Abstract Metaheuristic optimization algorithms frequently struggle to maintain an effective balance between exploration and exploitation, particularly on high-dimensional problems where premature convergence and reduced population diversity degrade performance. Opposition-based Learning (OBL) is a widely used remedy, yet its established variants, including the Dynamic Opposition-based Learning (DOBL) method, construct opposite solutions that can still trap the search in local optima. This study proposes the Chaotic Sech-Tanh Dynamic Opposition-based Learning (CHSTDOBL) strategy, which integrates two complementary mechanisms into the dynamic opposition framework: pseudo-random sequences generated by the Ikeda chaotic map, which inject aperiodic variability to resist premature convergence, and hyperbolic secant and tangent functions, which compress these sequences into a bounded range that enables controlled local refinement. The strategy was integrated into the Whale Optimization Algorithm and compared against five established OBL variants on 500-dimensional benchmark functions, the CEC 2013 test suite, and 12 constrained engineering design problems. CHSTDOBL outperformed or matched its competitors on 20 of 24 multimodal and 21 of 24 unimodal benchmark functions and was ranked first by the Friedman test. In the CEC 2013 suite, it attained the best mean and objective values on 12 and 13 functions, respectively. For constrained design problems, it achieved the best feasible objective value in eight of 12 cases, failing to retain the best-known optimum in only four, while producing consistently tighter solution distributions than seven competing optimizers. Its generality was confirmed by embedding it into eight recently proposed metaheuristic algorithms, establishing CHSTDOBL as a competitive, algorithm-agnostic enhancement.

Expensive optimization problems allow for only a small number of exact objective evaluations, and this is where most metaheuristics lose their value. This paper proposes SAWHALE, a surrogate-assisted and self-adaptive whale optimization framework built around two new asymmetric opposition-based learning operators. EDOFAS schedules entropy-driven oppositional probes at several scales, while OPADAMP perturbs the worst coordinates of promising solutions. Surrogate models price the candidates of a global phase and a local phase, and a logistic rule switches between the phases according to the state of the population. Four experiments examine the framework. A component study over nine whale variants at 500 and 1000 dimensions places EDOFAS first, with mean Friedman ranks of 1.650 and 1.575. On the CEC 2014 suite, the full framework attains the best mean rank against five surrogate-assisted optimizers, 2.233 at 30 dimensions and 2.267 at 50, with more Wilcoxon wins than losses against every one of them. An ablation over seven configurations keeps the complete design first at 1.333 and 2.033. On the CEC 2017 suite, the framework ranks first at 1.767 and 1.600 against six metaheuristics, including three newer whale variants, and the cost of the machinery on smooth unimodal ground is reported openly.

In this study, a framework for a hydrogen reformer is developed. The equilibrium compositions are predicted by using Gibbs free-energy minimization. In this context, six separate scenarios are developed for various reformer models in order to investigate the influence of different design parameters on hydrogen production and reformer performance. It is found that, for diesel, adiabatic steam reforming yields outlet temperatures ranging from 973 to 1273 K at pressures between 500 and 1500 kPa, with the highest hydrogen yield achieved at a steam-to-carbon ratio of 3.5. Isothermal steam reformers can achieve hydrogen production levels of 70%-80% at temperatures exceeding 1000 K. In the process of partial oxidation, temperatures exceeding 1200 K lead to a notable shift in gas composition, reducing CO from approximately 81% to 68% and increasing CH4 from around 18% to 32% as the O/C ratio and pressure increase. In contrast, autothermal reformers (ATRs) provide compositions that remain independent of pressure. As the framework is equilibrium-based, the reported compositions and parametric sensitivities represent thermodynamic upper-bound trends rather than predictive behavior.

