# Three Metaheuristic Approaches for Tumor Phylogeny Inference: An Experimental Comparison
## 5 Discussion  
In this paper, we have presented and experimentally assessed three different meta-heuristics (PSO, GP, and VNP) to infer tumor phylogenies under the Dollo model. We have compared these methods to the state-of-the-art Simulated Annealing approach (SASC).  
Among the three metaheuristics, PSO showed the most promising results, although it was not able to outperform SASC. PSO demonstrated accuracy comparable to SASC in most experiments and measures, but its performance dropped as the complexity of the problem increased.  
The main challenges faced by these methods stem from the fact that trees are not inherently a numeric space, which poses difficulties in defining distance, velocity, and direction on trees. Consequently, the design of appropriate definitions for these parameters is a crucial area for future research. These definitions should be computationally efficient and capable of capturing the properties that the PSO approach can exploit. Successful developments in this research direction have the potential to significantly enhance the accuracy of PSO. Moreover, we expect the parallelism capabilities of PSO to allow us to exploit many-cores infrastructures to allow an even larger exploration of the search space, leading to higher-accuracy tumor phylogenies.  
Conceptualization, S.C., G.D.V., V.F. and M.S.G.; methodology, S.C., G.D.V., V.F. and M.S.G.; software, V.F. and S.C.; validation, S.C.; formal analysis, S.C., G.D.V. and V.F.; investigation, S.C., G.D.V. and V.F.; resources, S.C. and G.D.V.; data curation, S.C. and G.D.V.; writing--original draft preparation, S.C., G.D.V. and V.F.; writing--review and editing, S.C., G.D.V., V.F. and M.S.G.; visualization, S.C.; supervision, G.D.V. and V.F.; project administration, G.D.V. and V.F.; funding acquisition, G.D.V. and V.F. All authors have read and agreed to the published version of the manuscript.  
Figure 8: Tree inferred by PSO for the oligodendroglioma MGH36 from [68]. The tree was computed employing a Dollo-3 phylogeny model. In this picture, a red node indicates a loss of mutation.  
Funding: This project has received funding from the European Union's Horizon 2020 research and innovation programme under the Marie Sklodowska-Curie grant agreement No 872539. Also, this research was partially supported by the Serbian Ministry of Education and Science under projects 174010.  
The implementation of the PSO is open source and available at [[https://github.com/IAL32/pso-cancer-evolution](https://github.com/IAL32/pso-cancer-evolution)]([https://github.com/IAL32/pso-cancer-evolution](https://github.com/IAL32/pso-cancer-evolution)). The implementation of the GP and VNS is open source and available at [[https://github.com/vladofilipovic/documents-science-public](https://github.com/vladofilipovic/documents-science-public)]([https://github.com/vladofilipovic/documents-science-public](https://github.com/vladofilipovic/documents-science-public)) within directory /journals/mdpi-algorithms-2023/prog. All the data used in the experimentation is available and reproducible at [[https://github.com/AlgoLab/meta_cancer](https://github.com/AlgoLab/meta_cancer)]([https://github.com/AlgoLab/meta_cancer](https://github.com/AlgoLab/meta_cancer)), all accessed on 11 June 2023.  
We thank [PERSON], [PERSON] and [PERSON] for many enlightening discussions on this topic.  
The authors declare no conflict of interest. The funders had no role in the design of the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript; or in the decision to publish the results.  
The following abbreviations are used in this manuscript:  
\begin{tabular}{l l} PSO & Particle Swarm Optimization. \\ GP & Genetic Programming. \\ GA & Genetic Algorithms. \\ FGTS & Fine-Grained Tournament Selection. \\ SA & Simulating Annealing. \\ VNP & Variable Neighbourhood Programming. \\ VNS & Variable Neighbourhood Search. \\ \end{tabular}