Minimal Perturbance in Dynamic Scheduling.
ABSTRACT This paper describes an algorithm, unimodular probing, conceived to optimally reconfigure schedules in response to a changing environ- ment. In the problems studied, resources may become unavailable, and scheduled activities may change. The total shift in the start and end times of activities should be kept to a minimum. This require- ment is captured in terms of a linear optimization function over lin- ear constraints. However, the disjunctive nature of many scheduling problems impedes traditional mathematical programming approaches. The unimodular probing algorithm interleaves constraint program- ming and linear programming. The linear programming solver is ap- plied to a dynamically controlled subset of the problem constraints, to guarantee that the values returned are discrete. Using a r epair strat- egy, these values are naturally integrated into the constra int program- ming search. We explore why the algorithm is effective and discuss its applicability to a wider class of problems. It appears th at other problems comprising disjunctive constraints and a linear o ptimiza- tion function may be suited to the algorithm. Unimodular probing outperforms alternative algorithms on randomly generated bench- marks, and on a major airline application.
Article: Probe Order Backtracking[show abstract] [hide abstract]
ABSTRACT: . The algorithm for constraint-satisfaction problems, Probe Order Backtracking, has an average running time much faster than any previously analyzed algorithm under conditions where solutions are common. The algorithm uses a probing assignment (a preselected test assignment to unset variables) to help guide the search for a solution. If the problem is not satisfied when the unset variables are temporarily set to the probing assignment, the algorithm selects one of the relations which is not satisfied by the probing assignment and selects an unset variable which a#ects the value of that relation. It then does a backtracking (splitting) step, where it generates subproblems by setting the selected variable each possible way. Each subproblem is simplified and then solved recursively. For random problems with v variables, t clauses, and probability p that a literal appears in a clause, the average time for Probe Order Backtracking is no more than v n when p # (ln t)/v plus lower-order t...02/1970;
Conference Proceeding: Belief Maintenance in Dynamic Constraint Networks.Proceedings of the 7th National Conference on Artificial Intelligence. St. Paul, MN, August 21-26, 1988.; 01/1988
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ABSTRACT: . Constraint propagation algorithms vary in the strength of propagation they apply. This paper investigates a simple configuration for adaptive propagation -- the process of varying the strength of propagation to reflect the dynamics of search. We focus on two propagation methods, Arc Consistency (AC) and Forward Checking (FC). AC-based algorithms apply a stronger form of propagation than FC-based algorithms; they invest greater computational effort to detect inconsistent values earlier. The relative payoff of maintaining AC during search as against FC may vary for different constraints and for different intermediate search states. We present a scheme for Adaptive Arc Propagation (AAP) that allows the flexible combination of the two methods. Meta-level reasoning and heuristics are used to dynamically distribute propagation effort between the two. One instance of AAP, Anti-Functional Reduction (AFR), is described in detail here. AFR achieves precisely the same propagation as a pure AC ...06/1998;