Dynamic constraint ordering heuristics for dynamic CSPs

Abstract

Many research studies have shown that the choice of a relevant order of variables and/or values can significantly improve the efficiency of search algorithms. However, in Constraint Satisfaction Problems CSPs, constraint ordering heuristics have received less attention than variables and values ordering heuristics. In the literature, only some few contributions have been done on this area, and mainly as a preprocessing phase before starting the search process. In this paper, we show that constraint ordering heuristics are promising and able to make relevant choices during the search process within a Dynamic CSP. Our proposed approach, called Dynamic Constraint Ordering heuristic DCO, selects dynamically constraints which are likely to lead to conflicts. So, we apply a "fail first" principle, in a manner that a dynamic intelligent backtracking event can be performed earlier. This method is able to guide a dynamic repair algorithm towards the hardest constraint subproblems and to tackle inconsistencies in order to correct solution assignment. The conducted experiments have confirmed that the proposed approach is interesting. Our results show clearly the efficiency of the heuristics combined with Partial-Order Dynamic Backtracking

Lazy Repairing Backtracking for Dynamic Constraint Satisfaction Problems

“…The dynamic scheduling offers the possibility to rebuild a new order among variables during the search. The Partial-order Dynamic Backtracking (PDB) [11] is one of the approaches using this technique. However, it suffers from a lack of flexibility in backtracking strategy although using a partial order which supports dynamism.…”

“…The partial order between variables is imposed by saved nogoods and safety conditions, a data structure of orders presented by the deleted nogoods. [11] is defined as an assertion of the form: x < y, with x and y variables.…”

“…The second improvement of EPDB is to satisfy the current constraint C i before selecting another one to verify. In fact, when a checked constraint C i is violated, PDB [11] changes the value of a C i concerned variable and another constraint is checked. The satisfaction of C i is not insured, but it will be re-checked later.…”

“…The nogoods are used by intelligent back-trackers to record information regarding dead-ends in order to avoid encountering them again. They are used in Partial-order Dynamic Backtracking (PDB) [11], which considers a complete set of assignments that are incrementally modified until all constraints are satisfied, or no solution is found. The advantage of PDB is that it allows great flexibility in the backtracking strategy which affects the flexibility of the search space exploration.…”