I have a problem when I want to optimize the global Cost of the vehicules' route. So for that I register a Cost Dimension for returning the cost associated to each arc. But at the same time I have restrictions in another dimensions such as Time & Distance. How can I achieve this? Maybe I just only have to use AddDimension for each callback, but I don't know how to set the Objective function in RoutingModel.
All in your question: Does restriction aka constraint should be part of the objective cost ? or this is just, well constraints the solver need to fulfill ?
Adding new dimension using AddDimension() is a good start IMHO.
note: You may also add the span or global span of any dimension to the objective cost by setting the corresponding coefficient (zero by default thus dimension won't participate to the objective cost and only add "constraint" to the solution)
ref: https://github.com/google/or-tools/blob/b37d9c786b69128f3505f15beca09e89bf078a89/ortools/constraint_solver/routing.h#L2482-L2496
Related
So far I am using the routing package of ortools with the arc cost evaluator:
costCallbackIndex = model.registerTransitCallback(this::costCallback);
model.setArcCostEvaluatorOfAllVehicles(costCallbackIndex);
But I have realized that I am more interested in maximizing the number of pickups and deliveries (they are optional, using model.addDisjunction with a drop penalty) than the overall sum of meters travelled. Since I am dealing with a lot of pickups and deliveries I don't want to put the extra strain of minimizing arc costs on the solver.
One option is to define a arc cost callback that always returns 0, but this might confuse the solver. I could also not call the method setArcCostEvaluatorOfAllVehicles and hence suggest to the solver that I am not interested in arc costs.
What is the recommended approach?
Why don't you just refrain from using setArcCostEvaluatorOfAllVehicles ?
In MiniZinc it is possible to use the search annotation impact, it is explained as follows on the official website:
annotation impact
Choose the variable with the highest impact so far during the search
What does this mean in practice? What is the highest impact? How is this calculated?
To understand the impact based variable selection, you have to understand first_fail. In constraint programming we generally want to solve the hardest sub-problem first, failing quickly if no solution can be found. The problem with first_fail is that it doesn't take into account the number of constraints that a variable is involved in, more would indicate that the a decision for the variable "harder", or the effect that choices on the variable had in other parts of the search-tree.
As a sidenote, dom_w_deg is can be seen as compromise between first_fail and impact, where the constraints are taken into account, but the past decision are not.
impact variable selection is supposed to be an improvement on first_fail where not just domain sizes are considered, but also the constraints it's involved in and how much "impact" historical choices had. The variable with the highest impact is the one that is expected to be the hardest to assign the right value, taking all of this information into account.
As you've seen, MiniZinc does not provide an exact specification of how the variable choice has to made. It is up to solver implementer to select a heuristic that fit the solver. Note that it would be hard to provide an exact heuristic guideline as it would heavily depend on how the solver tracks its variables and constraints.
For ideas on possible implementations of impact based heuristics, I would suggest reading the paper "On the Efficiency of Impact Based Heuristics" by Marco Correia and Pedro Barahona. You can also check your specific MiniZinc/FlatZinc solver for their implementation of the heuristic.
I am writing a matlab code where i calculate the max-min.
I am using matlab's "fminimax" to solve the following problem:
ki=G(i,:);
ki(i)=0;
fs(i)=-((G(i,i)*pt(i)+sum(ki.*pt)+C1)-(C2*(sum(ki.*pt)+C1)));
G: is a system matrix. pt: is the optimization variable.
When the actual system matrix is used, the "fminimax" stops after one iteration and returns the initial value of "pt", no matter what the initial value for "pt", i.e. no solution is found. (the initial value is defined as X0 in the documentation). The system has the following parameters: G is in the order of e-11, pt is in the order of e-1, and c1 is in the order of e-14.
when i try a randomly generated test matrix and different parameters, the "fminimax" finds a solution for the problem, and everything works fine. G in order of e-2, pt in order of e-2, c1 is in the order of e-7.
I tried to scale the actual system: "fminimax" lasted more than one iteration, however, it still returned the initial value of pt, i.e. it couldn't find a solution.
I tried to change the tolerance of the "fminmax", using "options" [StepTolerance, OptimalityTolerance, ConstraintTolerance, and functiontolerance]. There were no impact at all. still no solution.
I thought that the problem might be that the precision of "fminimax" is not that high, or it is not suitable to solve the problem. i think it is also slow.
i downloaded CPLX, and i wanted to transform the max-min problem into linear programing, using a method i found in a book. However, when i tried my code on a simple minimax it didn't give the same solution.
I thought of using CVX for example, but the problem is not convex.
What might be the problem?
P.S. the system matrix, G, has different realizations, i tried some of them. However, the "fminimax" responds in the same way for all of them, i.e. it wasn't able to find an adequate solution.
I am not convinced that the optimization solvers are broken. If the problem is nonconvex, then there can be multiple local minimizers. Given the information you have provided, we have no way of knowing whether you started at an initial condition.
The first place you need to start is by getting more information from the optimization exit condition... Did it finish because it hit the iteration limit? (I hope not since it isn't doing many iterations)... Did it finish because a tolerance was hit (e.g. the function did not change by more than xxxx)? Or perhaps it could not find a feasible solution? (I don't know if you have any constraints that need to be met).
More than likely, I wold guess that you are starting at a local minimizer without realizing it. So you need to determine whether you are indeed at a local minimizer by looking at the jacobian of the function evaluated at your initial guess. Either calculate it analytically or use a finite step approximation....
I remember reading once in the Matlab documentation about an optimisation algorithm which allowed the user to specify the "scale" of variation expected for each parameter during the search (at least initially).
I can't remember what this function is, but now I am using fminsearch and there is no such option. In fact, I can't even specify parameter bounds, and the documentation states that it takes 5% of the initial guess as a default step (or 25e-5 if 0). Because this seems to be a relative choice to the initial guess, it makes me think that perhaps I should re-normalise my parameters to a suitable scale, in order to indirectly define a suitable step for my optimisation problem.
For example, if I have a parameter which value is on the order of 10e5 but that I would like steps on the order of 100, then I should "divide it" by 500 during optimisation (obviously I would then multiply it when computing the objective function). However this becomes trickier if a parameter range is centred around 0 for example; then I can rescale it and offset it.
My question is; is it effectively what people usually do when using the downhill-simplex method, and is there a "standard" or "better" way to do it?
I am using MATLAB gamultiobj optimization
as I have 6 to 12 objective functions; the gamultiobj function inefficiently handling the problem, always terminated because the number of generations exceeded, not because the changes of the objective functions become smaller
I looked at the gamultiobj options documentations, but it didn't help
http://www.mathworks.com/help/gads/examples/multiobjective-genetic-algorithm-options.html
1- how can I increase the capability of gamultiobj function to handle this number of objective functions?
2- are there a better way at all (using MATLAB)?
Well,
this is my update:
1- I increased the number of generations, the population size, and assigned proper initial population using the common ga options, it worked better (I didn't know that they are working with gamultiobj too, but I knew, it isn't stated anywhere in the documentation explicitly).
2- after running and inspecting the results I realized that gamultiobj can handle many objective functions efficiently providing that they are independent. As long as the objective functions are strongly dependent (which is the case of my problem, unfortunately) the gamultiobj solver's efficiency dramatically decreases.
thanks !
You should increase the number of generations, possibly play with the options such as crossover, mutation, the constraint bounds in which you're going to get the solution.
The bounds are to specified correctly. and the initial population is also pretty much needed to get it to the correct set of parameters that you want to optimize