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Title of Journal: Math Meth Oper Res

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Abbravation: Mathematical Methods of Operations Research

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Springer-Verlag

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10.1002/cber.189102402260

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1432-5217

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Combinatorial integral approximation

Authors: Sebastian Sager Michael Jung Christian Kirches
Publish Date: 2011/04/16
Volume: 73, Issue: 3, Pages: 363-
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Abstract

We are interested in structures and efficient methods for mixedinteger nonlinear programs MINLP that arise from a first discretize then optimize approach to timedependent mixedinteger optimal control problems MIOCPs In this study we focus on combinatorial constraints in particular on restrictions on the number of switches on a fixed time grid We propose a novel approach that is based on a decomposition of the MINLP into a NLP and a MILP We discuss the relation of the MILP solution to the MINLP solution and formulate bounds for the gap between the two depending on Lipschitz constants and the control discretization grid size The MILP solution can also be used for an efficient initialization of the MINLP solution process The speedup of the solution of the MILP compared to the MINLP solution is considerable already for general purpose MILP solvers We analyze the structure of the MILP that takes switching constraints into account and propose a tailored Branch and Bound strategy that outperforms cplex on a numerical case study and hence further improves efficiency of our novel method


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