Multi-objective optimization: Difference between revisions

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{{Main article|Optimal control|Dynamic programming|Linear-quadratic regulator}}

In [[engineering]] and [[economics]], many problems involve multiple objectives which are not describable as the-more-the-better or the-less-the-better; instead, there is an ideal target value for each objective, and the desire is to get as close as possible to the desired value of each objective. For example, energy systems typically have a trade-off between performance and cost<ref>{{Cite journal|last1=Shirazi|first1=Ali|last2=Najafi|first2=Behzad|last3=Aminyavari|first3=Mehdi|last4=Rinaldi|first4=Fabio|last5=Taylor|first5=Robert A.|date=2014-05-01|title=Thermal–economic–environmental analysis and multi-objective optimization of an ice thermal energy storage system for gas turbine cycle inlet air cooling|journal=Energy|volume=69|pages=212–226|doi=10.1016/j.energy.2014.02.071|hdl=11311/845828 |doi-access=free}}</ref><ref>{{cite journal|last1=Najafi|first1=Behzad|last2=Shirazi|first2=Ali|last3=Aminyavari|first3=Mehdi|last4=Rinaldi|first4=Fabio|last5=Taylor|first5=Robert A.|date=2014-02-03|title=Exergetic, economic and environmental analyses and multi-objective optimization of an SOFC-gas turbine hybrid cycle coupled with an MSF desalination system|journal=Desalination|volume=334|issue=1|pages=46–59|doi=10.1016/j.desal.2013.11.039|hdl=11311/764704 |doi-access=free|hdl-access=free}}</ref> or one might want to adjust a rocket's fuel usage and orientation so that it arrives both at a specified place and at a specified time; or one might want to conduct [[open market operations]] so that both the [[inflation rate]] and the [[unemployment rate]] are as close as possible to their desired values.

Often such problems are subject to linear equality constraints that prevent all objectives from being simultaneously perfectly met, especially when the number of controllable variables is less than the number of objectives and when the presence of random shocks generates uncertainty. Commonly a multi-objective [[quadratic function#Bivariate (two variable) quadratic function|quadratic objective function]] is used, with the cost associated with an objective rising quadratically with the distance of the objective from its ideal value. Since these problems typically involve adjusting the controlled variables at various points in time and/or evaluating the objectives at various points in time, [[intertemporal optimization]] techniques are employed.<ref>{{cite book |doi=10.1109/IECON.2009.5415056 |isbn=978-1-4244-4648-3 |chapter=Chaos rejection and optimal dynamic response for boost converter using SPEA multi-objective optimization approach |title=2009 35th Annual Conference of IEEE Industrial Electronics |pages=3315–3322 |year=2009 |last1=Rafiei |first1=S. M. R. |last2=Amirahmadi |first2=A. |last3=Griva |first3=G.|s2cid=2539380 }}</ref>

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Product and process design can be largely improved using modern modeling, simulation, and optimization techniques.{{citation needed|date=February 2017}} The key question in optimal design is measuring what is good or desirable about a design. Before looking for optimal designs, it is important to identify characteristics that contribute the most to the overall value of the design. A good design typically involves multiple criteria/objectives such as capital cost/investment, operating cost, profit, quality and/or product recovery, efficiency, process safety, operation time, etc. Therefore, in practical applications, the performance of process and product design is often measured with respect to multiple objectives. These objectives are typically conflicting, i.e., achieving the optimal value for one objective requires some compromise on one or more objectives.

