# np complete – An unknown combinatorial optimization problem

I have $$N$$ available sensors and $$M$$ devices. Each device needs $$a$$ sensors. One sensor cannot be used on multiple devices. Each sensor has two properties defined by $$H$$ and $$R$$.

Let $$sigma_{i_H}$$ be the standard deviation of property $$H$$ for sensors on device $$i$$. Similarly, $$sigma_{i_R}$$ is the standard deviation of property $$R$$ for sensors on device $$i$$.

Now let $$s_{H}=sqrt{sum_{i=1}^{M} sigma_{i_H}^2 }$$ of all devices for the $$H$$ property. And $$s_{R}=sqrt{sum_{i=1}^{M} sigma_{i_R}^2 }$$ of all devices for the $$R$$ property.

The goal is to minimize $$mu=frac{s_H + s_R}{2}$$ .

Looking for guidance on which type of optimization problem this might be and for inspiration for different search algorithms.