Test functions for optimization: Difference between revisions

Revision as of 02:05, 10 December 2020

Revision as of 17:17, 10 February 2021

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|| <math>-20\le x,y \le 20</math>

|-

| [[Fonseca–Fleming function]]:<ref name="FonzecaFleming:1995">{{cite journal |firstfirst1=C. M. |lastlast1=Fonseca |first2=P. J. |last2=Fleming |title=An Overview of Evolutionary Algorithms in Multiobjective Optimization |journal=[[Evolutionary Computation (journal)|Evol Comput]] |volume=3 |issue=1 |pages=1–16 |year=1995 |doi=10.1162/evco.1995.3.1.1 |citeseerx=10.1.1.50.7779 |s2cid=8530790 }}</ref>

|| [[File:Fonseca and Fleming function.pdf|200px|Fonseca and Fleming function]]

|| <math>\text{Minimize} =

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||<math>-5\le x_{i} \le 5</math>, <math>1\le i \le 3</math>.

|-

| Schaffer function N. 1:<ref name="Schaffer:1984">{{cite thesis |type=PhD |last=Schaffer |first=J. David |date=1984 |title=Multiple Objective Optimization with Vector Evaluated Genetic Algorithms. |publisher=Vanderbilt University |journal=Proceedings of the First Int. Conference on Genetic Algortihms, Eded. G.J.E Grefensette, J.J. Lawrence Erlbraum |oclc=20004572 }}</ref>

|| [[File:Schaffer function 1.pdf|200px|Schaffer function N.1]]

|| <math>\text{Minimize} =

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||<math>-\pi\le x,y \le \pi</math>

|-

| Zitzler–Deb–Thiele's function N. 1:<ref name="Debetal2002testpr">{{cite journal |last1=Deb |first1=Kalyan |last2=Thiele |first2=L. |last3=Laumanns |first3=Marco |last4=Zitzler |first4=Eckart |title=Scalable multi-objective optimization test problems |journal=Proc. Of 2002 IEEE Congress on Evolutionary Computation |date=2002 |volume=1 |pages=825–830 |doi=10.1109/CEC.2002.1007032|isbn=0-7803-7282-4 |s2cid=61001583 }}</ref>

|| [[File:Zitzler-Deb-Thiele's function 1.pdf|200px|Zitzler-Deb-Thiele's function N.1]]

|| <math>\text{Minimize} =

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||<math>0\le x_{i} \le 1</math>, <math>1\le i \le 10</math>.

|-

| Osyczka and Kundu function:<ref name="OsyczkaKundu1995">{{cite journal |last1=Osyczka |first1=A. |last2=Kundu |first2=S. |title=A new method to solve generalized multicriteria optimization problems using the simple genetic algorithm |journal=Structural Optimization |date=1 October 1995 |volume=10 |issue=2 |pages=94–99 |doi=10.1007/BF01743536 |s2cid=123433499 |issn=1615-1488}}</ref>

|| [[File:Osyczka and Kundu function.pdf|200px|Osyczka and Kundu function]]

||<math>\text{Minimize} =

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|| <math>0\le x_{1},x_{2},x_{6} \le 10</math>, <math>1\le x_{3},x_{5} \le 5</math>, <math>0\le x_{4} \le 6</math>.

|-

| CTP1 function (2 variables):<ref name="Deb:2002"/><ref name="Jimenezetal2002">{{cite journal |last1=Jimenez |first1=F. |last2=Gomez-Skarmeta |first2=A. F. |last3=Sanchez |first3=G. |last4=Deb |first4=K. |title=An evolutionary algorithm for constrained multi-objective optimization |journal=Proceedings of the 2002 Congress on Evolutionary Computation. CEC'02 (Cat. No.02TH8600) |date=May 2002 |volume=2 |pages=1133–1138 |doi=10.1109/CEC.2002.1004402|isbn=0-7803-7282-4 |s2cid=56563996 }}</ref>

|| [[File:CTP1 function (2 variables).pdf|200px|CTP1 function (2 variables).<ref name="Deb:2002" />]]

|| <math>\text{Minimize} =