How to debug unbounded models

[hghayoom]

Hi Oscar. I am trying to model a problem and I need to have access to variables from previous steps.I made a simpler example to address the issue specifically, I can buy materials from different resources ( Buy[f=1:NFact,i = 1:NSource, j = 1:NPaths]). but they can be delivered at different times. So I defined a (@variable(sp, pipeline[1:5], SDDP.State, initial_value = 0)), and each one of these Buy[c,1,r] can be delivered at different times. I tried to follow the documentation . the stability report says that it is stable. I can get results in the version without considering the delay. I tried different things but I couldn't find a solution. I even put all of i's in pipeline[i].out equal so that it is simpler but I couldn't get results. I appreciate it if you could help me with that.

using SDDP, HiGHS, Test,Pkg,Plots , Plots.PlotMeasures,Gurobi

Horizon = 53
NFact=1
Nmat=1
NSource=7
NPaths=1
NDest=1

BUYCOST=24000
Sel_price=46000
Gamma=75/1000

model = SDDP.PolicyGraph(
    SDDP.LinearGraph(Horizon),
    bellman_function = SDDP.BellmanFunction(
        lower_bound = -50.0,
        cut_type = SDDP.MULTI_CUT,
        #cut_type=SDDP.SINGLE_CUT
    ),
    optimizer = Gurobi.Optimizer,

) do sp, t
    @variable(sp, 0<=Epsilon[i = 1:NDest] , SDDP.State, initial_value = 0.0)
    @variable(sp, pipeline[1:5], SDDP.State, initial_value = 0)
    @variables(sp, begin
            Production[i = 1:NFact]>=0
            pen_p[i = 1:NFact] >= 0
            pen_n[i = 1:NFact]>= 0
            pen1_p[i = 1:NFact] >= 0
            pen1_n[i = 1:NFact]>= 0

            Sell[f=1:NFact,i = 1:NDest, j = 1:NPaths] >=0# sell to Customer c in path r Sell_F1[di,ri]
            Buy[f=1:NFact,i = 1:NSource, j = 1:NPaths] >=0# Buy from mat m road r 
    end)
    @variable(sp, Demandt, SDDP.State, initial_value = 4552)

        # Add the random variable as a control variable
        @variable(sp, ε)

        Ω = [-312,188,688,1188]
        P = [9/24,12/24,2/24,1/24]
        SDDP.parameterize(sp, Ω, P) do ω
            return JuMP.fix(ε, ω)
        end
    @constraint(sp, Demandt.out == Demandt.in+ε )
    @constraint(sp, Epsilon[1].out==Demandt.in-sum(Sell[c,1,j] for c in 1:NDest for j in 1:NPaths)+Epsilon[1].in)

    @constraints(sp, begin
    [c = 1:NFact],Production[c]==sum(Sell[c,i,j] for i in 1:NDest for j in 1:NPaths)+pen_p[c] - pen_n[c]

    [c = 1:NFact],pipeline[5].in==Gamma*Production[c]+pen1_p[c] - pen1_n[c]
    end)
    @constraints(sp,begin
    pipeline[2].out == sum(Buy[c,1,r] for c in 1:NFact for r in 1:NPaths) #1China.Shanghai
    pipeline[3].out == sum(Buy[c,2,r] for c in 1:NFact for r in 1:NPaths) #2Indonesia.tanjungpriok
    pipeline[4].out == sum(Buy[c,3,r] for c in 1:NFact for r in 1:NPaths) #3Japan.Tokyo
    pipeline[2].out == sum(Buy[c,4,r] for c in 1:NFact for r in 1:NPaths) #4Australia.Fremantle
    pipeline[3].out == sum(Buy[c,5,r] for c in 1:NFact for r in 1:NPaths) #5Russia.Murmansk.Panama Canal
    pipeline[4].out == sum(Buy[c,6,r] for c in 1:NFact for r in 1:NPaths) #6canada  Vancouver
    pipeline[4].out == sum(Buy[c,7,r] for c in 1:NFact for r in 1:NPaths) #7China Arctic

       end)
    @constraint(sp, [i=2:5], pipeline[i].out == pipeline[i-1].in)
    @stageobjective(sp,
                sum(1e6*pen_p[i] for i in 1:NFact)
                +sum(1e6*pen_n[i] for i in 1:NFact)
                +sum(1e6*pen1_p[i] for i in 1:NFact)
                +sum(1e6*pen1_n[i] for i in 1:NFact)
                +1e6*Epsilon[1].out

                +sum(Buy[c,m,r]*BUYCOST for c in 1:NFact for r in 1:NPaths for m in 1:NSource)/1000
                -sum(Sell[f,m,r]*Sel_price for f in 1:NFact for r in 1:NPaths for m in 1:NDest)/1000

