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

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 .....)

[Walter Roberson]

How do you measure the optimality of any particular possibility ?

[Mohammad Al ja'idi]

hello Walter,

how can i understand the optimization technique to make optimization for my problem

[Walter Roberson]

You need to find at least one method of measuring how "good" any particular configuration is for your purposes. If the measurement is larger (most positive) for better configurations, then take the negative of it: you want something that is more negative for the better configurations.

Next you have to decide whether just the one method of measurement is enough, or if instead you have several competing measurements you are trying to satisfy. If you need to try to satisfy several things at once then you need a "multiobjective algorithm." There are not many multiobjective algorithms; if you can put everything into one measure, it is usually better to do that.

Then you need to think about cosntraints. Upper and lower bounds are best, linear inequalities and linear equalities are second best, and nonlinear constriants are worst. Not all constraints are supported by all miniizers so you need those to make further decisions.

[Mohammad Al ja'idi]

first of all, thank you for your interest and support

In my project i have many candidate Electric vehicle charging stations (as shown in the attached file), where the red dots represnt the Electric vehicles (EVs) and the blue triangles denote the candidate charging stations (CSs).

so far I have created a matrix has the 4 candidates CSs attributes such as the distances between the EVs and the candidate CSs and also the differences in elevation between the EVs and each candidate CSs

now how can i optimize my problem to find the optimal (1 or 2 or ..) CSs according to the optimization technique using Genetic algorithm (GA)

hope that you guid and help me to start my first optimization attempt

thank you in advance and hope to hearing from you soon

[Walter Roberson]

The optimal number of charge stations is one for every vehicle in each location that the vehicle might ever want to recharge.

[Mohammad Al ja'idi]

sorry, what do you mean by one CS for each EV, you mean if I have 2000 EVs then i should have 2000 CSs .. how come ???

[Walter Roberson]

If you are optimizing the distances travelled to charging stations then if the vehicles are already *at* the charging stations then the distance they have to travel would be 0 for each vehicle. Distance of 0 summed over all of the vehicles is 0. As there is no way to be a negative distance away, you cannot improve beyond that.

[Mohammad Al ja'idi]

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]

You have several possible answers:

1. 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
2. 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.
3. 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.
4. 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.
5. 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.
6. 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.