A dual temperature simulated annealing approach for solving bilevel programming problems

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Abstract

This paper presents a dual temperature simulated annealing approach to bilevel programming problems. Bilevel programming problems arise when one optimization problem, the inner problem, is a constraint of a second optimization problem, the outer problem. In this paper, the inner problem is stochastically relaxed with a parameter that can be used as a temperature scale in simulated annealing. Solving the outer problem with simulated annealing as well leads to the dual temperature approach. The technique is demonstrated with several linear, nonlinear, and mixed integer nonlinear bilevel programming problems, including a safe plant layout problem that simultaneously minimizes cost and the damage caused during a worst case scenario accident.

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    Citation Excerpt :

    The majority of methods to solve the mixed-integer bilevel programming problem are restricted to the linear problems and problems where the upper level decision variables only appear in the lower level problem objective and are separable (Saharidis & Ierapetritou, 2009). Moreover, the mixed-integer nonlinear bilevel programming problem has received a little attention in the literature, such as an algorithm using parametric analysis by Jan and Chern (1994), a stochastic simulated annealing algorithm proposed by Sahin and Ciric (1998) and a parametric integer programming algorithm by Köppe, Queyranne, and Ryan (2010). Then, Gümüs and Floudas (2005) introduced two deterministic global optimization methods that solve mixed-integer nonlinear bilevel programming problems.

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