Sensors Allocation using Linear Programming

Question

I am working on an optimization problem, I need to find the minimum number of sensors between objects.

I have 7 objects and need to find the minimum number of sensor to be able to distinguish those objects. I have a sensor to detect color, a sensor to detect the dimension and a sensor to detect the weight (very simple and dumb sensor that only replies with a yes or no). Each object is unique and I want to use the minimum number of sensors to be able to identify each object. I want to use a combination of all sensor.

How would I use an lp solver to help? What will my variables be and what will my constraints be?

Your help will be highly appreciated.

Regards

Answer 1

This sounds more like a machine learning problem than an optimisation problem. What you're really asking is what features you need to compute to make an accurate classification. This all depends on your objects -- can you distinguish all of them just by color? Or do you need additional attributes?

If you have those attributes for all the objects, you could build a decision tree (e.g. using WEKA) and look at that. The attributes used in the tree would give you an idea of what sensors you need. You should get a pretty good idea just looking at the data though.

If the position of the sensors is an issue as well, it might be worth having a look at optimisation. For what you've described, there's no need though.