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$15\mathrm{.}728\mathrm{.}79$

x$24\mathrm{.}037$

x$310\mathrm{.}467\mathrm{.}05$

x$46\mathrm{.}7911\mathrm{.}4$

x$59\mathrm{.}092\mathrm{.}11$

x$65\mathrm{.}372\mathrm{.}91$

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 equal.

$3$ 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$4$ x$5$ x$6$

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