        )

end
SDDP.numerical_stability_report(model)
SDDP.train(model, iteration_limit = 5, print_level = 2, log_frequency = 5)
simulations = SDDP.simulate(
    # The trained model to simulate.
    model,
    # The number of replications.
    20,
    # A list of names to record the values of.
    sampling_scheme = SDDP.InSampleMonteCarlo(
            terminate_on_cycle = false,
            terminate_on_dummy_leaf = true,
    ),)

        )

end
SDDP.numerical_stability_report(model)
SDDP.train(model, iteration_limit = 5, print_level = 2, log_frequency = 5)
simulations = SDDP.simulate(
    # The trained model to simulate.
    model,
    # The number of replications.
    20,
    # A list of names to record the values of.
    sampling_scheme = SDDP.InSampleMonteCarlo(
            terminate_on_cycle = false,
            terminate_on_dummy_leaf = true,
    ),)

[odow]

Let me walk you through my thought process for how I debug your model:

1. I run the code to check I can reproduce the bug, and I do this after each step.
2. I tidy the formatting. "Clean" code is much easier to reason about. I put all the constraints together. I put all the variables together. I delete all unnecessary lines. I look for simplifications, like replacing sum(1e6*pen_p[i] for i in 1:NFact) with 1e6 * sum(pen_p)`. The fewer characters there are, the less room for bugs.
   3. I remove all specialized options. Where possible, just stick with the defaults. If it doesn't work for the defaults, it likely won't work if you try multi-cut etc.
   4. The termination status is INFEASIBLE_OR_UNBOUNDED. To check if the model is infeasible or unbounded, we could try solving without an objective. If the model is unbounded, we should now return a feasible solution.
   5. After commenting the objective, it now runs for a few iterations. Therefore, we know the problem is unbounded. That must mean that a variable in the objective can grow without limit.
   6. We're minimizing, so variables with a positive coefficient want to be small, and variables with a negative coefficient want to be big. Buy, pen_p, pen_n, pen1_p, pen1_n, and Epsilon[1].out all have positive coefficients, but they have a lower bound of 0, so they can't be the problem.
   7. Sell has a negative coefficient and no upper bound. So it must be the problem.

All of this means that your model has a formulation error.

[odow]

Also, where did you and @bolbolim find the suggestion to use SDDP.BellmanFunction?

Just do instead:

model = SDDP.LinearPolicyGraph(
    stages = Horizon,
    sense = :Min,
    lower_bound = -50.0,
    optimizer = Gurobi.Optimizer,    
) do sp, t

You can specify MULTI_CUT using the cut_type keyword argument in train: https://odow.github.io/SDDP.jl/stable/apireference/#SDDP.train

[hghayoom]

Hi Oscar, Thanks for spending time to debug it. You are honestly amazing. The reason for this untidiness is that I start to model a problem from a small example, and I didn't know how big should be. therefore, in each step, I added a constraint and variable. but you are correct. definitely, I will make a tidy version. It helps a lot.

[hghayoom]

Also, where did you and @bolbolim find the suggestion to use SDDP.BellmanFunction?

Just do instead:

model = SDDP.LinearPolicyGraph(
    stages = Horizon,
    sense = :Min,
    lower_bound = -50.0,
    optimizer = Gurobi.Optimizer,    
) do sp, t

You can specify MULTI_CUT using the cut_type keyword argument in train: https://odow.github.io/SDDP.jl/stable/apireference/#SDDP.train

That is interesting. I think I got it from one of your examples. But I searched in all of your examples and I couldn't find it. I just used it once and after I realized it worked, I just copied it for the next examples. But I will change for the next runs. thanks for catching that

[hghayoom]

Also, where did you and @bolbolim find the suggestion to use SDDP.BellmanFunction?

Just do instead:

model = SDDP.LinearPolicyGraph(
    stages = Horizon,
    sense = :Min,
    lower_bound = -50.0,
    optimizer = Gurobi.Optimizer,    
) do sp, t

You can specify MULTI_CUT using the cut_type keyword argument in train: https://odow.github.io/SDDP.jl/stable/apireference/#SDDP.train Thanks for teaching how to debug. I think I found the problem. The problem is that I am giving to a unqeu variable multiple numbers rather than summing them in this constraint:

