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By Sbihi A.

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Extra info for A best first search exact algorithm for the Multiple-choice Multidimensional Knapsack Problem

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For ease of reference, we will use the term “ES” to refer to both approaches. ES uses a population-based learning algorithm. Each generation of possible solutions is formed by mutating and recombining the best members of the previous generation. ” Strategy parameters control the learning process. Thus, ES evolves both the parameters to be optimized and the parameters that control the optimization [2]. ES has the following desirable characteristics for the uses in our methodology: • ES can optimize the parameters of arbitrary functions.

A rotation matrix of correlation coeﬃcients as elements of the strategic parameters is introduced by Schwefel [11] but is not used in this context. Each complete individual consisting of both parameter sets is adapted by the evolutionary process. Hence, an external deterministic adaptation of the step sizes is not necessary, because the strategy parameters also undergo the selection process. Recombination interchanges the genetic data of two or more parent individuals by intermediate or discrete exchange schemes.

This is a precondition for the application of an evolution strategy without explicit restrictions. Restrictions in the tness function are usually time-consuming and increase the complexity of the optimization problem. The mapping DTS → IR|E |+|S | can also be interpreted as a genotype-phenotype mapping. The genotype encoding describes all possible triangulations in a vector. The vector is manipulated by evolutionary operators. The mapping transforms the vector into the respective 3D triangulation.