Hybridization Based on Complete Solution Archives
This chapter illustrates how a metaheuristic—in particular, evolutionary algorithms— can profit by cross-fertilization with basic principles of branch-and-bound: We extend the metaheuristic by a complete solution archive that stores all considered candidate solutions organized along the principles of a branch-and-bound tree. The approach is particularly appealing for problems with expensive evaluation functions or a metaheuristic applying indirect or incomplete solution representations in combination with non-trivial decoders. Besides just avoiding re-evaluations of already considered solutions, a fundamental feature of the solution archive discussed here is its ability to efficiently transform duplicates into typically similar but guaranteed new solution candidates. Thus, the solution archive can be seen to provide a kind of “informed mutation”. From a theoretical point of view, the metaheuristic is turned into a complete enumerative method without revisits, which is in principle able to stop in limited time with a proven optimal solution. Furthermore, the approach can be extended by calculating bounds for partial solutions possibly allowing us to cut off larger parts of the search space. In this way the solution-archive-enhanced metaheuristic can also be interpreted as a branch-and-bound optimization process guided by principles of the metaheuristic search.
KeywordsSpan Tree Candidate Solution Memetic Algorithm Variable Neighborhood Search Large Neighborhood Search
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