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Fig. 9.6 Bilevel vs biobjective optimisation example. The red triangle represents the region of
solution of the biobjective problem that is dominating the bilevel optimal solution (point C)
g j (x u , x l ) ≤ 0
G k (x u , x l ) ≤ 0
where
G k : X U × X L → R, k = 1 . . . , K
denote the upper level constraints and K is the number of upper level constraints
and
g j : X U × X L → R, j = 1 . . . , J
represent the lower level constraints and J is the number of lower level constraints,
respectively [5]. F and f are the upper and lower level objectives, respectively,
where p is the number of upper level objectives and q is the number of lower
level objectives. Also, X U ∈ R n and X L ∈ R m , where n and m are the number
of variables for upper and lower levels, respectively.