Proton exchange membrane fuel cells (PEMFCs) are highly promising for producing clean and efficient energy. However, their complex electrochemical behavior, shaped by activation, ohmic, and concentration losses, requires accurate modeling and precise parameter estimation to ensure optimized performance. In this study, guided manta ray foraging optimization (GMANTA), an improved version of the original Manta Ray Foraging Optimization algorithm, is used to estimate key parameters in semiempirical PEMFC voltage models. Studies that simultaneously analyze multiple commercially available PEMFC stacks, such as the Horizon 500 W, BCW 500 W, and SR-12, are relatively scarce in the literature. Consequently, incorporating three experimentally obtained datasets in this study helps fill this gap and provides a more comprehensive and realistic validation framework for metaheuristic optimization algorithms. The proposed method offers a unique contribution by enabling highly accurate parameter identification across varying pressures and temperatures, using a small population size and few iterations. The approach reduces the error between simulated and measured voltage-current (V-I) data, ensuring that the models effectively capture the underlying physical phenomena. To assess the robustness and reliability of the method, GMANTA is compared with eight other well-established metaheuristic algorithms, and differences in error rates among these algorithms are analyzed statistically.

This study integrates machine learning fundamentals with metaheuristic optimizers to introduce a novel optimization approach that builds upon existing research. The proposed strategy employs the Fuzzy C-means clustering algorithm to guide local search via dedicated optimization agents, and Q-learning to select the most suitable optimization algorithm at each iteration. Three recent metaheuristic optimizers—the Manta Ray Foraging Algorithm, African Vulture Algorithm, and Harris Hawks Optimization—are enhanced using these intelligent learning techniques to improve solution accuracy and robustness. In addition, a novel optimization strategy based on integrating search equations of Dynamic Oppositional-based Learning mechanisms and the Generalized Quadratic Interpolation method is proposed and embedded into the developed optimization framework, achieving higher efficiency in improving the exploration and exploitation balance of the algorithm. Hyperdimensional standard benchmark problems of varying complexity have been solved using the proposed hybrid method. The new method is also evaluated using challenging test functions from the CEC 2013 competition, which span multidimensional, 30D, 50D, and 100D unimodal, multimodal, and composite benchmarks. Compared with state-of-the-art optimizers, the proposed algorithm outperforms them in most scenarios, underscoring its effectiveness in tackling complex problems. Moreover, the study addresses a critical yet often overlooked aspect of shell-and-tube heat exchanger design: the impact of in-tube refrigerants on overall efficiency and cost. By assessing more than 50 refrigerants with varying thermophysical properties, the research identifies optimal configurations to minimize total expenditure, finding that systems operating with NH₃ and R161 yield the lowest overall costs compared with alternative configurations.

This research investigates the control of an Organic Rankine Cycle (ORC) system, which consists of four main components: a condenser, a turbine, a pump, and an evaporator. The heat exchangers are designed as double-pipe configurations, and their dynamic behavior is modeled using the moving boundary approach. The pump and turbine, due to their significantly faster dynamics compared to the heat exchangers, are represented with static equations. The cycle’s mathematical model is linearized by computing the Jacobian of the nonlinear function with respect to state, input, and disturbance variables. Model validation is performed by generating pseudo-random input sequences and applying them to both the developed ORC model and an Aspen model with identical specifications. The validation results show strong agreement between the two models, with only minor discrepancies. Subsequently, a linear model predictive control framework is established to regulate the linearized ORC model, incorporating several inequality constraints to ensure safe and efficient operation. Four control strategies are introduced, each focusing on distinct objectives such as enhancing thermodynamic efficiency or reducing entropy generation, while all share the common goal of tracking the turbine work output trajectory. Simulation results indicate that all four controllers effectively follow the specified turbine work output trajectory. The first law and second law controllers achieve the highest average efficiencies, with first law efficiency at 0.10250 and second law efficiency at 0.31732, respectively. The turbine work controller exhibits the highest total exergy destruction rate, recorded at 2100.17 W.

This study proposes a Hierarchical Manta-Ray Foraging Optimization (HMRFO) algorithm for calculating the equilibrium points of chemical reactions. To improve the solution diversity in the trial Manta-Ray population and enhance the general optimization effectivity of the algorithm, an ordered hierarchy is integrated into the original algorithm, taking into account the efficient search strategies of Elite-Opposition learning, Dynamic Opposition Learning, and Quantum search operator. Within this proposed concept, the Manta-ray population is divided into three main sub-populations: the Elite Oppositional learning scheme manipulates top elite individuals, Dynamic Oppositional learning search equations update average population members, and quantum-based learning equations process the worst members. The improved MRFO is applied to a hundred 30D and 500D optimization benchmark functions, and results have been compared to those obtained from state-of-art metaheuristic optimizers. Then, the proposed optimizer solved twenty-eight test problems previously employed in CEC-2013 competitions, and corresponding results were benchmarked against well-reputed metaheuristics. This research study also suggests a novel mathematical model for solving chemical equilibrium problems for ideal gas mixtures. Four challenging case studies related to chemical equilibrium problems have been performed by the HMRFO for varying test conditions, and it is observed that HMRFO can effectively cope with the tedious nonlinearities and complexities of the governing thermodynamic models associated with solving chemical equilibrium problems for gaseous reacting mixture components.