For example, when designing a paper mill, one can seek to decrease the amount of capital invested in a paper mill and enhance the quality of paper simultaneously. If the design of a paper mill is defined by large storage volumes and paper quality is defined by quality parameters, then the problem of optimal design of a paper mill can include objectives such as i) minimization of expected variation of those quality parameters from their nominal values, ii) minimization of the expected time of breaks and iii) minimization of the investment cost of storage volumes. Here, the maximum volume of towers is a design variable. This example of optimal design of a paper mill is a simplification of the model used in.<ref name=RoRiPi11>{{Cite journal | last1 = Ropponen | first1 = A. | last2 = Ritala | first2 = R. | last3 = Pistikopoulos | first3 = E. N. | doi = 10.1016/j.compchemeng.2010.12.012 | title = Optimization issues of the broke management system in papermaking | journal = Computers & Chemical Engineering | volume = 35 | issue = 11 | pages = 2510 | year = 2011 }}</ref> Multi-objective design optimization has also been implemented in engineering systems in the circumstances such as control cabinet layout optimization,<ref>{{cite arXiv|last1=Pllana |first1=Sabri |last2=Memeti |first2=Suejb |last3=Kolodziej |first3=Joanna |title=Customizing Pareto Simulated Annealing for Multi-objective Optimization of Control Cabinet Layout |eprint=1906.04825 |class=cs.OH |year=2019}}</ref> airfoil shape optimization using scientific workflows,<ref>{{cite journal |last1=Nguyen |first1=Hoang Anh |last2=van Iperen |first2=Zane |last3=Raghunath |first3=Sreekanth |last4=Abramson |first4=David |last5=Kipouros |first5=Timoleon |last6=Somasekharan |first6=Sandeep |title=Multi-objective optimisation in scientific workflow |journal=Procedia Computer Science |date=2017 |volume=108 |pages=1443–1452 |hdl=1826/12173|doi=10.1016/j.procs.2017.05.213|doi-access=free |hdl-access=free }}</ref> design of nano-[[CMOS]],<ref>{{Cite journal|title = Multiobjective design optimization of a nano-CMOS voltage-controlled oscillator using game theoretic-differential evolution|journal = Applied Soft Computing|date = 2015-07-01|pages = 293–299|volume = 32|doi = 10.1016/j.asoc.2015.03.016|first1 = T.|last1 = Ganesan|first2 = I.|last2 = Elamvazuthi|first3 = P.|last3 = Vasant}}</ref> [[System on a chip|system on chip]] design, design of solar-powered irrigation systems,<ref>{{Cite book|publisher = Springer International Publishing|date = 2013-01-01|isbn = 978-3-319-00541-6|pages = 147–154|series = Advances in Intelligent Systems and Computing|doi = 10.1007/978-3-319-00542-3_15|first1 = T.|last1 = Ganesan|first2 = I.|last2 = Elamvazuthi|first3 = Ku Zilati Ku|last3 = Shaari|first4 = P.|last4 = Vasant| title=Nostradamus 2013: Prediction, Modeling and Analysis of Complex Systems | chapter=Hypervolume-Driven Analytical Programming for Solar-Powered Irrigation System Optimization | volume=210 |editor-first = Ivan|editor-last = Zelinka|editor-first2 = Guanrong|editor-last2 = Chen|editor-first3 = Otto E.|editor-last3 = Rössler|editor-first4 = Vaclav|editor-last4 = Snasel|editor-first5 = Ajith|editor-last5 = Abraham}}</ref> optimization of sand mould systems,<ref>{{Cite book|publisher = Springer Berlin Heidelberg|date = 2013-01-01|isbn = 978-3-642-45317-5|pages = 145–163|series = Lecture Notes in Computer Science|first1 = T.|last1 = Ganesan|first2 = I.|last2 = Elamvazuthi|first3 = Ku Zilati Ku|last3 = Shaari|first4 = P.|last4 = Vasant| title=Transactions on Computational Science XXI | chapter=Multiobjective Optimization of Green Sand Mould System Using Chaotic Differential Evolution | volume=8160 |editor-first = Marina L.|editor-last = Gavrilova|editor-link=Marina Gavrilova|editor-first2 = C. J. Kenneth|editor-last2 = Tan|editor-first3 = Ajith|editor-last3 = Abraham|doi = 10.1007/978-3-642-45318-2_6}}</ref><ref>{{cite journal|title = Multi-objective optimization of green sand mould system using evolutionary algorithms|journal = The International Journal of Advanced Manufacturing Technology|date = 2011-05-07|issn = 0268-3768|pages = 9–17|volume = 58|issue = 1–4|doi = 10.1007/s00170-011-3365-8|first1 = B.|last1 = Surekha|first2 = Lalith K.|last2 = Kaushik|first3 = Abhishek K.|last3 = Panduy|first4 = Pandu R.|last4 = Vundavilli|first5 = Mahesh B.|last5 = Parappagoudar|s2cid = 110315544}}</ref> engine design,<ref>{{Cite web|title = MultiObjective Optimization in Engine Design Using Genetic Algorithms to Improve Engine Performance {{!}} ESTECO|url = http://www.esteco.com/modefrontier/multiobjective-optimization-engine-design-using-genetic-algorithms-improve-engine-perfo|website = www.esteco.com|access-date = 2015-12-01}}</ref><ref>{{cite book|chapter = Multi-Objective Robust Design Optimization of an Engine Mounting System|chapter-url = http://papers.sae.org/2005-01-2412/|date = 2005-05-16|___location = Warrendale, PA|first1 = E.|last1 = Courteille|first2 = F.|last2 = Mortier|first3 = L.|last3 = Leotoing|first4 = E.|last4 = Ragneau|doi = 10.4271/2005-01-2412|title = SAE Technical Paper Series|volume = 1| s2cid=20170456 |url = https://hal.archives-ouvertes.fr/hal-00913315/file/SAE_HAL.pdf}}</ref> optimal sensor deployment<ref>{{cite journal|last1=Domingo-Perez|first1=Francisco|last2=Lazaro-Galilea|first2=Jose Luis|last3=Wieser|first3=Andreas|last4=Martin-Gorostiza|first4=Ernesto|last5=Salido-Monzu|first5=David|last6=Llana|first6=Alvaro de la|title=Sensor placement determination for range-difference positioning using evolutionary multi-objective optimization|journal=Expert Systems with Applications|date=April 2016|volume=47|pages=95–105|doi=10.1016/j.eswa.2015.11.008}}</ref> and optimal controller design.<ref>{{Cite journal|title = Multiobjective model predictive control|journal = Automatica|date = 2009-12-01|pages = 2823–2830|volume = 45|issue = 12|doi = 10.1016/j.automatica.2009.09.032|first1 = Alberto|last1 = Bemporad|first2 = David|last2 = Muñoz de la Peña}}</ref><ref>{{cite journal|title = Multi-objective evolutionary algorithm for SSSC-based controller design|journal = Electric Power Systems Research|date = 2009-06-01|pages = 937–944|volume = 79|issue = 6|doi = 10.1016/j.epsr.2008.12.004|first = Sidhartha|last = Panda}}</ref>

=== {{anchor|MOGA}} Process optimization ===