Hi,
the MOO problem is reduced to a sequence of single-objective auxiliary problems where one objective is kept as main objective while the others are transferred to auxiliary constraint that bound them within some limits. Please see the pdf attached.
In order to compute the epsilon values, the first step is to compute the (lower and upper) bounds of each auxiliary objective, next, to split the range bounds in equidistant values. There will be a exponential number of problems over the number of objectives.
I hope I can help you. Good lucky
I recommend using the CPLEX Callable Library. Write a little C program that reads the data and then loops through the possible epsilon values, calling the CPLEX simplex optimiser to solve each LP subproblem.
If you use a Modelling languaje like AMPL or GAMS (OPL or Mosel) the yo only have to define a set with diferent values of the secondary objective and solve the problem with your first objective and the second one used as a constraint, variyng the RHS with the different values of the set elements.
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