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M. Antoniou and P. Korošec
Fig. 9.8 Nested method
Fig. 9.9 Singe level
reduction method
problem. A general schema is shown in Fig. 9.9. Karush-Kuhn-Tucker (KKT)
conditions 3 applied to the lower level have been often used in the evolutionary
computation community to reduce the bilevel optimisation problem into a singlelevel optimisation problem. This approach is able to solve problems that adhere
3 Karush-Kuhn-Tucker (KKT) conditions: when the lower level problem has some conditions, such
as that is convex and regular, it can be replaced with its KKT conditions. KKT conditions on the
lower level problem are generally used as constraints in the formulation of the KKT conditions of
the upper level optimisation problem [45]. This involves the second derivatives of the objectives
and constraints of the lower level problem as necessary conditions of the upper level optimisation
problem [22]. That way, the problems are reduced to a single-level optimisation problem. More
about this the reader can find in [48].
M. Antoniou and P. Korošec
Fig. 9.8 Nested method
Fig. 9.9 Singe level
reduction method
problem. A general schema is shown in Fig. 9.9. Karush-Kuhn-Tucker (KKT)
conditions 3 applied to the lower level have been often used in the evolutionary
computation community to reduce the bilevel optimisation problem into a singlelevel optimisation problem. This approach is able to solve problems that adhere
3 Karush-Kuhn-Tucker (KKT) conditions: when the lower level problem has some conditions, such
as that is convex and regular, it can be replaced with its KKT conditions. KKT conditions on the
lower level problem are generally used as constraints in the formulation of the KKT conditions of
the upper level optimisation problem [45]. This involves the second derivatives of the objectives
and constraints of the lower level problem as necessary conditions of the upper level optimisation
problem [22]. That way, the problems are reduced to a single-level optimisation problem. More
about this the reader can find in [48].