Solving Multiobjective Optimization Models in SAS® Optimization Q&A, Slides, and On-Demand Recording

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Watch this Ask the Expert session to learn how multi-objective optimization is used to analyze the best tradeoffs among numerous optimal solutions to help enable effective, strategic decision making. 

Watch the Webinar

You will learn how to:

• Build a multiobjective optimization model using the OPTMODEL procedure in SAS Optimization.
• Interpret the results of the model within the context of the business problem.
• Construct a Pareto frontier of optimal solutions to visualize the best set of tradeoffs between two competing objectives.
• Modify the optimization model to accommodate custom scenarios to answer additional business questions.
• Leverage the flexibility of the OPTMODEL programming syntax to achieve the objectives.

The questions from the Q&A segment held at the end of the webinar are listed below and the slides from the webinar are attached.

Q&A

Is it possible to build a multi-objective model with more than two objectives?

Yes, it is. There are a couple considerations for doing so, but there’s no reason you couldn’t have three or more objectives. Let me go back to this slide.

You'll notice we essentially have one axis for each objective. I was running two objectives, so I was working in two-dimensional space. If you have 3 objectives, you're effectively in three-dimensional space, and so on. So visually, that could create a bit of an issue if you're presenting a three-dimensional Pareto Frontier to customers. You can do it, and SAS has procedures like PROC G3D for plotting three-dimensional plots, but I’d argue they’re harder to visualize and interpret. One option you could do to get around that, if you're running multi-objective optimization models with three objectives, is to show multiple 2-D Pareto frontiers between two objectives at varying values of the third objective. So, the answer is yes you can. It does increase the complexity just a little bit, and requires a bit more thought around how to display the results.

Another consideration is when going from 2-D to 3-D space, and holding the learning rate constant, you’ll be forced to increase the number of iterations to accommodate the third objective (i.e., third dimension). This is where utilizing cofor{ } loops or the primalin option can have an even bigger impact to reduce the solve time for each iteration, but the process will nevertheless be expected to take longer due to more iterations being required.

Is the Blackbox solver using a specific ML algorithm?

More specific information on the Black-box solver can be found in the documentation here: SAS Help Center: The Black-Box Algorithm

Could the order of the objectives have been swapped to instead loop through the “Maximize Popularity” problem?

Yeah, absolutely. In this webinar, I chose the first objective to be “Maximize Popularity” and then iterated through the second objective, “Maximize Reach”. We could’ve swapped that to instead “Maximize Reach” first, then loop through “Maximize Popularity”. The new constraint in the 2^nd objective would’ve been: Reach >= (1 – ilr) * MaxReach, for each iteration. The process for generating the Pareto frontier would be the same. Visually, instead of working backwards on the x-axis (i.e., Popularity) with vertical bins at each iteration, we would instead be working down the y-axis (i.e., Reach), and the bins would be horizontal. But effectively it would work the same way.

Another consideration is determining whether one of the two models is more computationally difficult to solve compared to the other. In our example, Reach and Popularity were two fairly simple, straightforward models that could both be solved quickly, but if one model takes considerably longer to solve than the other, it makes sense to choose the simplest model as the second objective to loop through.

Recommended Resources

Network Analysis and Network Optimization in SAS Viya®

Operations Research with SAS Optimization®

Optimization Concepts for Data Science and Artificial Intelligence

Please see additional resources in the attached slide deck.

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