@constraints(sp,begin
pipeline[2].out == sum(Buy[c,1,r] for c in 1:NFact for r in 1:NPaths) #1China.Shanghai
pipeline[3].out == sum(Buy[c,2,r] for c in 1:NFact for r in 1:NPaths) #2Indonesia.tanjungpriok
pipeline[4].out == sum(Buy[c,3,r] for c in 1:NFact for r in 1:NPaths) #3Japan.Tokyo
pipeline[2].out == sum(Buy[c,4,r] for c in 1:NFact for r in 1:NPaths) #4Australia.Fremantle
pipeline[3].out == sum(Buy[c,5,r] for c in 1:NFact for r in 1:NPaths) #5Russia.Murmansk.Panama Canal
pipeline[4].out == sum(Buy[c,6,r] for c in 1:NFact for r in 1:NPaths) #6canada  Vancouver
pipeline[4].out == sum(Buy[c,7,r] for c in 1:NFact for r in 1:NPaths) #7China Arctic

   end)

for example I have used 
```julia
 pipeline[4].out 

three times and and made it equal to three parameters. after this modification, I could get resaults. Thank you sooooo much.

using SDDP, HiGHS, Test,Pkg,Plots , Plots.PlotMeasures,Gurobi

Horizon = 53
NFact=1
Nmat=1
NSource=7
NPaths=1
NDest=1

BUYCOST=24000
Sel_price=46000
Gamma=75/1000

model = SDDP.LinearPolicyGraph(
    stages = Horizon,
    sense = :Min,
    lower_bound = -50.0,
    optimizer = Gurobi.Optimizer,    
) do sp, t
    @variable(sp, 0<=Epsilon[i = 1:NDest] , SDDP.State, initial_value = 0.0)
    @variable(sp, pipeline[1:5], SDDP.State, initial_value = 0)
    @variables(sp, begin
            Production[i = 1:NFact]>=0
            pen_p[i = 1:NFact] >= 0
            pen_n[i = 1:NFact]>= 0
            pen1_p[i = 1:NFact] >= 0
            pen1_n[i = 1:NFact]>= 0

            Sell[f=1:NFact,i = 1:NDest, j = 1:NPaths] >=0# sell to Customer c in path r Sell_F1[di,ri]
            Buy[f=1:NFact,i = 1:NSource, j = 1:NPaths] >=0# Buy from mat m road r 
    end)
    @variable(sp, Demandt, SDDP.State, initial_value = 4552)

        # Add the random variable as a control variable
        @variable(sp, ε)

        Ω = [-312,188,688,1188]
        P = [9/24,12/24,2/24,1/24]
        SDDP.parameterize(sp, Ω, P) do ω
            return JuMP.fix(ε, ω)
        end
    @constraint(sp, Demandt.out == Demandt.in+ε )
    @constraint(sp, Epsilon[1].out==Demandt.in-sum(Sell[c,1,j] for c in 1:NDest for j in 1:NPaths)+Epsilon[1].in)

    @constraints(sp, begin
    [c = 1:NFact],Production[c]==sum(Sell[c,i,j] for i in 1:NDest for j in 1:NPaths)+pen_p[c] - pen_n[c]

    [c = 1:NFact],pipeline[5].in==Gamma*Production[c]+pen1_p[c] - pen1_n[c]
    end)
    @constraints(sp,begin
    pipeline[2].out == sum(Buy[c,1,r] for c in 1:NFact for r in 1:NPaths) #1China.Shanghai
    pipeline[3].out == sum(Buy[c,2,r] for c in 1:NFact for r in 1:NPaths) #2Indonesia.tanjungpriok
    pipeline[4].out == sum(Buy[c,3,r] for c in 1:NFact for r in 1:NPaths) #3Japan.Tokyo
    pipeline[1].out == sum(Buy[c,4,r] for c in 1:NFact for r in 1:NPaths)+sum(Buy[c,7,r] for c in 1:NFact for r in 1:NPaths) #4Australia.Fremantle
    pipeline[5].out == sum(Buy[c,5,r] for c in 1:NFact for r in 1:NPaths)+sum(Buy[c,6,r] for c in 1:NFact for r in 1:NPaths) #5Russia.Murmansk.Panama Canal
    # pipeline[4].out == sum(Buy[c,6,r] for c in 1:NFact for r in 1:NPaths) #6canada    Vancouver
    # pipeline[4].out == sum(Buy[c,7,r] for c in 1:NFact for r in 1:NPaths) #7China Arctic

       end)
    @constraint(sp, [i=2:5], pipeline[i].out == pipeline[i-1].in)
    @stageobjective(sp,
                sum(1e6*pen_p[i] for i in 1:NFact)
                +sum(1e6*pen_n[i] for i in 1:NFact)
                +sum(1e6*pen1_p[i] for i in 1:NFact)
                +sum(1e6*pen1_n[i] for i in 1:NFact)
                +1e6*Epsilon[1].out

                +sum(Buy[c,m,r]*BUYCOST for c in 1:NFact for r in 1:NPaths for m in 1:NSource)/1000
                -sum(Sell[f,m,r]*Sel_price for f in 1:NFact for r in 1:NPaths for m in 1:NDest)/1000

        )

end
SDDP.numerical_stability_report(model)
SDDP.train(model, iteration_limit = 5, print_level = 2, log_frequency = 5)
simulations = SDDP.simulate(
    # The trained model to simulate.
