Metaheuristic algorithms can be classified according to their source of inspiration into four primary categories: evolutionary algorithms, which mimic natural selection and genetic operators; swarm intelligence algorithms, which model the collective behavior of decentralized, self-organized biological systems; physics-based algorithms, which simulate physical laws and phenomena; and human-based algorithms, which are inspired by human cognitive or social behaviors. Table 1 provides a comprehensive classification of the sixteen most widely adopted metaheuristic algorithms in the mechanical engineering literature, along with their key parameters and typical applications.

A notable distinction among these algorithms is their parameter sensitivity. Algorithms such as GA, PSO, and DE require careful tuning of multiple control parameters (crossover rate, inertia weight, scaling factor), and their performance can vary significantly depending on these settings. In contrast, TLBO and Jaya are marketed as "algorithm-specific parameter-free" methods; they require only the common parameters of population size and maximum iterations, eliminating the need for algorithm-specific parameter tuning. This property has made TLBO and Jaya particularly attractive for mechanical engineering practitioners who may not possess deep expertise in computational intelligence [23].

A typical mechanical engineering optimization problem can be formulated in the following general form: Minimize f(x) subject to: g(x) ≤ 0, j = 1, 2, …, m; h (x) = 0, k = 1, 2, …, p; x L ≤ x ≤ x U, i = 1, 2, …, n

j k i i i

where x = [x1, x2, …, xn] is the vector of n design variables, f(x) is the objective function, gj(x) are inequality constraints, h (x) are equality constraints, and x L and x U are the lower and upper bounds of the i-th design

k i i

variable, respectively.

In mechanical engineering, the objective functions most commonly encountered include minimization of structural weight (critical in aerospace and automotive applications), minimization of manufacturing cost (material, tooling, and energy costs), minimization of deflection and deformation under service loads, minimization of stress concentrations and fatigue damage, maximization of structural stiffness (compliance minimization in topology optimization), maximization of fatigue life and reliability index, and maximization of thermal or energy conversion efficiency. The constraint functions in mechanical engineering are diverse and physically meaningful. Stress constraints ensure that the von Mises or principal stresses at critical locations do not exceed the material yield or ultimate strength with an appropriate safety factor. Displacement constraints limit the maximum deflection at service points to ensure functionality. Buckling constraints prevent elastic instability in slender members. Frequency constraints ensure that natural frequencies are separated from excitation frequencies to avoid resonance. Manufacturing constraints enforce minimum thickness, draft angles, and tooling accessibility. Fatigue constraints ensure adequate fatigue life under cyclic loading, often formulated using S-N curves or fracture mechanics criteria.

Constraint handling in metaheuristic optimization is a critical consideration. The most common approaches include penalty function methods (static, dynamic, and adaptive), feasibility-based rules (Deb's rules), repair operators that project infeasible solutions onto the feasible boundary, and multi-objective formulations that treat constraint violation as a separate objective. Deb's [24] feasibility rules, which prioritize feasible solutions over infeasible ones and rank infeasible solutions by their total constraint violation, have become the de facto standard in structural optimization with metaheuristics.

A defining characteristic of metaheuristic optimization in mechanical engineering, as distinct from applications in purely mathematical benchmarks, is the requirement for computationally expensive function evaluations. In virtually all structural, thermal, and vibration optimization problems, evaluating the objective function and constraints for a given design vector x requires solving a boundary value problem, typically via the Finite Element Method (FEM). The optimization loop thus takes the form of an outer metaheuristic algorithm that generates candidate design vectors, each of which is evaluated by an inner FEA solver that returns stress distributions, displacements, temperatures, natural frequencies, or other response quantities. This coupling creates a significant computational bottleneck. For a population of Npop individuals evolved over Ngen generations, the total number of FEA evaluations is approximately Npop × Ngen, which may range from 5,000 to 500,000 or more. If each FEA evaluation requires minutes to hours (as in large-scale nonlinear or multi-physics problems), the total optimization wall-clock time can become prohibitive. This challenge has motivated extensive research into surrogate-assisted optimization, where computationally cheap approximation models (Kriging, radial basis functions, polynomial response surfaces, artificial neural networks) are trained on a limited number of FEA evaluations and used to predict responses for the remaining candidate designs. Adaptive surrogate strategies, such as Efficient Global Optimization (EGO) based on the expected improvement criterion (Jones et al. [25]), have proven particularly effective in reducing the number of expensive FEA calls by 60–90% while maintaining solution quality.

