You are given the following objective values for a range of solutions in a $2-$

dimensional objective space where we want to maximise both objectives:

Decision vector f$1($xi$)$ f$2($xi$)$

x$111\mathrm{.}602\mathrm{.}21$

x$27\mathrm{.}315\mathrm{.}51$

x$34\mathrm{.}623\mathrm{.}14$

Given two solutions xrow and xcol, the dominance relationships are identified

with the following keys:

Key Description

$0$ xrow $$ xcol, i$.$e$.$ xrow dominates xcol.

$1$ xcol $$ xrow, i$.$e$.$ xcol dominates xrow.

$2$ xrow $=$ xcol, i$.$e$.$ xrow and xcol are identical.

$3$ xrow $$ xcol, i$.$e$.$ xrow and xcol are mutually non$-$dominated.

$($a$)$ Using the keys defined above complete the following matrix where each

cell represents the dominance relationship between the row solution and

the column solution.

x$1$ x$2$ x$3$

x$1$

$!$