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17.6  Other Hybridisation Forms

This module has covered a few forms of hybridisation between ic and eplex. There are a variety of problem decomposition techniques that support other forms of hybridisation. Three forms which employ linear duality are Column Generation, Benders Decomposition and Lagrangian Relaxation. All three forms have been implemented in ECLiPSe and used to solve large problems, and the ECLiPSe library colgen, described in the next chapter, supports Column Generation.

Often it is useful to extract several linear subproblems and apply a separate linear solver to each one. The eplex library offers facilities to support multiple linear solvers. Space does not permit further discussion of this feature.

Cooperating solvers have been used to implement some global constraints, such as piecewise linear constraints [21]. Linearisation of ic global constraints is another method of achieving tight cooperation.

Finally many forms of hybridisation involve different search techniques, as well as different solvers. For example stochastic search can be used for probing instead of a linear solver, as described in [28].

In conclusion, ECLiPSe provides a wonderful environment for exploring different forms of hybridisation.

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