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In mathematical optimization software, defining the weight and level (hard/soft) of each of the objectives/constraints is often difficult for the business people at software development time, due to the impact on different stakeholders. There are several ways to deal with this, one being multi-objective optimization.

Most business people typically love the idea of multi-objective optimization, in which they don't need to make though choices now, but the software will present them with a number of solutions (from the pareto front) to pick from, for every problem that the solver optimizes.

Does it ever work in production?

For a user to pick the best timetable out of 2 wildly different timetables on the pareto front, is very non-trivial. Especially because they didn't help to create the timetables to begin with. Often there are easily thousands of solutions on the pareto front. Making matters worse, the number of solutions in a pareto front scales exponentially with the number of objectives.

Do you know of any multi-objective optimization use cases that survived first contact with production usage? Cases that are actually still used by end-users in production? How does the UI handle showing multiple solutions?

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3 Answers 3

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I am not aware of the timetabling, but if you mean by production is something like supply chain optimization, the answer would be actually yes.

As the optimization methods are widely used in supply chain improvement, applying multi-objective optimization, specifically in where the decision-makers will need to choose between the different strategies like either JIT (pull) or push would be interesting.

For example, in the detailed schedule of a production line, the decision-makers need to know about what if by changing the production plan from "make to order" to "make to stock" and based on, how many the required resources have to be changed!!? (for some reason it's needed to stock WIP). In such a case, MOOP is a good choice.

For representing the results to the D-Ms, an excel based output (or others like web-based software) can be created with a bit explanation of the pros and cons for the main scenarios. Indeed, to avoid having many scenarios, using the customer's real expertise is so helpful.

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  • $\begingroup$ With "in production" I didn't mean the type of project. I meant the status of the project: not just an academic project, nor a research project, nor a POC project or a pilot project, but actually used by end-users on a daily basis. Are you aware of any supply chain (or otherwise) optimization projects in production that use multi-objective optimization? $\endgroup$
    – Geoffrey De Smet
    Commented Oct 13, 2021 at 16:30
  • $\begingroup$ @Geoffrey, that's right. What I said was from a real industry project that I was incorporating in. In the real situation, as the problem instance might be very large, using the exact solutions is presumably time-consuming. The good news is, some of the advanced production and scheduling software like SAP, have had some features to develop various MP models that can be solved by state of the art solvers. On the other side, there are some very fast advanced scheduling software that use state of the art heuristics to solve complex problems by defining multi goals and the real needed. $\endgroup$
    – A.Omidi
    Commented Oct 13, 2021 at 22:49
  • $\begingroup$ Intreseting. So how do you represent a set of solutions from the pareto front to the user in the UI? $\endgroup$
    – Geoffrey De Smet
    Commented Oct 14, 2021 at 7:56
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    $\begingroup$ @Geoffrey, your welcome. As far as I remember the final solutions that have been found consist of twenty different solutions. By surveying these solutions with the planning department they decided to choose the two most interesting solutions. I hope it will be helpful. ☺ $\endgroup$
    – A.Omidi
    Commented Oct 14, 2021 at 12:45
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    $\begingroup$ Interesting. Thank you! I've seen this approach too - but I've always felt like this handful of solutions don't do justice to all solutions in a pareto front. It feels more about given the user the illusion of control by giving him a choice out of 20 solutions arbitrarily found, out of thousands of solutions on the pareto front. But customer is king, of course. $\endgroup$
    – Geoffrey De Smet
    Commented Oct 14, 2021 at 19:47
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Not a direct answer, but I think that "interactive multiobjective optimization" has shown that it can overcome the obstacle of expontially man Pareto optimal solutions. I have attended talks and seminars by Kaisa Miettinen and her co-authors, and their approaches seem quite interesting. On her website (http://users.jyu.fi/~miettine/engl.html#software) , she links to some of the software they have developed.

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  • $\begingroup$ Interesting. Thanks for sharing! $\endgroup$
    – Geoffrey De Smet
    Commented Oct 13, 2021 at 7:32
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I'm not sure if this counts, since my impression is that the end users overlap the modelers, but a contact I have at The Nature Conservancy (a non-profit that works in the conservation field) confirmed to me that his group uses a multi-objective optimization model for selecting land conservation projects in which to invest. As I understand it, criteria include various impacts on both residents of neighboring properties and assorted fauna and flora species. He pointed me to an open-access paper (*) they wrote. They use a tool called Marxan. I have no idea what the UI looks like.

(*) Annis GM, Pearsall DR, Kahl KJ, Washburn EL, May CA, Franks Taylor R, et al. (2017). Designing coastal conservation to deliver ecosystem and human well-being benefits. PLoS ONE 12(2): e0172458. doi:10.1371/journal.pone.0172458

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  • $\begingroup$ Did that happen to calculate a pareto front? $\endgroup$
    – Geoffrey De Smet
    Commented Oct 14, 2021 at 19:43
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    $\begingroup$ I'm not sure. I consulted once with one of the authors and someone else (who authored a different pub) on a related problem. There, they calculated Pareto-efficient solutions, which I suspect is also true of the pub I cited. I don't think they calculated the full Pareto frontier, but I might be wrong. $\endgroup$
    – prubin ♦
    Commented Oct 15, 2021 at 15:37

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