Abstract
The solutions to many optimization paradigms arising from different application domains can be modeled as a tree graph, in such a way that nodes represent the variables to be optimized and edges evince topological relationships between such variables. In these problems the goal is to infer an optimal tree graph interconnecting all nodes under a measure of topological fitness, for which a wide portfolio of exact and approximative solvers have hitherto been reported in the related literature. In this context a research line of interest in the last few years has been focused on the derivation of solution encoding strategies suited to deal with the topological constraints imposed by tree graph configurations, particularly when the encoded solution undergoes typical operators from Evolutionary Computation. Almost all contributions within this research area focus on the use of standard crossover and mutation operators from Genetic Algorithms onto the graph topology beneath encoded individuals. However, the pace at which new evolutionary operators have emerged from the community has grown much sharply during the last decade. This manuscript elaborates on the topological heritability of the so-called Dandelion tree encoding approach under non-conventional operators. This experimental application-agnostic-based study gravitates on the topological transmission of Dandelion-encoded solutions under a certain class of multi-parent crossover operators that lie at the core of the family of \((\mu +1)\) evolution strategies and in particular, the so-called Harmony Search algorithm. Metrics to define topological heritability and respect will be defined and evaluated over a number of convergence scenarios for the population of the algorithm, from which insightful conclusions will be drawn in terms of the preserved structural properties of the newly produced solutions with respect to the initial Dandelion-encoded population.
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Notes
In formulations where subindices i and j are involved it is implicitly assumed that \(i>j\), i.e. undirected trees.
A similar behavior was observed for \(\mathbf {Q} \in \{\mathbf {Q}_{\mathrm{one}-X},\mathbf {Q}_{\mathrm{two}-X}\}\), whose plots have been omitted for brevity.
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Acknowledgements
This work has been funded in part by the Basque Government under the ELKARTEK program (BID3A Project, Grant Ref. 123456).
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Perfecto, C., Bilbao, M.N., Del Ser, J. et al. A simulation-based quantitative analysis on the topological heritability of Dandelion-encoded meta-heuristics for tree optimization problems. Soft Comput 21, 4939–4952 (2017). https://doi.org/10.1007/s00500-016-2436-z
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DOI: https://doi.org/10.1007/s00500-016-2436-z