Enhancing Hyper-To-Real Space Projections Through Euclidean Norm Meta-Heuristic Optimization

Official paper implementation for Last Iteration Optimization (LIO) hypercomplex optimization fine-tuning. The manuscript can be found here.

Folders structure

• notebooks/: Contains a single notebook briefly illustrating the idea proposed in the paper.
• lio/: Contains the code related to the proposed approach (in optimization.py), as well as the script to reproduce the provided results (run_all.sh) and compile them in a single csv file (compile_results.py). For further instructions, please read below.

Requirements

• This code requires Python >= 3.6;
• Please run pip install -r requirements.txt to fulfill the requirements.

Adopting LIO to your pipeline

The overall idea of function optimization and p-value optimization are detailed in the script optimization.py. Meanwhile, the function run_experiment(...) in the script run_experiment.py shows how to integrate global and LIO optimizations in a single, straightforward, function for optimization. Remaining functions in this script concern efficient parallel experiments execution.

Reproducing the paper results

There are two options to reproduce the reported results. The first consists in optimizing a single benchmarking function for a single amount of variables. To such an extent use the script run_experiment.py by supplying the provided arguments that are shown by running run_experiment.py --help. To compute the optimization statistics for 15 runs of the Brown function using 25 dimensions, for instance, use the following command:

python run_experiment brown -n_agents 10 -n_vars 25 -n_iters 1000 -n_runs 15

To run all experiments as reported in the paper, just execute the shell script run_all.sh, which will perform all experiments and store the results in lio/results/. This process may take a while, but it is possible to observe its progress via command line. Further, use python compile_results.py ./results/ compiled_csv_file.csv to compile all results in a single file.

Optimizing new functions

Brand new functions can be optimized by using the proposed approach by editting the file lio/benchmark.py. Just add a new function following the signature def target_fn(numpy.ndarrray) -> float by following the already implemented functions. Further, register it in the get_function(...) function at the bottom of this file, along with its lower and upper bounds. Currently all decision variables share the same limit values.

After following these steps, the function can be optimized via command line through the script run_experiment.py (please refer to the "Reproducing paper results" section for more infomration about it).

Citation

If you use LIO (either this implementation or its overrall idea), please cite us as follows:

@InProceedings{10.1007/978-3-030-93420-0_11,
  author="Ribeiro, Luiz Carlos Felix
  and Roder, Mateus
  and de Rosa, Gustavo H.
  and Passos, Leandro A.
  and Papa, Jo{\~a}o P.",
  editor="Tavares, Jo{\~a}o Manuel R. S.
  and Papa, Jo{\~a}o Paulo
  and Gonz{\'a}lez Hidalgo, Manuel",
  title="Enhancing Hyper-to-Real Space Projections Through Euclidean Norm Meta-heuristic Optimization",
  booktitle="Progress in Pattern Recognition, Image Analysis, Computer Vision, and Applications",
  year="2021",
  publisher="Springer International Publishing",
  address="Cham",
  pages="109--118",
  isbn="978-3-030-93420-0"
}