A well known approach to managing the numeric and the symbolic aspects of time is to view them as Constraint Satisfaction Problems (CSPs). Our aim is to extend the temporal CSP formalism in order to include activity constraints and composite variables. Indeed, in many real life applications the set of variables involved by the temporal constraint problem to solve is not known in advance. More precisely, while some temporal variables (called events) are available in the initial problem, others are added dynamically to the problem during the resolution process via activity constraints and composite variables. Activity constraints allow some variables to be activated (added to the problem) when activity conditions are true. Composite variables are defined on finite domains of events. We propose in this paper two methods based respectively on constraint propagation and stochastic local search (SLS) for solving temporal constraint problems with activity constraints and composite variables. We call these problems Conditional and Composite Temporal Constraint Satisfaction Problems (CCTCSPs). Experimental study we conducted on randomly generated CCTCSPs demonstrates the efficiency of our exact method based on constraint propagation in the case of middle constrained and over constrained problems while the SLS based method is the technique of choice for under constrained problems and also in case we want to trade search time for the quality of the solution returned (number of solved constraints).

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Preferences in temporal problems are common but significant in many real world applications. In this paper, we extend our temporal reasoning framework, managing numeric and symbolic information, in order to handle preferences. Unlike the existing models managing single temporal preferences, ours supports four types of preferences, namely: numeric and symbolic temporal preferences, composite preferences and conditional preferences. This offers more expressive power in representing a wide variety of temporal constraint problems. The preferences are considered here as a set of soft constraints using a c-semiring structure with combination and projection operators. Solving temporal constraint problems with preferences consists in finding a solution satisfying all the temporal constraints while optimizing the preference values. This is handled by a variant of the branch and bound algorithm, we propose in this paper, and where constraint propagation is used to improve the time efficiency. Experimental tests, we conducted on randomly generated temporal constraint problems with preferences, favor a variant of MAC as the constraint propagation strategy that should be used within the branch and bound algorithm.

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