用 scipy 约束

Question

I have a problem of multi-objective optimization under constraint (maximization), in fact I transformed it into a mono-objective problem via the weighting technique and I added 2 variable x1, x2 (to optimize) with a constraint 0 <x1 + x2 <1 so their sum must be strictly less than 1 to give rise to the 3rd objective function as described in the code below.

When I execute the sum is always greater than 1.

    for i in range(len(f1)):
        def f(x):
            x1= x[0]
            x2= x[1]
            return -(x1*f1[i]+ x2*f2[i]+ (1-x1-x2)*f3[i])

        def constraint(x):
            return x[0]+x[1]-1

        b= (0.2, 0.8)
        bnds= (b, b)
        x0=[0.5,0.4]

        cons= ({'type': 'ineq','fun':constraint})

        res = minimize(f,x0, method= 'SLSQP', bounds=bnds, constraints=cons)

        print('Vect_ponderation : ', res.x)

Output:

Vect_ponderation :  [0.8 0.8]
Vect_ponderation :  [0.8 0.8]
Vect_ponderation :  [0.8 0.8]
Vect_ponderation :  [0.8 0.8]

Answer 1

The documentation says:

Equality constraint means that the constraint function result is to be zero whereas inequality means that it is to be non-negative . Note that COBYLA only supports inequality constraints.

def constraint(x):
    return x[0] + x[1] -1

means:

x0 + x1 - 1 >= 0  # non-negative
<-> 
x0 + x1 >= 1

which is respected in your solution.

You probably want:

def constraint(x):
    return - x[0] - x[1] + 1

Also keep in mind, that there is no concept of strict inequality . You will need to introduce some epsilon constant a-priori like: eps = 1e-6 :

def constraint(x):
    return - x[0] - x[1] + 1 - EPS

Answer 2

As I understand, your problem is that the output has x1+x2>1 . I've checked optimize documentation and it says: 'inequality means that it is to be non-negative'. Thus, you have requested something opposite to what you think you have requested.

Suggestions:

• You have very simple function, so try providing jacobian as an additional parameter. The fit is much more efficient then.

• Try to present minimal reproducible example . This makes answering much easier. Your question lacks f1 , f2 , and f3 definitions.

• Try to ask a question. I've found something that might be the problem you're trying to solve, but I'm not sure because there is no question (ie, sentence with question mark) in your question.