Incorporating Constraint Checking Costs in Constraint Satisfaction Problem Suryakant Sansare

Presentation What is Constraint Satisfaction Problem What is a cost model ? Domains explored Heuristics used Analysis of results Future Work Conclusion

What is Constraint Satisfaction Problem (CSP) Consists of a set of variables and constraints or restrictions on the legal values of these variables. Eg. Map Coloring problem A solution to CSP is a set of values for the variables such that all or most of the constraints are satisfied.

What is Cost Model ? Costs for a Constraint Network can be communication costs, temporal costs Why do we need to consider costs? They are inherently present in the domain. They affect the overall efficiency of the search process. Two cost models : Constraint set cost Constraint value cost

Domains N-queens Sports Scheduler Easy to visualize. Well understood. Regular constraint structure. Sports Scheduler More realistic model. Less regular constraint network. Association of cost better corresponds to the cost distribution in real world.

Heuristics N-queens Sports Scheduler Most constrained first variable ordering. Deferred constraints. (costly constraints last) Lowest cost first. Highest cost first. Sports Scheduler Lowest Cost First value ordering heuristic. Random Value ordering heuristic. Most constrained team first heuristic.

Experiments N-queens Sports Scheduler Costs were unit costs. Varied the number of costly constraints. Took results for 10 runs for each heuristic. Sports Scheduler Two types of cost distribution Uniform Exponential Varied team size and number of games each team played

Results

Results

Future Work Run more experiments. Find more heuristics for the sports scheduler domain. Run experiments for cases where all the stadiums are not available all the time. Try different cost models.

Conclusion Costs are inherent in certain real world domains. Consideration of these costs during problem solving is necessary and effective.