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'''Design optimizationoptimisation''' 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="edo2021">{{Cite book|url=http://flowlab.groups.et.byu.net/mdobook.pdf|title=Engineering Design Optimization|last1=Martins|first1=Joaquim R. R. A.|last2=Ning|first2=Andrew|date=2021-10-01|publisher=Cambridge University Press|isbn=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>
# Feasibility: Values for set of variables that satisfies all constraints and minimizes/maximizes Objective.
== Design optimizationoptimisation problem ==
{{Main|OptimizationOptimisation problem}}
The formal mathematical ([[Canonical form|standard form]]) statement of the design optimizationoptimisation problem is <ref>{{Cite book|url=https://web.stanford.edu/~boyd/cvxbook/bv_cvxbook.pdf|title=Convex Optimization|last1=Boyd|first1=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|isbn=9780521833783|language=en}}</ref>
<math>\begin{align}
== Application ==
Design optimizationoptimisation applies the methods of [[mathematical optimizationoptimisation]] to design problem formulations and it is sometimes used interchangeably with the term [[engineering optimizationoptimisation]]. When the objective function ''f'' is a [[Vector-valued function|vector]] rather than a [[Scalar field|scalar]], the problem becomes a [[multi-objective optimizationoptimisation]] one. If the design optimizationoptimisation problem has more than one mathematical solutions the methods of [[global optimizationoptimisation]] are used to identified the global optimum.
'''Optimization Checklist''' <ref name="pyp2017" />
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 optimizationoptimisation 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?id=wy5hBwAAQBAJ&q=design+optimization+with+matlab+achille+messac&pg=PR17|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 optimizationoptimisation posing their own specific challenges in formulating and solving the resulting problems; these include, [[shape optimizationoptimisation]], [[wing-shape optimizationoptimisation]], [[topology optimizationoptimisation]], [[architectural design optimizationoptimisation]], [[Power optimizationoptimisation (EDA)|power optimizationoptimisation]]. Several books, articles and journal publications are listed below for reference.
== Journals ==
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