How can I choose the best initial state according to 1,000 different scenarios?

Question

I run a Monte Carlo simulation that generates more than 1000 different scenarios. For each scenario, I run an optimization algorithm and get the switches' status. The status of switches is 0 (close) or 1 (open). At the end of each scenario, I get a series of zeros and ones like [0 1 1 0 0 1 0]. The initial state of each switch is 0, and you shouldn't change the state of switches until you have no choice because changing status is time-consuming and resulting in customer outage. I consider this in the optimization problem. Monte-Carlo simulation generates 1000 scenarios. In each scenario, switches change position according to the optimization problem. Thus, if I somehow set the initial state of switches in a position requiring fewer changes in 1000 scenarios than before, I achieve my goal. For five switches, we have the below information.

https://imgur.com/yHqkMUL

I ask my question like this: According to this table, can you suggest the best initial state for each switch. Is there any way to analyze my data? Thank you in advance for considering answering my question. Best regards.

Answer 1

If I understand your question properly, you want to select an initial state for each switch to minimize changes that might be necessary after optimization. Since the states are binary, you can't calculate an expected value. Instead you calculate an odds ratio to decide on best state.

Quick way to estimate would be to take the mean for the values of each switch over all the runs. If there is a true preference, you should have a proportion or p. of something other than .5.

Based on the sample size, your actual decision bounds (based on 2 sigma limits) would be [.47 .53].

so if your proportion for a switch is less than .47 you should set it to 0, if more than .53, set it to 1