1976. {{ISBN|0122185501}}. [[OCLC]]&nbsp;2715969.

* P., Williams, H. (2013). ''Model building in mathematical programming'' (5th ed ed.). Chichester, West Sussex: Wiley. {{ISBN|9781118506189}}. [[OCLC]]&nbsp;810039791.

* ''Integrated design of multiscale, multifunctional materials and products''. McDowell, David L., 1956-. Oxford: Butterworth-Heinemann. 2010. {{ISBN|9781856176620}}. [[OCLC]]&nbsp;610001448.

* M.,, Dede, Ercan. ''Multiphysics simulation : electromechanical system applications and optimization''. Lee, Jaewook,, Nomura, Tsuyoshi,. London. {{ISBN|9781447156406}}. [[OCLC]]&nbsp;881071474.

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=== Structural Topology Optimization ===

{{refbegin}}

*{{cite "journal |title=Generating optimal topologies in structural design using a homogenization method". ''|journal=Computer Methods in Applied Mechanics and Engineering''. '''|volume=71''' (|issue=2): |pages=197–224. |date=1988-11-01. [[Digital object identifier|doi]]:=10.1016/0045-7825(88)90086-2. [[International Standard Serial Number|ISSN]]&nbsp;issn=0045-7825 |url= | last1 = Bendsøe | first1 = Martin Philip | last2 = Kikuchi | first2 = Noboru|hdl=2027.42/27079 |hdl-access=free }}

*{{cite Bendsøe,book |first=Martin P (1995). ''|last=Bendsøe |title=Optimization of structural topology, shape, and material''. Berlin; New York: |publisher=Springer. {{ISBN|date=1995 |isbn=3540590579 }}.

*{{cite Behrooz.,book |first=Hassani, (1999).|last=Behrooz ''|title=Homogenization and Structural Topology Optimization : Theory, Practice and Software''. Hinton, E. (Ernest). London: |publisher=Springer London.|date=1999 {{ISBN|isbn=9781447108917 |oclc=853262659 }}. [[OCLC]]&nbsp;853262659.

*{{cite book |last1=Bendsøe |first1=Martin P. |last2=Sigmund |first2=O. |title=Topology optimization : theory, methods, and applications |publisher=Springer |edition=2nd |date=2013 |isbn=9783662050866 |oclc=50448149 |url=https://books.google.com/books?id=ZCjsCAAAQBAJ&pg=PR1}}

*{{cite book |editor-last=Rozvany |editor-first=G.I.N. |editor-last2=Lewiński |editor-first2=T. |title=Topology optimization in structural and continuum mechanics |publisher=Springer |date=2014 |isbn=9783709116432 |oclc=859524179 |url=https://books.google.com/books?id=B8HHBAAAQBAJ&pg=PP1}}

{{refend}}

{{Design}}

* "Generating optimal topologies in structural design using a homogenization method". ''Computer Methods in Applied Mechanics and Engineering''. '''71''' (2): 197–224. 1988-11-01. [[Digital object identifier|doi]]:10.1016/0045-7825(88)90086-2. [[International Standard Serial Number|ISSN]]&nbsp;0045-7825.

* Bendsøe, Martin P (1995). ''Optimization of structural topology, shape, and material''. Berlin; New York: Springer. {{ISBN|3540590579}}.

* Behrooz., Hassani, (1999). ''Homogenization and Structural Topology Optimization : Theory, Practice and Software''. Hinton, E. (Ernest). London: Springer London. {{ISBN|9781447108917}}. [[OCLC]]&nbsp;853262659.

* P., Bendsøe, Martin (2003). ''Topology optimization : theory, methods, and applications''. Sigmund, O. (Ole), 1966-. Berlin: Springer. {{ISBN|3540429921}}. [[OCLC]]&nbsp;50448149.

* ''Topology optimization in structural and continuum mechanics''. Rozvany, G. I. N.,, Lewiński, T.,. Wien. {{ISBN|9783709116432}}. [[OCLC]]&nbsp;859524179.

*

[[Category:Design]]