Constraint programmingConstraint Programming (CP)-see Rossi et al. (2006), for instance-is a powerful technology to model and solve combinatorial (optimization) problems, which are ubiquitous in industry. CP works either via systematic tree search interleaved with constraint propagation (the elimination of impossible values) at every node of the search tree, or via constraint-based local search. CP is an ideal integration technology for hybrid solving, including methods from classical operations research as well, such as mixed integer programming (IP), and Boolean satisfiability. CP is now a mature technology and has been successfully used for tackling a wide range of real-life complex applications, especially for short-term scheduling, personnel rostering, and configuration problems.
Air traffic managementThe aim of this special issue was to collect original papers on applying constraint programming within the area of air traffic management (ATM), including air traffic control (ATC).Given the demands on today's ATM system, there is a constant need to optimize its performance in terms of costs, efficiency (minimal delay), or environmental impact. These performance criteria are often conflicting-many noise reduction measures at airports reduce capacity; many capacity enhancing measures carry a large cost-and therefore finding an optimal trade-off becomes the real objective.A wide array of techniques have been used in ATM optimization research, spanning expert systems, queuing models, heuristics, dynamic programming, (mixed) IP, constraint programming, and even evolutionary computation paradigms. A growing body of research is reported on in specialized conferences and journals, the most notable being the biannual USA/Europe ATM R&D Seminar 2 and the ATC Quarterly 3 .Because of the importance to their business operation, most of the ATM stakeholders will fund relevant studies. Air navigation service providers (in Europe, these are often national agencies responsible for civilian ATC) are constantly looking for optimizations in their airspace structure and sectorization, conflict detection and resolution, arrival and departure sequencing, or staff rostering. The European Central Flow Management Unit 4 is concerned with optimal slot allocation 1 The preparation of this special issue has been co-financed by the European Organisation for the Safety of Air Navigation (EUROCONTROL) under its innovative research grant scheme (Grant 08-121447-C). The content of this special issue does not necessarily reflect the official position of EUROCONTROL on the matter. 2