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I am working on a problem which involves optimizing for minimum power consumption in a large compressor network interconnected through pipelines (think of a connected graph with nodes as compressors and arcs as pipelines). I need to impose a constraint. when more than one compressors share a single pipeline on their discharge side i.e. their individual discharge pressures should ideally be equal.

Now, when I read in the historical plant operational data recorded through the sensors, I notice that these variables are fairly close but not precisely equal already. This could likely be due to sensor error. My question is how to model such constraints in an optimization problem so that you account for the slight variability among the variables instead of imposing a strict equality constraints.

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  • $\begingroup$ What you do is make a physically correct model that is close enough to the actual case to predict such things as pulsatile pressure propagation, gas flow versus pressure drop, and the like. Trouble is that is more physics than statistics. $\endgroup$ – Carl Jun 8 '19 at 7:57
  • $\begingroup$ It may be that your question can be answered here, but if you would prefer it migrated to SEs [physicis.SE] Q&A site, just flag your Q & ask the moderators to do so. $\endgroup$ – gung - Reinstate Monica Jun 8 '19 at 12:11
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    $\begingroup$ In the interim, it may help if you can post a small example dataset, w/ a small example graph, & the exact constraints you need to include. $\endgroup$ – gung - Reinstate Monica Jun 8 '19 at 12:13
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    $\begingroup$ This is cross-posted (withotu mentioning being cross-posted - for shame) at or.stackexchange.com/questions/314/… . Operations Research Stack Exchange may ultimately be a better location for such optimization questions. But it is now in private beta, which I think means that only people who "Committed" in the proposal phase can post there. It supposedly (hopefully?) will move to public beta within a week or so, which will then allow any Stack Exchange user to register and post there. $\endgroup$ – Mark L. Stone Jun 8 '19 at 12:25