Shortest path with more than one traveler and time constraints

Question

Please have a look at this problem...Thank you..
(the problem is ok with one traveler. but when two or more come into the picture they really mess things up)
Here it is
I have a number of destinations that devides evenly up between a
number of travelers. (5 travelers with 20 destinations = 4
destinations each)
All destination can be visited by all travelers but it can ony be visited once
Each destination has to be visited and
each traveler has to visit the same amount of destinations.
The total amount of traveling has to be minimized.
Grid references have been given to work out the distance between each
destination. (the distances have not been worked out prior to the
start of the problem)
The starting point of each traveler is not at any of the destinations
and is different to each other. This point is also known and can be
used to calculate the distance to any destination.
there is an extra part of the problem (which I think I can sort out but if its of interest here it is any way): Each destination can only be
visited at a certain time of the day (ie between 7- 9 and 9-12 and
12-3 and 3-6)
A typical problem would have about 300 destinations and about 50
travelers every day. ie about 6 destination a day per traveler.
Could any one please give me an idea of how you would go about working the
routes out for each traveler that minimizes travelling distance as there is no algorithm that does this kind of routing.
I would really like some help with this one please. I have many ideas of how to do it but i really feel like it is not optimised...
I have to complete this in one week and have no AI experiance ( I would like to do this without AI or anything to do with ant colonies and or swarm optimization)
Thank you.

Answer 1

The reason that the time is in fact a simple constraint is because this is a homework problem and the kids only have a week to work on it. If it were a real world problem you you not conveniently have the number of travelers divide evenly into the number of cities.
If it were not some homework problem you would not have a constraint that reads "Oh by the way, for extra credit, you can only visit some cities at certain times during the day." It would either be a real constraint or not.
The other indication that it is a homework problem is that the student was given a week to do it. I will perhaps be going out on a limb here, but NO reasonable business gives some bozo one week to complete an assignment for which the bozo is so clueless that he has to hit the net and ask random people if they can tell him how to do it.
Had there been any need to model travel time, then velocity of travelers would have been mentioned at some point. If the traveler were actually doing anything in a city, time to load or unload the truck would have been given. And lastly, what real world problem would add a constraint that no two travelers could go to the same city. What if it is shorter to get from A to C by going through B which has already been visited. This constraint was the tip that the solution was a partition of a set of cities.
My gross simplification is merely that this is a homework problem and therfore if I haven't been told otherwise I am free to assume that a traveler moving at infinite velocity is perfectly OK. This means that my traveler waits at the door to a city until it opens, picks off that city and all other in zero time, until it bangs up against a city that opens at a later time, where it must again wait till opening time. The only thing that prevents him from completing his circuit is if an early city comes after a late city. A simple sort is all you need.
Lastly, even if you want to toss in a more complicated velocity model, it does little more than mildly complicate the sort comparison calculation so instead of making the comparison
  boolean ICanMakeIt = city.openingTime <= city[i+1].openingTime
it becomes
  boolean ICanMakeIt = city.exitTime +
Traveler[j].vel*dist(i,i+1) <= city[i+1].closingTime
I think you are mistaken in declaring this to be a difficult modeling problem