routing problem optimization code

i have a graph with nodes and links and each link have two weights ( number of people and time) and i want to find a circular route start and end at specified node the circular route should have max number of people and don't exceed a specifed time limit

[Torsten]

What about conditions on the route ? Each node must be visited ? Each node on the route can only be visited once ?

[Mostafa]

it is not necessary to visit each node and each node can be visited only one time

Answer 1

[Torsten]

https://math.stackexchange.com/questions/1658457/longest-path-with-constraint

[Mostafa]

Can i get pre written code for any example

[Mostafa]

Thanks alot

[Torsten]

If you can't implement the dynamic programming approach, use a linear optimization tool (e.g. linprog).

If you can't implement the problem in linprog, generate all cycles starting and ending in your specified node and choose the optimal one.

If you can't generate all cycles starting and ending in your specified node, well, then it's time to study a book on the subject.