Talk:Multi-objective optimization

Revision of the Multi-objective optimization -article

As with the MCDA-article the Wikipedia article on MCDA, we have been discussing the idea of making contributions to the article on multi-objective optimization in Wikipedia in the lists of the International Society on MCDM and INFORMS Section on MCDM. According to our opinion, the current version is somewhat hard to follow and missing some essential parts of multi-objective optimization. Thus, we would like to propose that we will change the contents of the article to the following:

1. Multi-objective optimization: Problem and Definitions
   • Definition of the problem and other definitions
2. Multiobjective optimization applications
   • Applications of multiobjective optimization
   • This section would extend the current Applications-section
3. Solving a multiobjective optimization problem
   • Different definitions of what it means to solve a multiobjective optimization problem
   • According to different researchers, this could to be to
     1. find a preferred Pareto optimal solution,
     2. find a Pareto front approximation, or
     3. generate the whole Pareto front.
   • In this section, it is clarified how this affects how the problem is approached
   • This section would also include the classification of multiobjective optimization methods to no-preference, a priori, a posteriori and interactive methods
4. Scalarization
   • Different methods for scalarizing multiobjective optimization problems
   • Having this section avoids having to repeat scalarizations in further sections
5. No-preference methods
   • Some no-preference methods
6. A priori methods
   • Some A priori methods
7. A posteriori methods
   • Some a posteriori methods
   • This section partly extends the current Solution methods -section
8. Interactive methods
   • Some interactive methods
9. Hybrid Methods
   • Methods combining methods from different classes
10. Approximation methods in multiobjective optimization
    • This section would include many of the methods surveyed in <ref>S. Ruzika and M. Wiecek. Approximation Methods in Multiobjective Programming, J Optimiz Theory App 126, p. 473-501<\ref> and some other methods
11. Visualizations
    • Methods for visualizing solutions to a multiobjective optimization problem
12. Software
    • Multiobjective optimization software

We could make a collaborative effort in writing the first draft of the proposed article and then everybody could improve it. At the same time, we would like to start Wikipedia articles on Linear and discrete multiobjective optimization and evolutionary multiobjective optimization. We would then briefly describe within the article how these fields relate and differ.

Please, comment and improve our proposition.

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Comment by Mullur in 2007

I will be adding quite a few examples and methods from my experience of multiobjective optimization. Please contribute by adding more stuff/fixing any incorrect things. --Mullur1729 03:21, 30 March 2007 (UTC)

Why I'm deleting the graphs

Sorry, but I'm very experienced with multi-objective optimization and in particular with the graphical representation of such problems, but I just find the two graphs to be worse than useless -- I spent a long time staring at them and still don't really understand them. They have two additive components of the objective function on the two axes, and one of those functions is itself highly non-linear. The captions say that the objective function parameters a and b affect the convexity or non-convexity of the "outcome set" (presumably intended to mean the efficient frontier) -- this makes no sense, since the efficient set is a statement of what is possible independent of any preference parameters. And as far as I can see the graph purports to present the problem without any assumptions about how much x₁ must be sacrificed in order to obtain a given increase in x₂, which is the information the efficient set is supposed to contain.

The standard and straightforward approach is to plot the objectives themselves, x₁ and x₂, on the axes, show a (possibly convex) efficient frontier, plot (possibly concave) indifference curves (iso-value curves for the objective function), and look at the feasible point that is on the best possible indifference curve. Duoduoduo (talk) 20:35, 24 June 2011 (UTC)

Perhaps the preference-dependent Pareto set was intended? (C.f. Yves Balasko's recent book.)  Kiefer.Wolfowitz 21:05, 24 June 2011 (UTC)

Conceivably so, but the section should start out with the basic and easiest-to-understand approach. If I can't understand the graphs, very few readers will be able to, but they might waste their time trying.

In any event, as far as I can see from the caption, no information about technological trade-offs is assumed, which makes it impossible for it to be right. Duoduoduo (talk) 21:16, 24 June 2011 (UTC)