Partial reinforcement optimizer: an evolutionary optimization algorithm [formula presented]

Ahmad Taheri, Keyvan RahimiZadeh*, Amin Beheshti, Jan Baumbach, Ravipudi Venkata Rao, Seyedali Mirjalili, Amir H. Gandomi

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

13 Citations (Scopus)


In this paper, a novel evolutionary optimization algorithm, named Partial Reinforcement Optimizer (PRO), is introduced. The major idea behind the PRO comes from a psychological theory in evolutionary learning and training called the partial reinforcement effect (PRE) theory. According to the PRE theory, a learner is intermittently reinforced to learn or strengthen a specific behavior during the learning and training process. The reinforcement patterns significantly impact the response rate and strength of the learner during a reinforcement schedule, achieved by appropriately selecting a reinforcement behavior and the time of applying reinforcement process. In the PRO algorithm, the PRE theory is mathematically modeled to an evolutionary optimization algorithm for solving global optimization problems. The efficiency of the proposed PRO algorithm is compared to well-known Meta-heuristic Algorithms (MAs) using Wilcoxon and Friedman statistical tests to analyze results from 75 benchmarks of the CEC2005, CEC2014, and CEC-BC-2017 test suits, which include unimodal, multimodal, hybrid, and composition functions. Additionally, the proposed PRO algorithm is applied to optimize a Federated Deep Learning Electrocardiography (ECG) classifier, as a real case study, to investigate the robustness and applicability of the proposed PRO. The experimental results demonstrate that the PRO algorithm outperforms existing meta-heuristic optimization algorithms by providing a more accurate and robust solution.

Original languageEnglish
Article number122070
Pages (from-to)1-20
Number of pages20
JournalExpert Systems with Applications
Issue numberPart F
Publication statusPublished - 15 Mar 2024


  • Evolutionary computation
  • Partial reinforcement theory
  • Meta-heuristic optimization
  • Federated deep learning
  • ECG


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