# A Hybrid Optimization Framework with Dynamic Transition Scheme for Large-Scale Portfolio Management
## 3 Methodology
### Dynamic Information Transition
Essentially, the DCST scheme is a very adaptive state transition mechanism for guiding the search in which each state transition is determined according to the current contributions of the underlying search algorithms. In other words, the current system state of the DCST is decided by the accumulative performance of each individual search algorithm in the past iterations. To carefully evaluate the performance of the proposed framework, the HYPO approach is compared to other reputed meta-heuristic algorithms on a set of well-known large-scale benchmark functions and a set of portfolio management problems of different dimensions from the real-world financial markets. The results clearly reveal that the HYPO framework significantly outperforms other algorithms on most of the test cases, especially in tackling the large-scale optimization problems with complex features in which the decision variables are not independent. Furthermore, ablation studies are conducted to investigate the possible impacts of directions and information of exchange between the underlying search algorithms. The comparative results undoubtedly demonstrate the effectiveness of the proposed \"contribution-based\" state transition scheme and the significance of the specific types of transferred information. More importantly, there are some possible directions that are worth investigating in future studies. First, except for the adjustment of the direction to transfer the relevant information, how to flexibly select different type(s) of information during the exchange process should be carefully examined in order to adapt to the underlying search environments. Second, more meta-heuristic algorithms can be introduced to construct a pool of search strategies in which the adaptive framework may have a wider spectrum of meta-heuristic approaches to select during the search. Last but not least, it is worthwhile to apply the hybrid meta-heuristic framework to tackle large-scale optimization problems in other real-life applications such as flight scheduling, neural network hyperparameter tuning, and circuit design, etc. Conceptualization, Z.L. and V.T. ; methodology, Z.L. and V.T. ; software, Z.L. ; validation, Z.L. ; formal analysis, Z.L. and V.T. ; writing--original draft preparation, Z.L. ; writing--review and editing, V.T. ; supervision, V.T. All authors have read and agreed to the published version of the manuscript. This research received no external funding. Not applicable. The CEC2019 dataset can be found at [[http://www.tflgo.org/special_sessions/cc2019](http://www.tflgo.org/special_sessions/cc2019)]([http://www.tflgo.org/special_sessions/cc2019](http://www.tflgo.org/special_sessions/cc2019)), (accessed on 10 September 2022). The portfolio optimization dataset is collected from the Yahoo Finance ([[https://finance.yahoo.com](https://finance.yahoo.com)]([https://finance.yahoo.com](https://finance.yahoo.com))), (accessed on 10 September 2022), and the processed data can be downloaded from [[https://github.com/SteamerLee/HYPO](https://github.com/SteamerLee/HYPO)]([https://github.com/SteamerLee/HYPO](https://github.com/SteamerLee/HYPO)), (accessed on 10 September 2022). ## Conflicts of Interest

The authors declare no conflict of interest. ## References

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