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Puma optimizer (PO): a novel metaheuristic optimization algorithm and its application in machine learning

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Abstract

Optimization techniques, particularly meta-heuristic algorithms, are highly effective in optimizing and enhancing efficiency across diverse models and systems, renowned for their ability to attain optimal or near-optimal solutions within a reasonable timeframe. In this work, the Puma Optimizer (PO) is proposed as a new optimization algorithm inspired from the intelligence and life of Pumas in. In this algorithm, unique and powerful mechanisms have been proposed in each phase of exploration and exploitation, which has increased the algorithm’s performance against all kinds of optimization problems. In addition, a new type of intelligent mechanism, which is a type of hyper-heuristic for phase change, is presented. Using this mechanism, the PO algorithm can perform a phase change operation during the optimization operation and balance both phases. Each phase is automatically adjusted to the nature of the problem. To evaluate the proposed algorithm, 23 standard functions and CEC2019 functions were used and compared with different types of optimization algorithms. Moreover, using the statistical test T-test and the execution time to solve the problem have been discussed. Finally, it has been tested using four machine learning and data mining problems, and the results obtained from all the analysis signifies the excellent performance of this algorithm against all kinds of problems compared to other optimizers. This algorithm has performed better than the compared algorithms in 27 benchmarks out of 33 benchmarks and has obtained better results in solving the clustering problem in 7 data sets out of 10 data sets. Furthermore, the results obtained in the problems of community detection and feature selection and MLP were superior. The source codes of the PO algorithm are publicly available at https://www.mathworks.com/matlabcentral/fileexchange/157231-puma-optimizer-po.

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Abbreviations

PO:

Puma optimizer

rand :

A random number between [0,1]

UM:

Unimodal

randn :

Random numbers in the normal interval

MM:

Multimodal

mean :

Mean function

CM:

Composition

Iter :

Current number of iterations

SM:

Scalable Multimodal function

FM:

Fixed-dimension multimodal function

Puma male :

Best search agent

MaxIter :

Max number of iterations

Npop :

Total number of search agent

cos :

Function of cosine

X i :

Current search agent

Ub :

The Upper bound of search spaces

Cost :

The cost of the solution

Lb :

The lower bound of search spaces

exp :

Exponential function

EB:

Evolutionary based

SB:

Swarm-based

HP:

Human-based

iterations:

Max number of iterations

PB:

Physic-based

Best:

The best result

population:

Number of pumas

Worst:

The worst result

Mean:

Average results

MLP:

Multi-layer perceptron

STD:

Standard deviation

FS:

Feature selection

CD:

Community detection

FCCD:

The face-centered central composite design

DC:

Data clustering

SCA:

Sine cosine algorithm

FHO:

Fire hawk optimizer

SAO:

Smell agent optimization

TSA:

Tunicate swarm algorithm

GWO:

Gray wolf algorithm

MFO:

Moth-flame optimization algorithm

WOA:

Whale optimization algorithm

DMOA:

Dwarf mongoose optimization algorithm

PSO:

Particle swarm optimization

BAT:

Bat algorithm

GA:

Genetic algorithm

ABC:

Artificial bee colony

FFA:

Farmland fertility algorithm

BBO:

Biogeography-Based optimizer

SMA:

Slime mould algorithm

CSO:

Cuckoo search optimization

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Science, University of Hradec Králové, 500 03, Hradec Králové, Czech Republic

    Benyamin Abdollahzadeh & Pavel Trojovský

  2. Department of Civil and Architectural Engineering, University of Miami, Coral Gables, FL, USA

    Nima Khodadadi

  3. Department of Computer Science, School of Engineering, Afagh Higher Education Institute, Urmia, Iran

    Saeid Barshandeh

  4. Department of Computer Engineering, Urmia Branch, Islamic Azad University, Urmia, Iran

    Farhad Soleimanian Gharehchopogh

  5. Department of Communications and Electronics, Delta Higher Institute of Engineering and Technology, Mansoura, 35111, Egypt

    El-Sayed M. El-kenawy

  6. Hourani Center for Applied Scientific Research, Al-Ahliyya Amman University, Amman, 19328, Jordan

    Laith Abualigah

  7. Computer Sciences Department, University of Tabuk, Tabuk 47913, Saudi Arabia

    Laith Abualigah

  8. Computer Science Department, Al al-Bayt University, Mafraq, 25113, Jordan

    Laith Abualigah

  9. Centre for Artificial Intelligence Research and Optimization, Torrens University Australia, Adelaide, Australia

    Seyedali Mirjalili

  10. Research and Innovation Center, Obuda University, Budapest, 1034, Hungary

    Seyedali Mirjalili

Authors
  1. Benyamin Abdollahzadeh
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  2. Nima Khodadadi
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  3. Saeid Barshandeh
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  4. Pavel Trojovský
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  6. El-Sayed M. El-kenawy
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  8. Seyedali Mirjalili
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Contributions

Methodology, BA, NK; Software, BA, NK; Investigation, SB and SK and LA; Writing–original draft, BA and NA; Writing–review & editing, SK, PT and FS; Supervision, SM; Project administration, SM All authors have read and agreed to the published version of the manuscript.

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Correspondence to Nima Khodadadi.

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Appendix 1

Appendix 1

See Tables 25, 26, 27, 28.

Table 25 Details of unimodal benchmark functions
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Table 26 Details of multimodal benchmark functions
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Table 27 Details of fixed-dimension multimodal benchmark functions
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Table 28 The 100-digit challenge basic test functions
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Abdollahzadeh, B., Khodadadi, N., Barshandeh, S. et al. Puma optimizer (PO): a novel metaheuristic optimization algorithm and its application in machine learning. Cluster Comput (2024). https://doi.org/10.1007/s10586-023-04221-5

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