I need to find some multiobjective optimization constrained test problems that their objective functions be quadratic and their constraint be linear functions. Also, I need some nonlinear constraint multiobjective optimization test problem. I was wondering if anyone can introduced to me a package of handle functions contains these test functions for using in MATLAB. I should note that, these test problems must have specific Nondominated (Parato) frontiers. Because I want to validate my works by them.
I will appreciate any assistant about the above matter.
Thanks for your hint
But, As I told, I need to multiobjective test problems. Travelling Salesman Problem (TSP) is a single objective problem. Also, it is important for me that these test problems be smooth and I need to several multiobjective test problems with the above mentioned property.
you can refer multiobjective design optimization benchmark problems such as disc brake, gear train, welded beam, spring etc.
you can refer any MOO papers and kalyanmoy deb paper on NSGAII for solving multiobjective design optimization benchmark problems
Refer to the following link for MATLAB code of NSGA II :
http://www.mathworks.in/matlabcentral/fileexchange/31166-ngpm-a-nsga-ii-program-in-matlab-v1-4.
Moreover, there is a special book of Kalyanmoy Deb on multi-objective optimization. Of course, he is an expert of multi-optimization but from mechanical engg. field.
Other multi-objective codes are also available on net. Google it using "multi objective matlab codes" as search phrase. Hope you will get much useful codes.
Here you have some of the MOO test problems.
Conference Paper Engineering Case Studies Using Parameter less Penalty Non-do...
The nature of the problem you described is called "Quadratic Programming Problem". I think the most important site useful for your problem is
http://www.neos-guide.org/content/quadratic-programming
The test problems are given on
http://www.iwr.uni-heidelberg.de/groups/agbock/ONLINEQP/download.php?l=en
Other sites where you will get a list of MOOP problems are given below. Of course, you will have to find appropriate problems of your concern from the list or follow a specific link:
1. https://en.wikipedia.org/wiki/Test_functions_for_optimization
2. http://www.iitk.ac.in/kangal/papers/k2006001.pdf
3. http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.461.5863&rep=rep1&type=pdf
4. http://in.mathworks.com/matlabcentral/fileexchange/46744-7-multi-objective-problems--van-valedhuizen-s-test-suite-
5. http://dces.essex.ac.uk/staff/zhang/MOEAcompetition/cec09testproblem0904.pdf
Excel has a package based on the generalized reduced gradient method that allows restricted optimization, but you have to activate it.
You may use Biobjective mixed integer programs instances by Natashia Boland, Hadi Charkhgard, and Martin Savelsbergh at:
http://novaprd-lb.newcastle.edu.au/vital/access/manager/Repository/uon:13218
You may find the lot of constrained and unconstrained test problems for MOEAs in:
Professor Zhang webpage:
http://dces.essex.ac.uk/staff/qzhang/moeadcompetition09.htm.
Professor suganthan webpage:
http://www.ntu.edu.sg/home/epnsugan/
I think you can solve the size of your model by LINGO demo version.
You can download from the LINDO HP.
I upload the explanation of LINGO model at my RG HP.
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