    model,
    # The number of replications.
    20,
    # A list of names to record the values of.
    sampling_scheme = SDDP.InSampleMonteCarlo(
            terminate_on_cycle = false,
            terminate_on_dummy_leaf = true,
    ),)

[odow]

Thanks for spending time to debug it. You are honestly amazing.

No problem.

I'm still evolving the style of how I write models, but this is what I've been going for recently. I find it helpful to name every state variable with x_, every control variable with u_, every random variable with ω_, and penalty variables with Δ_.

I've also started using UPPERCASE for constants, although you could also use something like c_buy_cost.

using SDDP, Gurobi

T_MAX = 53
N_FACILITIES = 1
N_SOURCE = 7
N_PATHS = 1
N_DEST = 1
BUY_COST = 24_000
SELL_PRICE = 46_000
GAMMA = 75 / 1_000

model = SDDP.LinearPolicyGraph(
    stages = T_MAX,
    sense = :Min,
    lower_bound = -50.0,
    optimizer = Gurobi.Optimizer,    
) do sp, t
    @variables(sp, begin
        x_epsilon[1:N_DEST] >= 0, SDDP.State, (initial_value = 0)
        x_pipeline[1:5], SDDP.State, (initial_value = 0)
        x_demand_t, SDDP.State, (initial_value = 4552)
        u_production[1:N_FACILITIES] >= 0
        u_sell[1:N_FACILITIES, 1:N_DEST, 1:N_PATHS] >= 0
        u_buy[1:N_FACILITIES, 1:N_SOURCE, 1:N_PATHS] >= 0
        Δ_p[1:N_FACILITIES] >= 0
        Δ_n[1:N_FACILITIES] >= 0
        Δ1_p[1:N_FACILITIES] >= 0
        Δ1_n[1:N_FACILITIES] >= 0
        ω_ε
    end)
    @stageobjective(sp,
        1e6 * sum(Δ_p + Δ_n + Δ1_p + Δ1_n) +
        1e6 * x_epsilon[1].out +
        1e-3 * BUY_COST * sum(u_buy) -
        1e-3 * SELL_PRICE * sum(u_sell)
    )
    @constraints(sp,begin
        x_demand_t.out == x_demand_t.in + ω_ε 
        x_epsilon[1].out == x_demand_t.in - sum(u_sell[:,1,:]) + x_epsilon[1].in
        [c = 1:N_FACILITIES], u_production[c] == sum(u_sell[c,:,:]) + Δ_p[c] - Δ_n[c]
        [c = 1:N_FACILITIES], x_pipeline[5].in == GAMMA * u_production[c] + Δ1_p[c] - Δ1_n[c]
        [i = 2:5], x_pipeline[i].out == x_pipeline[i-1].in
        x_pipeline[1].out == sum(u_buy[:,4,:]) + sum(u_buy[:,7,:])
        x_pipeline[2].out == sum(u_buy[:,1,:])
        x_pipeline[3].out == sum(u_buy[:,2,:])
        x_pipeline[4].out == sum(u_buy[:,3,:])
        x_pipeline[5].out == sum(u_buy[:,5,:]) + sum(u_buy[:,6,:])
    end)
    Ω = [-312, 188, 688, 1188]
    P = [9, 12, 2, 1] / 24
    SDDP.parameterize(sp, Ω, P) do ω
        return JuMP.fix(ω_ε, ω)
    end
end
SDDP.train(model; iteration_limit = 5)
simulations = SDDP.simulate(model, 20)

[hghayoom]

this style of writing code is very helpful. And I will start to follow it. You're the best man.

[odow]

I'll point you (and future readers) to this section of the JuMP docs, which provides good advice for debugging unbounded models (as well as other failures): https://jump.dev/JuMP.jl/stable/tutorials/getting_started/debugging/#Debugging-an-unbounded-model

[odow]

Closing because this seems resolved. Feel free to re-open (or start a new thread) if you have other questions.

[hghayoom]

Hi again Oscar. I am trying to save some of the variables in the simulation for example u_production[1]

simulations = SDDP.simulate(model, 20,[:u_production[1]])

I only can save these variables if I save them separately in a temp variable in the body of the model as a constraint. for example

@variable(TempProd1>=0)
@constraint(TempProd1=u_production[1])

and then

simulations = SDDP.simulate(model, 20,[:TempProd1])

because I have a lot of variables and I want to check the accuracy of their number(especially use them for your publication graph) I have defined a looot of variables for each one.

I tried multiple things and I couldn't find a solution. I appreciate it if you could help

Bests, Hadi

[odow]

Do instead:

simulations = SDDP.simulate(model, 20, [:u_production])
simulations[1][1][:u_production][1]