Preference CSPs

This is an extension of CSPs that we developed in our work on crossword puzzles.

Basic idea is that we've got variables, values, and constraints, just like a CSP. However, each variable-value pair has a score, and we are trying to find the solution with maximum total score.

Examples:

• Crosswords: Hard constraints are defined by the puzzle. Score is related to degree of match between candidate word (variable value) and clue. It also factors in how well that value fits makes opportunities for other words to fit into the grid.
• Scheduling: Hard constraints are things like no professor can teach two classes at once and only one room has a class at a time. Preferences concern where a professor would like to go to each the class and which professors should teach which classes.
• Planning: Hard constraints are the goal. Preferences could be things like action costs. Thus, we could express finding the cheapest plan that reaches the goal.