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##### Activity
• Sep 29 2021 12:20
ErikOrm removed as member
• Jun 08 2021 17:45
fhk starred flowty/flowty
• Apr 07 2021 11:38
spoorendonk closed #4
• Apr 07 2021 11:38
spoorendonk commented #4
• Mar 31 2021 07:03

spoorendonk on master

vrptw time before demand (compare)

• Mar 31 2021 06:58

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• Mar 30 2021 16:03

spoorendonk on use-knapsack

• Mar 30 2021 16:03

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knapsack less output num customers from arg and 5 more (compare)

• Mar 30 2021 16:03
spoorendonk closed #7
• Mar 30 2021 16:01
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• Mar 30 2021 16:01

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• Mar 30 2021 16:01

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• Mar 30 2021 14:45
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• Mar 30 2021 14:45

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• Mar 30 2021 14:41
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• Mar 30 2021 14:41

spoorendonk on use-knapsack

knapsack less output num customers from arg and 2 more (compare)

• Mar 30 2021 13:30

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remove an optimize (compare)

• Mar 30 2021 11:20
spoorendonk synchronize #7
• Mar 30 2021 11:20

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update workflow (compare)

• Mar 30 2021 11:09
spoorendonk opened #7
Erik Hellsten
@erohe_gitlab
did I misunderstand it? isn't the k-splittable MCF just that you limit the number of paths for eacdh commodity?
Simon Spoorendonk
@spoorendonk
yes
and each path can carry some flow $0 \leq \lambda \leq d^k$
double \$
Erik Hellsten
@erohe_gitlab
;)
Simon Spoorendonk
@spoorendonk
so a design varaible per path that you can count is the "normal" way of doing it
Erik Hellsten
@erohe_gitlab
I shall be honest and say that I don't know what the normal way is. It would work, in theory, but it might not be viable in practice. It is a lot of additional integer variables, which are painful to branch on
do we have any more elegant approaches? what does Mette do in their paper?
Simon Spoorendonk
@spoorendonk
she has $\lambda_p - u_p \eta_p \leq 0$ and $\sum_{P \in P^k} \eta_p \leq L$ for each commodity
Then she replaces the $\eta$ variables so the constraints above become $\sum_{p \in P} \frac {\lambda_p} {u_p} \leq L$
Erik Hellsten
@erohe_gitlab
$\sum_{P\in P^k}\eta_p\le L$, right?
Simon Spoorendonk
@spoorendonk
yes
Erik Hellsten
@erohe_gitlab
ok, so she does just that. Probably means that there are no easy other way
:(
Simon Spoorendonk
@spoorendonk
$u_p = \min_{u_e, e \in p}$
probably not. Replacing the constraints is a relaxation of the original k-splittalbe problem. Then you need to do some fancy branching to get a valid IP solution
hmm. I will stick with the integer flows for now. And the k=1 case
Erik Hellsten
@erohe_gitlab
I cannot yet see the brilliance in replacing the eta-variables

hmm. I will stick with the integer flows for now. And the k=1 case

Seems reasonable = )

