A new temporal CSP framework handling composite variables and activity constraints

Abstract

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)