Pareto points computation
Function prtp(B) is intended for detecting Pareto points.
Contents
DEFINITION
Let Fi(X), i=1...n, are objective functions for minimization. A point X* is said to be Pareto optimal one if there is no X such that Fi(X)<=Fi(X*) for all i=1...n, with at least one strict inequality.
DESCRIPTION
A=prtp(B) ,
B - m x n input matrix: B=
[F1(X1) F2(X1) ... Fn(X1);
F1(X2) F2(X2) ... Fn(X2);
.......................
F1(Xm) F2(Xm) ... Fn(Xm)]
A - an output matrix with rows which are Pareto
points (rows) of input matrix B.[A,b]=prtp(B) . b is a vector which contains serial numbers of matrix B Pareto points (rows).
EXAMPLE
B=[0 1 2; 1 2 3; 3 2 1; 4 0 2; 2 2 1;...
1 1 2; 2 1 1; 0 2 2]
[A b]=prtp(B)
B =
0 1 2
1 2 3
3 2 1
4 0 2
2 2 1
1 1 2
2 1 1
0 2 2
A =
0 1 2
4 0 2
2 1 1
b =
1 4 7