Section: New Results

Constraint Programming

Participants : Roberto Amadini, Maurizio Gabbrielli, Jacopo Mauro.

The Constraint Programming (CP) paradigm is a general and powerful framework that enables to express relations between different entities in form of constraints that must be satisfied. The concept of constraint is ubiquitous and not confined to the sciences: constraints appear in every aspect of daily life in the form of requirements, obligations, or prohibitions. Historically, the FOCUS group has always had an interest in CP, see e.g., [53] , [54] . The possible applications of CP are in fact numerous and disparate. As an example, CP can be used for the deployment of services in the cloud [21] , [39] .

CP essentially consists of two layers: (i) a modeling level, in which a real-life problem is identified, examined, and formalized into a mathematical model by human experts; (ii) a solving level, aimed at resolving as efficiently and comprehensively as possible the model defined in (i) by means of software agents called constraint solvers. Over the last years we dealt with a particular aspect of CP, that is, the so called portfolio approaches [12] , [27] , [10] . In a nutshell, a portfolio approach in CP can be seen as the problem of predicting which is (are) the best constraint solver(s) —among a portfolio of available solvers— for solving a given CP problem. A constraint solver that relies on a portfolio of underlying, individual solvers is also dubbed a portfolio solver.

Our studies on portfolio approaches lead to development of the SUNNY-CP portfolio solver [26] , [25] . SUNNY-CP relies on underlying state-of-the-art constraint solvers for solving a given CP problem encoded in the MiniZinc language, nowadays a de-facto standard for modeling CP problems. Initially developed as a sequential solver [26] , SUNNY-CP has been later on enhanced by enabling the simultaneous execution of its solvers on different cores [25] . This extension allowed SUNNY-CP to win the gold medal in the open track of 2015 MiniZinc Challenge [cite], the annual competition for CP solvers.

However, we did not restrict the work on portfolio approaches to the CP field only. Indeed, we also performed some preliminary studies for evaluating SUNNY (i.e., the algorithm on which SUNNY-CP relies) in other application domains like, e.g., Boolean satisfiability (SAT), Quantified Boolean Formula (QBF), and Answer-Set Programming (ASP) [47] , [24] .