Intro to Multicriteria Optimization

Post by wolfgke » Wed, Aug 17, 2016, 10:24 AM UTC

pmalynin wrote: post #14

bumbledraven wrote: post #5

> The reason this is a more complicated situation is that an ordering of vectors in RkRk does not exist... how would one order the vectors u = (1,2,3), v = (2,1,3), w = (3,2,1)? It seems straightforward to order those vectors by first comparing the first component, then the second, then the third. The result is u,v,w. It's as if you wanted to sort a multi-column report in Excel. What am I missing?

Consider a simpler case of two dimensional real vectors. Lets consider the vector space of R^2, since all finite dimensional vector spaces of same dimensionality are isomorphic, R^2 is isomorphic to the complex numbers. How would you order the complex numbers?

Post by oli5679 » Wed, Aug 17, 2016, 12:06 PM UTC

  >>>import numpy as np

  >>>from scipy.optimize import minimize

  >>>X0 = np.array([1.5, 0.7, 1.2, 100])

  >>>options={'xtol': 1e-4, 'disp': True})

  >>>X* = minimize(obj, x0, method='nelder-mead', options)

Post by sevensor » Wed, Aug 17, 2016, 1:14 PM UTC

mccourt wrote: post #13

sevensor wrote: post #11

Earlier quoted context omitted.

> most people would be willing to arrive 0.0000001 hours later to save 998 dollars Unfortunately, if you don't know how your model behaves, you can't tell when you're setting γ whether you're actually going to get a solution that's way past the point of diminishing returns. You may not even be able to tell after the fact. This is one of the reasons for doing sensitivity analysis on γ. (Your ε-constraint scalarization…

You make a perfectly accurate point that, in practice, it is unlikely one would be able to make such a prediction without significant info about the model. The above comment was meant in more of a post hoc "we've executed our multicriteria optimization, approximated our Pareto frontier, now let's make a decision" sense, not within a specific scalarization context. Indeed sensitivity analysis on the gamma parameter is…

Post by sevensor » Wed, Aug 17, 2016, 1:57 PM UTC

mccourt wrote: post #12

sevensor wrote: post #10

Earlier quoted context omitted.

Does your platform support more than one level of preemption / lexicographic goal setting? (Like the ε-constraint scalarization technique, but with a second, third, nth set of goals between the first set and the objective?)

Our customers who are working with multicriteria problems have, thus far, had primarily two criteria, thus we have been helping them manage their two criteria problems into a scalar setting. As such, we do not, at this moment, permit the layers of ordering strategy you suggest through our API. To do so internally would introduce a complicated bifurcation between problems phrased with real-valued observations (as is o…

Post by oli5679 » Wed, Aug 17, 2016, 2:06 PM UTC

ogrisel wrote: post #24

oli5679 wrote: post #23

For anyone looking for a free optimization tool in python, sypy.opimize is easy to use. Eg if I have a complicated function revenue([A,B,C,D]) I can define obj([A,B,C,D]) = -1* revenue([A,B,C,D]) and use: >>>import numpy as np >>>from scipy.optimize import minimize >>>X0 = np.array([1.5, 0.7, 1.2, 100]) >>>options={'xtol': 1e-4, 'disp': True}) >>>X* = minimize(obj, x0, method='nelder-mead', options) http://docs.scipy…

scipy.optimize can only do single-criterion optimization (scalar-valued objective function instead of vector-valued objective functions).