Multi-objective mixed integer problems [sf#18]

[darioizzo]

Originally created by mmarcusx on 2013-04-15 09:21:20.

We need a simple multi-objective mixed integer problem to evaluate the performance of NSGA-II and future algorithms on it.

[darioizzo]

Originally posted by darioizzo on 2013-04-27 17:32:24.

• status: open --> closed
• assigned_to: Dario Izzo

[darioizzo]

Originally posted by darioizzo on 2013-04-27 17:32:24.

ZDT5 is now implemented and committed in the development branch.

[darioizzo]

Originally posted by mmarcusx on 2013-04-28 18:26:43.

• status: closed --> open

[darioizzo]

Originally posted by mmarcusx on 2013-04-28 18:26:43.

ZDT5 is purely based on integers. It is not a "mixed" Integer problem. We still need one.

[darioizzo]

Originally posted by mjainit on 2013-05-05 19:55:30.

Hi,

I want to work on this problem. Which mixed-integer problem do you recommend to implement? Any links to paper regarding that problem if possible?

Thanks

[darioizzo]

Originally posted by darioizzo on 2013-05-06 20:02:16.

We do not have a good idea on what exactly to implement, This ticket is also about finding in the litearture some suitable problem, discuss it in pagmo-devel mailing list and then implement it ....

[darioizzo]

Originally posted by mjainit on 2013-05-08 13:31:35.

I'm browsing some of the literature about the Multi-objective optimization. I'll let you know about suitable problems to implement.

Thanks

[darioizzo]

Originally posted by mjainit on 2013-05-15 13:06:07.

I checked in different literatures such as Deb's book, Coello's Book on Multi-objective optimization. I came across many problems. I couldn't find any mixed-integer test problem, however I came across one real world problem, Spring Design Problem, Which is fulfilling the requirements. What should I do? Should I implement Spring design problem, or Is there any link of literature discussing Mixed integer multi-objective test problems?

This problem is also discussed in following paper [1], But general idea is, A helical compression spring needs to be designed for minimum volume and minimum stress. There are total three variables, number of spring coils N, the wire diameter d, and the mean coil diameter D. N is integer, d is discrete (42 non-equispaced values) and D is real variable. Variable vector = X = (x1,x2,x3) = (N,d,D). And there are total eight inequality constraints.

[1]B K Kannan, Kramer, An Augmented Lagrange Multiplier Based Method for Mixed Integer Discrete Continuous Optimization and its Applications to Mechanical Design

[darioizzo]

Originally posted by mmarcusx on 2013-05-16 12:46:06.

Dear Jainit,

Thank you for your literature research. The spring problem sounds interesting and while certainly interesting to have it in PaGMO, it will not help us to validate the current NSGA-II implementation. The reason for this is that NSGA-II as implemented has no constrained handling technique so it will not accept the spring problem as input. We should look for something else.

[darioizzo]

Originally posted by mjainit on 2013-05-18 08:39:25.

Hi Marcus,

I looked in some more papers on multi-objective optimization test problems. But I couldn't find the suitable problem. And I guess, Our first priority is to implement mixed integer problem to validate the NSGA-II implementation, Right now Implementing spring problem is not a good idea as you have said. Would you give me any pointers regarding what to look or where to search more about suitable problems?

Thanks!

[darioizzo]

Originally posted by darioizzo on 2013-05-28 14:12:53.

• status: open --> accepted

[darioizzo]

Originally posted by darioizzo on 2013-10-08 06:52:10.

• Milestone: 1.1.5 --> 1.2

[darioizzo]

Originally posted by darioizzo on 2013-10-08 06:52:11.

Moved to 1.2 as 1.1.5 is going to be released soon and this ticket will not be closed by then.