Constraint Propagation in Flexible Manufacturing by Toan Phan Huy

By Toan Phan Huy

This booklet presents an intensive research of scheduling difficulties that come up in a versatile production setting with scarce source offer. Generalizations of the well-known activity store scheduling challenge are mentioned. As a uncomplicated and customary process for fixing those difficulties constraint propagation is utilized in a variety of resolution tools. The effectiveness of constraint propagation is established through the answer of a excessive variety of benchmark challenge situations.

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3 Exhaustive Search The sole application of constraint propagation is usually not sufficient for solving the CSP or the COP. Although for certain problem instances the search space reduction may be of considerable size, a systematic and exhaustive search is usually still necessary for finding a solution or an optimal solution. One simple strategy is the generate-and-test algorithm that we have encountered further above. However, as we have pointed out, this method is of a rather small practical value, since even after a possible search space reduction, an explicit enumeration of all potential solutions is hopeless in terms of computational complexity.

They should have similar characteristics. In particular, good solutions should be "close" to other good solutions. Further, moving from a current solution to the next one, there should be a good chance of improving the originator solution. Hence, the properties of correlation and improvement justify the application of a local search instead of a random search. 4. LOCAL SEARCH 29 Diversity and Connectivity The neighbourhood structure should consider diversified moves which cover a wide area of the solution space.

Since no confusion should be possible, we will skip the term disjunctive and only talk of cliques of 9. Whenever useful we will also say that 0' is a clique of 0 instead of 9. Let us now define clique decompositions of a disjunctive graph. Informally, a clique decomposition is a set of cliques, so that each disjunction is covered. 4 (Clique Decompositions) Let 9 (0, C, D, W) be a disjunctive graph and 0 cliques of 9. = = {Ol"" 1. 0 is a clique decomposition of 9 iff D = Ud'=l,. ,d{ i Od', if. n· ,Od} a set of t+ j I i, j E 2.

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