This computational study proposes utilizing the advantages of machine learning algorithms to develop a flow condensation model for horizontal smooth channels. A diverse database of 6,532 data samples, encompassing 27 pure refrigerant fluids, is utilized to model the proposed condensation heat transfer coefficient. Nine machine learning algorithms founded upon intelligently devised mathematical methods have been applied to the vast database to extract the most beneficial non-dimensional parameters to model the convective condensation heat transfer coefficient. Between the trained machine learning models, Extreme Gradient Boosting and deep neural network algorithms provide the best estimations, with respective coefficient determination values of 0.9874 and 0.9822. The most influential dimensionless numbers derived from the Extreme Gradient Boosting algorithm, which produces the most accurate estimations, are used to develop a novel heat transfer coefficient model for flow condensation. With a corresponding mean absolute error value of 15.92% and mean relative error value of -2.38%, it achieves much better predictions than those obtained from the literature on convective flow condensation. The validity of the projections extracted from the proposed correlation has also been analyzed based on the excluded database, and the superiority of the heat transfer model in extrapolating the experimental data is successfully verified.

Accurate prediction of flow boiling heat transfer in small-scale channels is primordial for optimizing miniature heat exchanger design. This study leverages a comprehensive database to enhance predictive modeling of saturated flow boiling in horizontal small-diameter channels. The primary dataset includes 15,490 data points from 48 published experimental studies, covering 18 pure refrigerants, along with a holdout dataset of 961 data points for model validation. Four machine learning (ML) models were assessed, with Extreme Gradient Boosting model delivering the best performance, yielding a mean absolute error (MAE) of 5.02% and a coefficient of determination of 0.9878 using dimensionless input features. However, a performance drop of 20-30% is observed for all ML models on the holdout dataset, indicating limited generalization. A systematic evaluation of existing empirical correlations also reveals poor predictive performance due to their reliance on limited datasets. To address these limitations, a new correlation is developed, integrating fluid-dependent factors and accounting for flow regime variations across the vapor quality range. The proposed correlation achieves an MAE of 16.61%, with 83.93% of predictions within +/- 30% error band. Validation against the holdout dataset further confirms its reliability, yielding an MAE of 17.24 and 82% of predictions within the +/- 30% error band.

This research proposes a novel hybrid metaheuristic optimization framework that combines the Aquila Optimization algorithm with the Sine-Cosine Optimizer to find equilibrium points of reacting components under specified operational reaction conditions. The method aims to address the exploitative limitations of the standard Aquila algorithm by incorporating oscillatory sine-cosine movements into the hybrid optimizer, which is one of the significant drawbacks of the base Aquila algorithm that should be addressed. The effectiveness of the hybrid approach is thoroughly tested on a suite of 100 multidimensional unimodal and multimodal benchmark cases, with results compared to those from well-known literature optimizers. Additionally, twenty-eight 30-dimensional benchmark functions from the 2013 Congress on Evolutionary Computation competition are used to evaluate the prediction performance. Three multidimensional constrained engineering design problems are also solved, and their results are compared with those from other literature optimizers. The findings show that the hybrid algorithm produces the best estimates and ranks first among competing algorithms based on average ranking results. To further verify its robustness and accuracy, three more complex chemical equilibrium problems are solved using the Gibbs Free Energy minimization method. The predictions are benchmarked against recent metaheuristic algorithms for each case, demonstrating that the proposed hybrid effectively overcomes the challenges of highly nonlinear and non-convex free energy surfaces, achieving higher solution consistency while finding minimum objective function values across different chemical equilibrium scenarios.

