From Grammars to Parameters: Automatic Iterated Greedy Design for the Permutation Flow-Shop Problem with Weighted Tardiness

Recent advances in automatic algorithm configuration have made it possible to configure very flexible algorithmic frameworks in order to fine-tune them for particular problems. This is often done by the use of automatic methods to set the values of algorithm parameters. A rather different approach uses grammatical evolution, where the possible algorithms are implicitly defined by a context-free grammar. Possible algorithms may then be instantiated by repeated applications of the rules in the grammar. Through grammatical evolution, such an approach has shown to be able to generate heuristic algorithms. In this paper we show that the process of instantiating such a grammar can be described in terms of parameters. The number of parameters increases with the maximum number of applications of the grammar rules. Therefore, this approach is only practical if the number of rules and depth of the derivation tree are bounded and relatively small. This is often the case in the heuristic-generating grammars proposed in the literature, and, in such cases, we show that the parametric representation may lead to superior performance with respect to the representation used in grammatical evolution. In particular, we first propose a grammar that generates iterated greedy (IG) algorithms for the permutation flow-shop problem with weighted tardiness minimization. Next, we show how this grammar can be represented in terms of parameters. Finally, we compare the quality of the IG algorithms generated by an automatic configuration tool using the parametric representation versus using the codon-based representation of grammatical evolution. In our scenario, the parametric approach leads to significantly better IG algorithms.