Add constraint in GurobiPy using conditional decision variable

Question

I am new to optimisation and have a fairly basic query.

I have a model with two decision variables x and y that vary in time. I'd like to add a conditional constraint on y at time t depending upon x[t-1], such that I've implemented the following code:

for t in model.timesteps:
        if t>1:
            if model.x[t-1] <= 1:
                model.addConstr(model.y[t] >= 100)
            elif model.x[t-1] <= 0.5:
                model.addConstr(model.y[t] >= 50)
            elif model.x[t-1] <= 0.3:
                model.addConstr(model.y[t] >= 20)

However, the above code produces the error:

File "tempconstr.pxi", line 44, in gurobipy.TempConstr.bool gurobipy.GurobiError: Constraint has no bool value (are you trying "lb <= expr <= ub"?)

Having done a little reading on previous related queries on this page, I believe I might need to use a binary indicator variable in order to implement the above. However, I'm not certain as to whether this would solve the above issue.

Could anyone point me in the right direction here please?

Many thanks in advance!

Is x[t-1] ever > 1? Are you worried about the edge cases like x[t-1] = 0.50001? — Greg Glockner
– Greg Glockner, Commented Oct 8, 2020 at 17:02
Hi, thanks for the response! No, x[t-1] is between [0,1] and edge cases are not an issue. — conor_coding
– conor_coding, Commented Oct 8, 2020 at 20:20

Greg Glockner · Accepted Answer · 2020-10-09 22:31:22Z

1

First, I assume your order of operations is incorrect; you intended that the right-hand side is 20 for 0 ≤ x[t-1] ≤ 0.3, 50 for 0.3 < x[t-1] ≤ 0.5 and 100 for 0.5 < x[t-1] ≤ 1.0.

The bigger issue is that you were mixing Python programming with MIP modeling. What you need is to convert that logic into a MIP model. There are several ways to do this. One is to use a piecewise linear constraint to represent the right-side values of the y[t] constraints. However, I prefer to model this explicitly. There are a few similar options; here is one I think is easy to understand: add binary variables z[0], z[1] and z[2] to represent the 3 ranges of x[t-1]; this gives the following code:

for t in model.timesteps:
  if t>1:
    z = model.addVars(3, vtype='B', name="z_%s" % str(t))
    model.addConstr(x[t-1] <= z.prod([0.3, 0.5, 1.0]))
    model.addConstr(y[t] >= z.prod([20, 50, 100]))
    model.addConstr(z.sum() == 1)

edited Oct 9, 2020 at 22:31

answered Oct 9, 2020 at 21:39

Greg Glockner

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ironzionlion · Accepted Answer · 2024-09-26 09:23:25Z

0

Gurobi doesn't support to add a model constraint by defining first its value.

Instead of model.addConstr(model.y[t] >= 100)

Try model.addConstr(100 <= model.y[t])

Source: https://support.gurobi.com/hc/en-us/articles/360039628832-Constraint-has-no-bool-value-are-you-trying-lb-expr-ub

answered Sep 26, 2024 at 9:23

ironzionlion

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