This theoretical research study proposes a novel hybrid algorithm that integrates an improved quasi-dynamical oppositional learning mutation scheme into the Mountain Gazelle Optimization method, augmented with chaotic sequences, for the thermal and economical design of a shell-and-tube heat exchanger operating with nanofluids. The Mountain Gazelle Optimizer is a recently developed metaheuristic algorithm that simulates the foraging behaviors of Mountain Gazelles. However, it suffers from premature convergence due to an imbalance between its exploration and exploitation mechanisms. A two-step improvement procedure is implemented to enhance the overall search efficiency of the original algorithm. The first step concerns substituting uniformly random numbers with chaotic numbers to refine the solution quality to better standards. The second step is to develop a novel manipulation equation that integrates different variants of quasi-dynamic oppositional learning search schemes, guided by a novel intelligently devised adaptive switch mechanism. The efficiency of the proposed algorithm is evaluated using the challenging benchmark functions from various CEC competitions. Finally, the thermo-economic design of a shell-and-tube heat exchanger operated with different nanoparticles is solved by the proposed improved metaheuristic algorithm to obtain the optimal design configuration. The predictive results indicate that using water + SiO2 instead of ordinary water as the refrigerant on the tube side of the heat exchanger reduces the total cost by 16.3%, offering the most cost-effective design among the configurations compared. These findings align with the demonstration of how biologically inspired metaheuristic algorithms can be successfully applied to engineering design.

This research study introduces a Q-learning enhanced hyper-heuristic framework for the accurate estimation of energy consumption rates of electric buses. Fundamentals of reinforcement learning concepts are hybridized with the integrated newly emerged metaheuristic methods of Aquila optimizer, Barnacles Mating Optimizer, Gradient-based Optimizer, Harris Hawks Optimization, and Poor and Rich Optimization algorithms to solve high-dimensional optimization problems with higher accuracy. In this context, the Q-learning algorithm is considered a high-level heuristic for administering the selection and move acceptance mechanisms, while search agents of those mentioned above low-level competitive metaheuristic algorithms meticulously explore the search space to find the optimum global point. Q-learning guides the operating hyper-heuristic in selecting the suitable low-level optimizer based on the Q-table score during iterations. An intelligent control mechanism is devised to get a reward or penalty for the actions of the low-level algorithms. The proposed method is evaluated on thirty-two optimization benchmark problems composed of unimodal and multimodal test functions. Then, each constituent algorithm and the hyper-heuristic model are applied to thirty-dimensional benchmark functions of CEC 2017 and twenty-eight test instances of CEC 2013. Four different challenging, complex real-world engineering design cases are also solved to assess the predictability of the proposed method on constrained problems. Finally, the proposed hyper-heuristic is employed to derive the fuel consumption estimates of electric buses. It is seen that the Multiple linear regression model, whose unknown parameters are extracted by the hyper-heuristic framework, gives the best predictions.

The Runge-Kutta Optimization (RUNGE) algorithm is a recently proposed metaphor-free metaheuristic optimizer borrowing practical mathematical foundations of the famous Runge-Kutta differential equation solver. Despite its relatively new emergence, this algorithm has several applications in various branches of scientific fields. However, there is still much room for improvement as it suffers from premature convergence resulting from inefficient search space exploration. To overcome this algorithmic drawback, this research study proposes a brand-new quasi-dynamic opposition-based learning (QDOPP) mechanism to be implemented in a standard Runge-Kutta optimizer to eliminate the local minimum points over the search space. Enhancing the asymmetric search hyperspace by taking advantage of various positions of the current solution within the domain is the critical novelty to enrich general diversity in the population, significantly improving the algorithm's overall exploration capability. To validate the effectivity of the proposed RUNGE-QDOPP method, thirty-four multidimensional optimization benchmark problems comprised of unimodal and multimodal test functions with various dimensionalities have been solved, and the corresponding results are compared against the predictions obtained from the other opposition-based learning variants as well as some state-of-art literature optimizers. Furthermore, six constrained engineering design problems with different functional characteristics have been solved, and the respective results are benchmarked against those obtained for the well-known optimizers. Comparison of the solution outcomes with literature optimizers for constrained and unconstrained test problems reveals that the proposed QDOPP has significant advantages over its counterparts regarding solution accuracy and efficiency.

