ps_solver.m: This is a matlab implementation of the Pascoletti Sarafini scalarization for solving multiple criteria optimisation problems (MOPs).
Given a multiobjective optimisation problem (MOP):
(MOP) min C·x
s.t.
A·x ≦ b
x≧0
x∊ℝ^n, C∊ℝ^{nxQ}, A∊ℝ^{mxn}, b∊ℝ^m
We can use the Pascoletti Serafini (PS(a,r)), to iteratively find out all weakly non-dominated points:
(PS(a,r)) min t
s.t. a + t·r - f(x) ∊ ℝ^Q_≧
x∊S, a∊ℝ^Q, r∊ℝ^Q
- choose r∊ℝ^Q_> to always attain a solution
- choose a∊ℝ^Q to be all points on hyperplane with negative gradient intersecting the Ideal point of (MOP)
- limit the hyperplane at the lexmins