Mother Tree Optimization for Conditional Constraints and Qualitative Preferences

The Constraint Satisfaction Problem (CSP) is a robust framework for representing and solving many challenging and complex problems under constraints. More specifically, a CSP includes a set of variables defined over discrete domains of values, and a set of constraints restricting the values that the variables can simultaneously take. Solving a CSP consists of finding a complete assignment of values to variables such that all the constraints are satisfied. Given that the CSP is an NP-complete problem, finding a feasible solution requires an exponential time cost in practice. To overcome this difficulty in practice, we have proposed a discrete version of our bio-inspired Mother Tree Optimization (MTO) method that we called Discrete MTO-CSP (DMTO-CSP). The Conditional CSP (CCSP) extends the CSP with variables added or removed, dynamically, following some activity constraints. CCSPs can be very relevant in many dynamic applications, such as configuration and planning, where the possible changes are known a priori and can be enumerated. In these applications, we often have to manage a set of constraints together with some users' preferences. This has motivated us to extend the CCSP model to qualitative preferences represented with the CP-net graphical model. We then propose an adapted variant of DMTO-CSP, that we call DMTO-CCSP, to solve CCSPs and CCSPs with preferences. In order to assess the performance of DMTO-CCSP, we conducted several comparative experiments on random CCSP instances generated using a variant of the known RB model. The results demonstrate the efficiency of DMTO-CSP compared to the known backtrack search technique.