This research study aims to enhance the optimization performance of a newly emerged Aquila Optimization algorithm by incorporating chaotic sequences rather than using uniformly generated Gaussian random numbers. This work employs 25 different chaotic maps under the framework of Aquila Optimizer. It considers the ten best chaotic variants for performance evaluation on multidimensional test functions composed of unimodal and multimodal problems, which have yet to be studied in past literature works. It was found that Ikeda chaotic map enhanced Aquila Optimization algorithm yields the best predictions and becomes the leading method in most of the cases. To test the effectivity of this chaotic variant on real-world optimization problems, it is employed on two constrained engineering design problems, and its effectiveness has been verified. Finally, phase equilibrium and semi-empirical parameter estimation problems have been solved by the proposed method, and respective solutions have been compared with those obtained from state-of-art optimizers. It is observed that CH01 can successfully cope with the restrictive nonlinearities and nonconvexities of parameter estimation and phase equilibrium problems, showing the capabilities of yielding minimum prediction error values of no more than 0.05 compared to the remaining algorithms utilized in the performance benchmarking process.

The scientific field of optimization has witnessed an increasing trend in the development of metaheuristic algorithms within the current decade. The vast majority of the proposed algorithms have been proclaimed as superior and highly efficient compared to their contemporary counterparts by their own developers, which should be verified on a set of benchmark cases if it is to give conducive insights into their true capabilities. This study completes a comprehensive investigation of the general optimization capabilities of the recently developed nature-inspired metaheuristic algorithms, which have not been thoroughly discussed in past literature studies due to their new emergence. To overcome this deficiency in the existing literature, optimization benchmark problems with different functional characteristics will be solved by some of the widely used recent optimizers. Unconstrained standard test functions comprised of thirty-four unimodal scalable optimization problems with varying dimensionalities have been solved by these competitive algorithms, and respective estimated solutions have been evaluated relying on the performance metrics defined by the statistical analysis of the predictive results. Convergence curves of the algorithms have been construed to observe the evolution trends of objective function values. To further delve into comprehensive analysis on unconstrained test cases, CEC 2013 problems have been considered for comparison tools since their resemblances of the following features of real-world complex algorithms. The optimization capabilities of eleven metaheuristics algorithms have been comparatively analyzed on twenty-eight multidimensional problems. Finally, fourteen complex engineering problems have been optimized by the algorithms to scrutinize their effectiveness on handling the imposed design constraints.

Gradient-based optimizer (GRAD) belongs to the recently developed population-based metaheuristic algorithms inspired by the development of Newton-type methods. Despite its new emergence, there are many successful applications of this optimizer in the existing literature; however, chaos integrated version of this algorithm has not been extensively studied yet. In his study, twenty-one different chaotic maps have been incorporated into the standard GRAD algorithm to maintain a reliable balance between exploration and exploitation mechanisms, which is not robustly constructed within the original algorithm. First ninety-nine thirty dimensional artificially generated optimization benchmark problems comprised of sixty-eight multimodal and thirty-one unimodal functions have been solved by these chaotic variants of the GRAD algorithm to determine the five best performing methods between them. Clear dominancy of the chaotic algorithms is clearly observed over the entire range of benchmark cases in terms of solution accuracy and robustness. Then, to validate the optimization capability of the chaos integrated GRAD algorithms, the best method among them is tested on fourteen constrained real world engineering problems, and its respective feasible results are benchmarked against those obtained from cutting edge metaheuristic optimizer. It is seen that the chaotic GRAD algorithm is able to effectively compete with other state-of-art algorithms on both solving unconstrained and constrained engineering problems. Moreover, it is observed that the Chebyshev chaotic map improved GRAD algorithm outperforms its contemporaries in both unconstrained and constrained cases.

This research study proposes a novel mutation scheme mainly based on the manipulation equations of Tangent Search Optimization and mutualism phase of Symbiotic Organism Search algorithms to be implemented on the Equilibrium Optimization algorithm to enhance the solution diversity among the population individuals. Beneficial coordination between these governing search mechanisms enables maintaining diversity in the population. It eliminates the stagnation towards the local sub-optimal solutions over the search domain, significantly alleviating the inherent drawbacks of Equilibrium Optimizer. To assess the efficiency of the proposed diversity-enhanced Equilibrium Optimization algorithm (DEQUIL) on unconstrained problems, thirty-four multidimensional optimization test instances comprised of unimodal and multimodal benchmark problems have been solved, and respective performances are verified against those obtained from well-reputed new emerged metaheuristic algorithms. A comprehensive comparison based on the decisive metrics, including statistical analysis, performance index analysis, scalability tests, diversity analysis, and convergence rates demonstrates the effectiveness of the hybrid search methodology. Later, fourteen real-world constrained engineering problems with varying complexities were solved by the proposed DEQUIL method. The prediction performance of DEQUIL is compared with a wide range of available literature optimizers to scrutinize the improvements in problem-solving capabilities and seen that it can successfully cope with the complex constrained design problems outperforming the majority of the compared algorithm in most design cases.

