Multi-objective optimization: Difference between revisions

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=== Mathematical programming ===

Well-known examples of mathematical programming-based a posteriori methods are the Normal Boundary Intersection (NBI),<ref name="doi10.1137/S1052623496307510">{{Cite journal | last1 = Das | first1 = I. | last2 = Dennis | first2 = J. E. | doi = 10.1137/S1052623496307510 | title = Normal-Boundary Intersection: A New Method for Generating the Pareto Surface in Nonlinear Multicriteria Optimization Problems | journal = SIAM Journal on Optimization | volume = 8 | issue = 3 | pages = 631 | year = 1998 | hdl = 1911/101880| s2cid = 207081991 | hdl-access = free }}</ref> Modified Normal Boundary Intersection (NBIm),<ref name="S. Motta">{{cite journal|last=S. Motta|first=Renato|author2=Afonso, Silvana M. B. |author3=Lyra, Paulo R. M. |title=A modified NBI and NC method for the solution of N-multiobjective optimization problems|journal=Structural and Multidisciplinary Optimization|date=8 January 2012|doi=10.1007/s00158-011-0729-5|volume=46|issue=2|pages=239–259|s2cid=121122414}}</ref> Normal Constraint (NC),<ref name="ReferenceA">{{cite journal|first1=A.|last1=Messac|first2=A.|author-link1=Achille Messac|last2=Ismail-Yahaya|first3=C.A.|last3=Mattson|title=The normalized normal constraint method for generating the Pareto frontier|journal=Structural and Multidisciplinary Optimization|volume=25|issue=2|pages=86–98|year=2003|doi=10.1007/s00158-002-0276-1|s2cid=58945431}}</ref><ref name="ReferenceB">{{cite journal|first1=A.|last1=Messac|first2=C. A.|last2=Mattson|title=Normal constraint method with guarantee of even representation of complete Pareto frontier|journal=AIAA Journal|volume=42|issue=10|pages=2101–2111|year=2004|doi=10.2514/1.8977|bibcode=2004AIAAJ..42.2101M}}</ref> Successive Pareto Optimization (SPO),<ref name="ReferenceC">{{cite journal|first1=Daniel|last1=Mueller-Gritschneder|first2=Helmut|last2=Graeb|first3=Ulf|last3=Schlichtmann|title=A Successive Approach to Compute the Bounded Pareto Front of Practical Multiobjective Optimization Problems|journal=SIAM Journal on Optimization|volume=20|issue=2|pages=915–934|year=2009|doi=10.1137/080729013}}</ref> and Directed Search Domain (DSD)<ref>{{Cite journal |last=Erfani |first=Tohid |last2=Utyuzhnikov |first2=Sergei V. |date=2011-052010 |title=Directed search ___domain: a method for even generation of the Pareto frontier in multiobjective optimization |url=http://www.tandfonline.com/doi/abs/10.1080/0305215X.2010.497185 |journal=Engineering Optimization |language=en |volume=43 |issue=5 |pages=467–484 |doi=10.1080/0305215X.2010.497185 |issn=0305-215X}}</ref> methods, which solve the multi-objective optimization problem by constructing several scalarizations. The solution to each scalarization yields a Pareto optimal solution, whether locally or globally. The scalarizations of the NBI, NBIm, NC, and DSD methods are constructed to obtain evenly distributed Pareto points that give a good approximation of the real set of Pareto points.

=== Evolutionary algorithms ===