# ex001.mod
# Original AMPL coding by Sven Leyffer, University of Dundee
#
# A simple multi-objective optimization problem due to 
# I. Das and J.E. Dennis, " {A closer look at drawbacks of 
# minimizing weighted sums of objectives for Pareto set 
# generation in multicriteria optimization problems,
# Dept. of CAAM Tech. Report, TR-96-36, Rice University, 1996.

# ... sets & parameters
set I := 1..5;			# ... dimension of the problem

# ... variables
var x{i in I};

# ... objective functions
minimize  f1: sum{i in I}( x[i]^2 );
minimize  f2: 3*x[1] + 2*x[2] - x[3]/3 + 0.01*(x[4] - x[5])^3;

# ... constraints
subject to

   c1: x[1] + 2*x[2] - x[3] - 0.5*x[4] + x[5] = 2;

   c2: 4*x[1] - 2*x[2] + 0.8*x[3] + 0.6*x[4] + 0.5*x[5]^2 = 0;

   c3: sum{i in I}( x[i]^2 ) <= 10;