This research study proposes a Q-learning-based metaheuristic algorithm framework for thermal design optimization of a shell-and-tube evaporator operating with different refrigerant mixtures, which is a highly complex real-world design problem and has not been investigated yet, in previous literature approaches before. The proposed method, called QL-HEUR, uses Q-learning as a high-level heuristic to iteratively guide the competitive recently emerged low-level metaheuristic algorithms. QL-HEUR is applied to 32 unconstrained optimization benchmark functions, and results are evaluated in statistical analysis. Moreover, three multidimensional constrained optimization problems will be solved. Respective solutions unravel that QL-HEUR is very effective in finding optimum solutions to constrained and unconstrained optimization problems. QL-HEUR is employed on the design optimization of a shell-and-tube heat exchanger running with different mixture pairs as a challenging real-world benchmark case. For the design case in which R134a–R1234yf (0.8:02) mixture is considered, 8.71

Aquila Optimization Algorithm (AQUILA) is a newly emerged metaheuristic optimizer for solving global optimization problems, which is based on intrinsic hunting behaviors of the foraging aquila individuals. However, this stochastic optimization method suffers from some algorithm-specific drawbacks, such as premature convergence to the local optimum points over the search hyperspace due to the lack of solution diversity in the population. To conquer this algorithmic deficiency, an ensemble of Wavelet mutation operators has been implemented into the standard AQUILA to enhance the explorative capabilities of the algorithm by diversifying the search domain as much as possible. Furthermore, a brand-new local search scheme empowered by the synergetic interactions of elite opposition-based learning and a simple-yet-effective exploitative manipulation equation is introduced into the base AQUILA to intensify on the previously visited promising regions. The proposed learning schemes are stochastically applied to the obtained solutions from the base Aquila algorithm to refine the overall solution quality and amend the premature convergence problem. It is also aimed to investigate whether the collective application of Wavelet mutation operators with different types entails a significant improvement in the general search effectivity of the algorithm rather than their individual efforts. Numerical experiments made on a suite of unconstrained unimodal and multimodal benchmark functions reveal that this hybridization with AQUILA has improved the general solution accuracy and stability to very high standards, outperforming its contemporary counterparts in the comparative statistical analysis. Furthermore, an exhaustive benchmark analysis has been performed on fourteen constrained real-world complex engineering problems.

This theoretical research study proposes a novel Chaotic Quasi-Oppositional Arithmetic Optimization Algorithm (COAOA) for thermo-economic optimization of a shell and tube condenser working with refrigerant mixtures. Arithmetic Optimization Algorithm (AOA) is a recently emerged metaheuristic algorithm considering different mathematical operators to optimize the candidate solutions over a wide range of search domains. The effectiveness the COAOA is assessed by applying it to a set of benchmark optimization problems and comparing the obtained solutions with that of the original AOA and its quasi-oppositional variant. The COAOA has been employed to acquire the minimum value of the total annual cost of the shell and tube condenser by iteratively varying nine decision variables of mass flow rate, shell diameter, the tube inside diameter, tube length, number of tube passes, tube layout, tube pitch ratio, the total number of baffles, and diameter ratio. Three different case studies are solved using different refrigerant pairs used for in-tube flow to show the proposed metaheuristic optimizer's efficiency and effectivity on real-world mixed-integer optimization problem. Optimal results retrieved for different mixture pairs with varying mass fractions are compared with each other, and parametric configuration yielding the minimum total cost is decided. Finally, a comprehensive sensitivity analysis is performed to investigate the influences of the design variables over the considered problem objective. Overall analysis results indicate that COAOA can be an excellent optimizer to obtain a shell and tube condenser's optimal configuration within a reasonable computation time.