Managing Conditional and Composite CSPs

Abstract

Conditional CSPs and Composite CSPs have been known in the CSP discipline for fifteen years, especially in scheduling, planning, diagnosis and configuration domains. Basically a conditional constraint restricts the participation of a variable in a feasible scenario while a composite variable allows us to express a disjunction of variables or sub CSPs where only one will be added to the problem to solve. In this paper we combine the features of Conditional CSPs and Composite CSPs in a unique framework that we call Conditional and Composite CSPs (CCCSPs). Our framework allows the representation of dynamic constraint problems where all the information corresponding to any possible change are available a priori. Indeed these latter information are added to the problem to solve in a dynamic manner, during the resolution process, via conditional (or activity) constraints and composite variables. A composite variable is a variable whose possible values are CSP variables. In other words this allows us to represent disjunctive variables where only one will be added to the problem to solve. An activity constraint activates a non active variable (this latter variable will be added to the problem to solve) if a given condition holds on some other active variables. In order to solve the CCCSP, we propose two methods that are respectively based on constraint propagation and Stochastic Local Search (SLS). The experimental study, we conducted on randomly generated CCCSPs demonstrates the efficiency of a variant of the MAC strategy (that we call MAC+) over the other constraint propagation techniques. We will also show that MAC+ outperforms the SLS method MCRW for highly consistent CCCSPs. MCRW is however the procedure of choice for under constrained and middle constrained problems and also for highly constrained problems if we trade search time for the quality of the solution returned (number of solved constraints).