Unimodular Probing for Minimal Perturbance in Dynamic Resource Feasibility Problems

This paper describes unimodular probing { a new technique that has been used to solve a class of dynamic scheduling problems. In benchmarks a unimodular probing algorithm has outperformed two well-established approaches: backtrack search with local consistency and spe-cialised heuristics, and mixed integer programming (MIP). The problems amenable to unimodular probing involve disjunctive constraints , discrete variables, and a linear optimisation function. In addition , some of the constraints should be totally unimodular { for example, temporal precedence and distance constraints. Problems in this class are diicult for CSP techniques because of the optimisation requirement, and for MIP because of the number of discrete (integer) variables. Our studies have focussed on DCSPs, with an optimisation criterion of minimal perturbance to an existing solution. Unimodular probing builds on an ordinary backtracking repair algorithm with constraint propagation. However, by contrast with previous DCSP algorithms, unimodular probing uses linear programming (LP) optimisation to guide and bound the search. Not only has unimodular probing performed well on randomly generated benchmarks, but it has also been successfully applied in a large industrial application involving hundreds of resources and thousands of tasks.