Backtracking Techniques for Hard Scheduling Problems

This paper studies a version of the job shop scheduling problem in which some operations have to be scheduled within non-relaxable time windows (i.e. earliesv'latest possible stan time windows). This problem is a well-known NP-complete Constraint Satisfaction Roblem (CSP). A popular method for solving this type of problems consists in using depth-first backtrack scarch. Our earlier work focused on developing efficient Consistency enforcing techniques and efficient vmiabl&alut ordering heuristics to improve the efficiency of this search prcrcedure. In this paper. we combine these techniques with new lwk-back schemes that help the search procedure recover from so-called deadend search states (i.e. partial solutions that cannot be completed without violating somc constraints). More specifically, we successively describe three "intelligent" backtracking schems: (1) Dynundc Consistency Enforcemnr dynamically identifies critical subproblems and determines how far to backtrack by selectively enforcing higher levels of consistency among vmiables participating in these critical subproblems, (2) L a m i n g From Fuilwe dynamically modifies the order in which variables are instantiated based on earlier conflicts, and (3) Heuristic Buc&umping gives up searching areas of the search space that are deemed too difficult. n e s e schemes me shown to (1) further reduce the average complexity of the search procedure, (2) enable our system to efficiently solve problems that could not bc solved otherwise due to excessive computational cost, and (3) be more effective at solving job shop scheduling problems than 0thlook-back schemes advocated in the literature.