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A plan/solution
x
1
dominates
a plan/solution
x
2
if and only if
the two following
conditions are true:
x
1
is no worse than x
2
in all objectives,
i.e. f
j
(x
1
) ≤ f
j
(x
2
)
∀
j=1,...,
M.
x
1
is strictly better than x
2
in at least one objective
,
i.e. f
j
(
x
1
) < f
j
(x
2
) for at least one j
∈
{1,...,M}.
Inverse Optimisation and Planning
A Multi-Objective (MO) Problem
Among a set of solutions
P,
the
non-dominated set of
solutions
P'
are those that
are
not dominated
by any other member of the set
P:
The Pareto Optimal Set
.
When the set
P is
the entire feasible search space then the set
P'
is called
the global
Pareto Optimal Set
.
The image
f(x) of the
Pareto Optimal Set
is called the
Pareto Front (PF)
.
The
Pareto Optimal Set
is defined in the
parameter space
, while the
Pareto Front
is
defined in the
Objective Space
.
Dominance & Pareto Front