optimization problem to get the optimal number of the node(s) using GA

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Mohammad Al ja'idi 2019-5-1

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https://ww2.mathworks.cn/matlabcentral/answers/459606-optimization-problem-to-get-the-optimal-number-of-the-node-s-using-ga

评论： Walter Roberson 2019-5-2

Hi,

I have numbers of nodes and each node has its values, how can i optimize the problem to get the optimal number of the node(s) using GA.

ex. i have 20 nodes and i need to make optimization to find the optimal number (3 or 4 or 5 .....)

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Mohammad Al ja'idi 2019-5-2

Hello Walter.

as i mentioned before, i would like to optimize the number of the charging stations. i supposed that i know the distances between EVs and CSs and i already calculated these distances between each CS and all EVs, what i would to optimize is the number of the CSs in the study are as i attached previously.

thanks

mohammad

Walter Roberson 2019-5-2

You have several possible answers:

The optimal number of charging stations is 0, simply because it is not possible to have fewer of them. No EV can ever get charged, but you did not place any requirement that any EV must be able to be charged, so that is not relevant
The optimal number of charging stations is 1. Every EV can get charged. They may need to wait to get charged, but you did not place any requirement that any EV must be able to be charged within a specific amount of time, so that is not relevant.
The optimal number of charging stations is one for every place that an EV might want to think about charging. You did not define "optimal" as smallest number, so we are free to define "optimal" in terms of shortest distance and wait that the EV would have to travel to charge.
You start from the "outside", and place charging stations towards the inside according to the maximum driving distance of the worst EV in that sector. The worst EV would be able to just barely drive there to charge, but it would be able to charge. You did not place any requirement that any EV must be able to return back after charging and still get back to recharge, so we are free to optimize as saying that any given EV can only be devoted towards getting to a charging station and is useless for anything else.
You start from the "outside" and place charging stations towards the inside according to half the maximum driving distance of the worst EV in that sector. The worst EV would be able to drive there, arrive half full, charge to full, drive home arriving half full, and drive back immediately to recharge (arriving with no charge), after which it could spend all of its time driving back and forth between its home and the charging station. You did not place any requirement that any EV must be able to do anything else other than go back and forth between its home and the charging station, so we are free to optimize towards reducing the absolute number of charging stations to the point where one or more EV are useless for any other purpose than going back and forth charging and returning home.
In at least on configuration, you could place a charging station at the centroid of the EV locations. It would serve all of the EVs that are within half of their maximum driving distance away. The number of locations that are within a particular distance of a centroid tends to increase with the square of the distance, so you would tend to expect that this station would have to serve many more vehicles than any of the other charging stations (which would end up being placed to cover branches of the remaining connections.) The wait times at this central location would tend to increase. When the density of EV got high enough, you could expect that the wait times at the charging station would become a serious fraction of the trickle drainage time that all batteries have, so EV would end up having to do nothing other than get back in line to charge again -- for example the expected wait time to recharge would start to exceed 1 year when the vehicle density is large enough. However, you did not prohibit that from happening: you just asked to optimize the number of charging stations, and there is a valid argument to be made that having a single charging station with a one year line-up is more "optimal" than having two charging stations each with six month line-ups -- for example if the cost of a charging station is $250,000 then the cost of the single charging station with a one year line-up would be $250,000 but the cost of two charging stations each with six-month line-ups would be $500,000 which is clearly less "optimal" when the only measure is construction cost.

I could list some other possibilities, but I think it should be clear by now that your definition of "optimize" is not adequate.

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