Optimal control on a graph with application to train scheduling problems

Authors:
C. J. Goh;A. I. Mees
Affiliations:
Department of Mathematics, The University of Western Australia Nedlands, Western Australia 6009;Department of Mathematics, The University of Western Australia Nedlands, Western Australia 6009
Venue:
Mathematical and Computer Modelling: An International Journal
Year:
1991

Citing 3
Cited 0

Integer and combinatorial optimization

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MISER: a FORTRAN program for solving optimal control problems

Advances in Engineering Software
Control parametrization: a unified approach to optimal control problems with general constraints

Automatica (Journal of IFAC)

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Abstract

The concept of network optimization is indispensible in many large scale systems which (possibly after suitable transformation) possess the structure of a network. Algorithms which were developed for solving static network problems have limitations when applied to dynamical networks. This paper is an effort at modelling dynamical network systems by suitably defined differential equations on the arc flows and node requirements. A dynamic network optimization problem may then be formulated as an optimal control problem defined on a graph, with the possible involvement of integer variables. The formulation of a train scheduling problem is discussed to demonstrate the applicability and versatility of the approach.