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pythonoptimizationminimax

pyOpt multi-objective minimax example

Abstract problem to be solved:

we have n d-dimentional design variables, say {k_0, k_1, ..., k_n}

maximize the minimum of [f(k_0), f(k_1), ... f(k_n)], where f() a nonlinear function, i.e. maximin

constraint: mean([k_0, k_1, ...,k_n])==m, m known constant

Can someone provide an example of how this can be solved (maximin, d-dim variables) via pyOpt?

EDIT: i tried this: 

import scipy as sp
from pyOpt.pyOpt_optimization import Optimization
from pyOpt.pyALPSO.pyALPSO import ALPSO
def __objfunc(x,**kwargs):
    f=min([x[0]+x[1],x[2]+x[3]])
    g=[0.0]
    g[0]=(((x[0]+x[1])+(x[2]+x[3]))/2.0)-5
    fail=0
    return f,g,fail

if __name__=='__main__':
    op=Optimization('test', __objfunc)
    op.addVarGroup('p0',4,type='c')
    op.addObj('f')
    op.addCon('ineq','i')
    o=ALPSO()
    o(op)
    print(op._solutions[0])

suppose 2-dimentional design variables

is there any better way?

Solution

  • I probably would reformulate this as:

    enter image description here

    The min() function you used is non-differentiable (and thus dangerous). Also the mean() function can be replaced by a linear constraint (which is easier).

    I am not familiar with the ALPSO solver, but this reformulation would usually be helpful for more traditional solvers like SNOPT, NLPQL and FSQP.