A shortest path-based approach to the multileaf collimator sequencing problem

AbstractThe multileaf collimator sequencing problem is an important component in effective cancer treatment delivery. The problem can be formulated as finding a decomposition of an integer matrix into a weighted sequence of binary matrices whose rows satisfy a consecutive ones property. Minimising the cardinality of the decomposition is an important objective and has been shown to be strongly NP-hard, even for a matrix restricted to a single column or row. We show that in this latter case it can be solved efficiently as a shortest path problem, giving a simple proof that the one-row problem is fixed-parameter tractable in the maximum intensity. We develop new linear and constraint programming models exploiting this result. Our approaches significantly improve the best known for the problem, bringing real-world sized problem instances within reach of exact algorithms

Operations Research Methods for Optimization in Radiation Oncology

Operations Research has a successful tradition of applying mathematical analysis to a wide range of applications, and problems in Medical Physics have been popular over the last couple of decades. The original application was in the optimal design of the uence map for a radiotherapy treatment, a problem that has continued to receive attention. However, Operations Research has been applied to other clinical problems like patient scheduling, vault design, and image alignment. The overriding theme of this article is to present how techniques in Operations Research apply to clinical problems, which we accomplish in three parts. First, we present the perspective from which an operations researcher addresses a clinical problem. Second, we succinctly introduce the underlying methods that are used to optimize a system, and third, we demonstrate how modern software facilitates problem design. Our discussion is supported by several publications to foster continued study. With numerous clinical, medical, and managerial decisions associated with a clinic, operations research has a promising future at improving how radiotherapy treatments are designed and delivered

Global Constraint Catalog, 2nd Edition (revision a)

This report presents a catalogue of global constraints where each constraint is explicitly described in terms of graph properties and/or automata and/or first order logical formulae with arithmetic. When available, it also presents some typical usage as well as some pointers to existing filtering algorithms