Simon Spoorendonk
@spoorendonk

I cannot yet see the brilliance in replacing the eta-variables

you get a lambda only problem, but it is a ralxation

Erik Hellsten
@erohe_gitlab
haha, sweet. I started writing some comments on the models you sent in the link, but it changed as I wrote ^^
The first model seems fine. Though it is very hard to write the transit time constraints for the edge formulation. I'm also a bit curious to whether limiting the flow on each arc for a commodity to be integer, is strictly identical to limiting the flow on each path to be integer. It is easy to find a counter-example, but I could be that they have the same space of optimal solutions
Erik Hellsten
@erohe_gitlab
in the second model, starting with "under the hood", the first constraint is probably unnecessary, and z should be integer, not binary, right?
Simon Spoorendonk
@spoorendonk
the transit time constraints are crap in a edge formulation. The good thin with flowty is you never need to actually write them, just fill in the m.addResourceDisposable function when modelling.
Erik Hellsten
@erohe_gitlab
yeah, exactly =) the main reason I'm working with CG in the first place = )
Simon Spoorendonk
@spoorendonk
not entirely sure about the integer bounds n edges either
Erik Hellsten
@erohe_gitlab
without transit times, I feel rather certain that any solution that satisfies integrality on every edge, has an equivalen solution which satisfies integraility for every path. With transit-time constraints, it is less obvious
Simon Spoorendonk
@spoorendonk
yep change z to Z
Simon Spoorendonk
@spoorendonk
so for an integer variable in subproblem you always get {0,1} lambdas, however if discretize the suproblem and introduce identical suproblems with binary variables you get integer lambdas
for continuous you can do the same with [0,1] intervals (assuming your variable ub is integer)
I think...
that would be how you end up in model 2
Erik Hellsten
@erohe_gitlab
I am not quite following ':D
what counts as an integer variable in the subproblem? For us the subproblems are RCSPPs, so they are always integer, no? but that doesn't meant that lambda naturally becomes integer, right?
Erik Hellsten
@erohe_gitlab
I also accepted the merge request. But you have developer status in the project, right? So if you want to, also feel free to go wild and just change things as you desire.
Simon Spoorendonk
@spoorendonk
with developer status I cannot change the master branch by default. Yuo can change it in settings -> repository -> protected branches. Otherwise I just do merge reqs
Erik Hellsten
@erohe_gitlab
oh, ok. Well, that should do it. =)
Simon Spoorendonk
@spoorendonk

The first model seems fine. Though it is very hard to write the transit time constraints for the edge formulation. I'm also a bit curious to whether limiting the flow on each arc for a commodity to be integer, is strictly identical to limiting the flow on each path to be integer. It is easy to find a counter-example, but I could be that they have the same space of optimal solutions

what counts as an integer variable in the subproblem? For us the subproblems are RCSPPs, so they are always integer, no? but that doesn't meant that lambda naturally becomes integer, right?

in relation to the above. If edge flow variables are integers in can ultimately result in integer path variables.

so the RCSPP can be seen as solving a discretized version with binary flows for $d^k$ identical subproblems, and thereby result in integer path variables
Erik Hellsten
@erohe_gitlab
But all "paths" are already integer in all of our models. The question is just regarding the integrality of the lambda flow-decision variables. And of course, we could split our lambda into $d^k$ binary variables, but that would just introduce unnecessary symmetry issuses, wouldn't it? We would still need to relax those binary variables in the CG framework and branch to make them take integer variables. It would work equally well to just have $\lambda_{kp}\in \mathcal{Z}\cup[0, d^k]$.
Simon Spoorendonk
@spoorendonk
I think I get what you are saying. Setting integer on the edge variables does not guarantee a path but only integer flow. To have integer flow on paths one would need to solve a path problem per unit flow and add them up (the discretization wth identical subproblem approach). When the identical subproblems are aggregated that is when symmetry is disappears. Due to aggregation we have $\lambda \in \mathbb{Z}$
Modelling this with type="I" is maybe not super clear
Erik Hellsten
@erohe_gitlab
Yeah, something like that. I'm still a little confused, it feels like we talk a little about different things, but seems fair enough. If you want, we could have a call sometime, and discuss it further.
Erik Hellsten
@erohe_gitlab
I also added the strong constraints to the model. The next step would be to se if we can add them dynamically with some sort of callback =)
Simon Spoorendonk
@spoorendonk

Yeah, something like that. I'm still a little confused, it feels like we talk a little about different things, but seems fair enough. If you want, we could have a call sometime, and discuss it further.

I think you are right :). A call next week maube

I also added the strong constraints to the model. The next step would be to se if we can add them dynamically with some sort of callback =)

working on it, got could up in some multi threading for solving subproblems in parallel

Erik Hellsten
@erohe_gitlab
Sweet! =D
Simon Spoorendonk
@spoorendonk
hmm, got it working with cont flows in domain [0,d^k] but for integer flows (not k-splitable) the branching is off. It is a bigger rewrite so shelved for now
Erik Hellsten
@erohe_gitlab
ok, cool! =)