Systematic Review Evaluates Crested Porcupine Optimizer Progress, Benchmarks, and Technical Limitations

A systematic review adhering to the PRISMA 2020 guidelines has evaluated the development, performance benchmarks, and expanding applications of the Crested Porcupine Optimizer across 174 peer-reviewed studies published between January 2024 and November 2025. Introduced in 2024 by Abdel-Basset and colleagues, the bio-inspired algorithm translates the defensive behaviors of crested porcupines into a dynamic optimization architecture designed for nonlinear and high-dimensional problem domains. Across the surveyed literature identified from the Scopus database, 131 investigations focused on applying the baseline optimization algorithm to practical engineering and computational tasks, while 43 studies formulated algorithmic improvements. This extensive assessment details how the framework functions mathematically, measures its comparative search capabilities against classical metaheuristics, and identifies critical methodological deficits that continue to challenge the field.

The biological architecture of the optimizer mirrors four sequential defensive reactions exhibited by crested porcupines as predatory threats draw nearer. When a predator remains at a substantial distance, represented as Area A, the algorithm activates a visual attack mechanism that initiates wide-ranging global exploration by adjusting candidate positions according to normal distributions and relative spacing. Should the simulated predator ignore this initial display and approach into Area B, the algorithm deploys a sound attack routine where position vectors are updated based on differences between randomly selected group members to regulate spatial dispersion. If the threat advances further into Area C, an odor attack phase introduces directional parameters, defense factors, and diffusion coefficients to transition from broad spatial exploration toward localized exploitation. Finally, when preceding defense strategies fail and the threat enters Area D, a physical attack model executes an inelastic collision formulation driven by a convergence factor and average predator forces to perform intensive local search around optimal regions.

To navigate the persistent trade-off between convergence velocity and population diversity, the computational framework incorporates cyclic population reduction. Rather than maintaining a static number of candidate solutions throughout execution, the model implements a periodic schedule governed by minimum population thresholds, cycle frequencies, and evaluation budgets. The population size contracts gradually as function evaluations progress, simulating how only threatened individuals actively engage defense mechanisms, before periodically resetting to full capacity across designated cycles. This structural dynamism operates alongside an overall worst-case computational time complexity defined as O(Tmax · d), where Tmax represents the maximum permitted function evaluations and d denotes the problem dimensionality. Because termination is anchored to evaluation counts rather than generational iterations across static swarms, population size variations do not inflate the underlying asymptotic complexity bound.

Standardized empirical evaluations conducted under a uniform testing protocol in MATLAB R2021a demonstrate the algorithm’s baseline capabilities across IEEE CEC2017 benchmark suites. Operating with a population budget of 120 individuals over 1,000 iterations across 30 independent runs, the optimizer was benchmarked at dimension 30 against established optimizers including Particle Swarm Optimization, Grey Wolf Optimization, Whale Optimization Algorithm, Genetic Algorithms, and GOOSE. On unimodal benchmark function F1, the optimizer achieved a mean fitness value of 2.27 × 10³ and ranked first in overall fitness, accompanied by a median computation runtime of 0.075 seconds. Multimodal benchmark F6 yielded a mean fitness of 6.00 × 10² with a 0.257-second computation time, whereas hybrid benchmark F12 recorded a mean fitness of 1.75 × 10⁵ in 0.120 seconds. In composition test function F30, the optimizer registered a mean fitness of 1.83 × 10⁴ with an execution duration of 0.796 seconds, demonstrating stability across complex search landscapes despite incurring slight runtime overheads from dynamic parameter calculations.

Across the 43 reviewed variant studies, researchers proposed 117 discrete algorithmic improvement strategies to address inherent operational constraints. Perturbation mechanisms formed the largest category, accounting for 45 strategies across 31 variants, primarily integrating heavy-tailed step operators such as Lévy flights, Cauchy mutations, and adaptive t-distributions to dislodge stagnated candidates from sub-optimal basins. Population initialization refinements represented the second most prevalent modification, comprising 31 strategies across 29 variants that replaced uniform random sampling with chaotic mappings like Chebyshev, Tent, and ICMIC, low-discrepancy Good Point Sets, Latin hypercube sampling, and opposition-based learning. Adaptive parameter control encompassed 27 strategies utilizing dynamic weights, variable neighborhood search structures, and reinforcement learning routines, while hybrid architectures contributed 11 strategies, multi-objective extensions provided two implementations, and discrete binary conversions accounted for one framework.

Comparative evaluations of leading variants across dimensions 10, 30, 50, and 100 revealed noticeable performance divergences across benchmark functions. The multi-strategy variant MSCPO, which incorporates chaotic Bernoulli initialization, adaptive t-distribution perturbations, and Golden Lévy variations, established superior convergence consistency across complex multimodal and composite functions. In Wilcoxon rank-sum testing at dimension 30, MSCPO secured 28 wins and attained the leading Friedman mean rank of 1.31034, while the opposition-learning and Lévy-driven VACPO variant achieved 21 wins. Conversely, the unmodified base optimizer occupied an intermediate position with a Friedman rank of 4.51724. As dimensional scaling increased to 50 and 100 dimensions, several perturbation-intensive variants, including MICPO and MCI_CPO, suffered severe performance degradations and instability, underscoring that indiscriminate perturbation can disrupt search trajectories when navigating highly expanded coordinate systems.

