Bilevel programming problems (BLPP) are encountered when one optimization is embedded within another one as a constraint. BLPPs arise in many areas of engineering, where hierarchical decision models are not uncommon. Almost all areas of engineering can provide some example where two decision models interact and the outcome of one decision influences another; applications can be found in areas as diverse as traffic control and reactive distillation.
A typical BLPP formulation is given below:
The outer optimization problem, which minimizes F(x, y), is constrained by the inequality G(x, y) ≥ 0 and the equality H(x, y) = 0 constraints and an inner optimization problem. This inner optimization minimizes its objective function by varying y, while subject to its own inner and outer constraints. The inner variables y may also appear in the outer constraints and objective function, and the inner constraints and objective function may be parameterized by x.
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© 2001 Kluwer Academic Publishers
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Sahin, K., Gumus, Z., Ciric, A. (2001). Bilevel Programming: Applications in Engineering . In: Floudas, C.A., Pardalos, P.M. (eds) Encyclopedia of Optimization. Springer, Boston, MA. https://doi.org/10.1007/0-306-48332-7_34
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DOI: https://doi.org/10.1007/0-306-48332-7_34
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