[Clp] Lexicographic Linear Optimization

[Andy Somogyi]

Hi All

Would anyone here have some tips on how to efficiently implement a lexicographic linear optimization in CLP?, 

Basically something similar to the approach outlined in:

K. Höffner, S. M. Harwood, and P. I. Barton, “A reliable simulator for dynamic flux balance analysis,” Biotechnology and bioengineering, vol. 110, no. 3, pp. 792–802, 2013.


Currently, I’m doing a pretty cheese approach of performing an iteration over the optimization function coefficients, where I zero all of the coefficients, except for the present one, calculating the primal solution, then set this as a constraint and continue on to the next coefficient, i.e. 

for i,c in orderedObjectives:
    zeroModelObjectives();
    setModelObjective(i,c);
    primal();
    setModelConstraint(i, getPrimalSolution(i));


Surely this is a very inefficient approach. 

The reason for doing this is that I need a unique solution to the LP problem, and I need that solution to vary continuously in response to smoothly varying constraints.  

Thanks

— Andy Somogyi, PhD
Research Associate, 
Biocomplexity Institute, 
Indiana University Dept of Physics