In practical implementation domains, machine learning represents the most concentrated research sector, encompassing 84 peer-reviewed publications. The algorithm is routinely deployed as an automated global tuner for continuous hyperparameters across gradient-boosted decision trees including XGBoost, LightGBM, and CatBoost, as well as kernel machines such as Support Vector Machines and Least Squares Support Vector Machines. In deep learning architectures, it optimizes hidden layer capacities, learning rates, convolutional filter dimensions, and temporal attention mechanisms across networks such as BPNN, CNN, BiLSTM, and Transformer variants. Published studies report notable empirical performance gains, including error reductions exceeding 63 percent in railway settlement forecasting with CPO-BPNN and classification accuracies surpassing 99 percent in industrial fault detection systems. Similarly, 32 publications in signal processing and modal analysis apply the optimizer to configure penalty parameters and decomposition thresholds in Variational Mode Decomposition and Empirical Mode Decomposition frameworks across vibration diagnostics, power grid forecasting, and biomedical monitoring.

Despite widespread empirical adoption and Google Scholar citations expanding from 2024 through November 2025, the review emphasizes severe methodological and theoretical limitations across the existing literature. A pervasive issue is high-dimensional stagnation, where performance drops significantly as problem dimensions multiply due to search direction dilution, premature population clustering around incumbent solutions, and coordinate deactivation. Crucially, the literature remains entirely empirical, lacking formal mathematical proofs of convergence, parameter stability guarantees, or Lyapunov potential analyses across its piecewise, cyclic reduction operators. Furthermore, application studies rarely enforce matched computational budgets, omitting comparisons against robust hyperparameter baselines such as Bayesian optimization or Hyperband, while frequently conflating algorithmic search benefits with the intrinsic expressive capacity of complex hybrid neural network structures.

To transition the Crested Porcupine Optimizer into a methodologically sound computational paradigm, the review outlines clear priorities for future investigation. Researchers must establish standardized testing protocols featuring rigorous ablation studies, multiple random initialization seeds, and corrections for multiple statistical comparisons. Theoretical advancements require formalizing convergence behavior via periodically time-inhomogeneous Markov chain models and Foster-Lyapunov drift conditions capable of handling time-varying population cycles. Additionally, developing robust self-adaptive parameter regulation mechanisms will reduce reliance on empirical parameter tuning, while expanding formal formulations toward multi-objective archives, constrained formulations, mixed-integer domains, and distributed computing frameworks will determine the optimizer’s long-term utility across advanced engineering and scientific applications.

Beyond machine learning and signal processing, the systematic review identified six specialized studies focusing on control engineering. Investigators applied the algorithm to tune controller gains across diverse physical setups, replacing manual trial-and-error procedures. In electric vehicle charging infrastructure, researchers configured proportional-integral controllers to minimize current ripples, while dual-loop architectures integrated quasi-proportional resonance elements. Other control implementations tuned three-degree-of-freedom fractional-order controllers for microgrid frequency stabilization and optimized non-singular fast terminal sliding mode controllers for robotic trajectory tracking. In high-speed rail pantograph systems, a hybrid framework combining an optimized linear quadratic regulator with deep reinforcement learning reduced the standard deviation of contact forces by more than 77 percent compared to baseline control designs.

Engineering applications accounted for nine evaluated investigations, spanning energy scheduling, mechanical design, and spatial robotics. In green energy systems, researchers used the algorithm to coordinate electric vehicle charging with hydrogen production and storage schedules, while automotive studies optimized power distribution in plug-in hybrids to lower greenhouse emissions to 17,400 grams. Structural optimization studies also achieved quantifiable enhancements; optimizing the geometry of polygonal fins in automotive thermoelectric generators increased net power generation by 6.75 percent and thermal conversion efficiency by 7.06 percent over competing whale optimization algorithms. Additional engineering deployments established collision-free paths for concrete pumping construction robots, guided inspection routes across photovoltaic power stations, and accurately estimated resistance coefficients across aging pipeline networks.

Publication patterns across the 174 included studies, which were screened from an initial pool of 525 Scopus records, also revealed clear structural tendencies across dissemination venues. Academic journals published substantially more CPO literature than conferences, with journals predominantly hosting application-focused papers while conference proceedings exhibited a balanced split between algorithm variants and domain implementations. The survey further observed that nearly all existing literature targets continuous search spaces. Only one included study explicitly addressed discrete structures, employing a sigmoid mathematical mapping to convert continuous variables into binary values for training Bayesian networks in bearing fault diagnosis, highlighting mixed-integer and combinatorial problem solving as another underrepresented area in current optimization research.

Subject of Research: Systematic evaluation of Crested Porcupine Optimizer variants, benchmarks, and applications

Article Title: A systematic review of the crested porcupine optimizer: variants and applications

Article References: Yu, H., As’arry, A., Ma, H., Norsahperi, N. M. H., Tang, S., Yusop, Z. M., & Supeni, E. E. B. (2026). A systematic review of the crested porcupine optimizer: variants and applications. Applied Intelligence, 56(14), Article 422. https://doi.org/10.1007/s10489-026-07453-1

Image Credits: AI Generated

DOI: 10.1007/s10489-026-07453-1

Keywords: Crested Porcupine Optimizer, metaheuristic algorithms, PRISMA 2020, swarm intelligence, CEC2017 benchmark, cyclic population reduction, hyperparameter optimization, variational mode decomposition, machine learning, Lévy flight, chaotic mapping, global optimization, convergence analysis, signal processing, algorithmic variants, engineering optimization