The integration architecture typically involves an automated workflow: the metaheuristic algorithm writes design variable files, invokes a commercial FEA solver (ANSYS, Abaqus, NASTRAN, COMSOL), parses the output results files, evaluates constraints and objectives, and feeds back to the optimizer. Scripting languages such as Python and MATLAB serve as the integration layer, with tools such as pyOpt, DAKOTA, and OpenMDAO providing established frameworks for coupled optimization-simulation workflows.

Five major academic databases were searched for peer-reviewed journal articles and conference proceedings published between January 2000 and December 2025. The search queries combined terms related to metaheuristic algorithms with terms related to mechanical engineering applications, connected by Boolean operators. The complete search strategy and results are summarized in Table 2.

Articles were included if they: 1) applied at least one metaheuristic algorithm to a mechanical engineering design or process optimization problem, 2) reported quantitative optimization results (objective function values, constraint satisfaction, computational cost), 3) were published in peer-reviewed journals or major conference proceedings, and 4) were written in English. Articles were excluded if they: 1) applied metaheuristics solely to mathematical benchmark functions without an engineering application, 2) focused exclusively on algorithm development without engineering validation, 3) were review articles, editorials, or book chapters, or 4) addressed non-mechanical engineering domains (electrical, chemical, civil infrastructure).

For each included study, the following data were extracted: algorithm(s) used, mechanical engineering application domain, problem dimensionality, objective function(s), constraint types, optimal solution quality, computational cost (number of function evaluations, wall-clock time), comparison with other methods, and use of surrogate models or hybridization.

PRISMA flow diagram illustrating the systematic screening process. A total of 4,669 records were identified across five databases. After removal of 717 duplicates, 3,952 unique records were screened by title and abstract, yielding 1,029 articles for full-text review. Application of inclusion and exclusion criteria resulted in 312 articles included in the final synthesis, distributed across structural design (n=94), manufacturing (n=72), thermal systems (n=48), vibration (n=38), mechanism/robotics (n=34), and fatigue/reliability (n=26).

Structural optimization represents the most extensively studied application domain for metaheuristic algorithms in mechanical engineering, accounting for approximately 30% (n=94) of the reviewed studies. The overarching objective in structural optimization is to minimize the weight (or cost) of a structure while ensuring that stress, displacement, buckling, and frequency constraints are satisfied. Three primary categories of structural optimization are distinguished: sizing optimization (determining optimal cross-sectional areas of members), shape optimization (determining optimal geometric coordinates of nodes or boundary curves), and topology optimization (determining the optimal material distribution or connectivity within a design domain).

Manufacturing process optimization constitutes the second-largest application domain (n=72 studies), reflecting the critical economic importance of selecting optimal machining parameters, welding conditions, and process settings. Unlike structural optimization, where the objective is primarily weight minimization, manufacturing optimization typically involves multi-objective formulations that simultaneously seek to minimize surface roughness, tool wear, and energy consumption while maximizing material removal rate and production throughput.

Thermal and energy systems design constitutes a growing application domain (n=48 studies), driven by increasing demands for energy efficiency, environmental sustainability, and cost reduction in Heating, Ventilation, Air Conditioning (HVAC), power generation, and renewable energy systems.

Vibration control and dynamic analysis applications represent an important and growing domain (n=38 studies) for metaheuristic optimization. Key problems include optimal placement and tuning of vibration absorbers, structural modification for frequency shifting, active vibration control system design, and damping optimization. The objective is typically to minimize vibration amplitude at critical points, maximize separation between natural frequencies and excitation frequencies, or minimize the total weight of added damping elements while achieving a target vibration reduction.

Vibration optimization problems are particularly well-suited for metaheuristic algorithms because they often involve mixed continuous-discrete variables (continuous stiffness and damping parameters combined with discrete damper locations), non-convex objective landscapes with multiple local minima, and frequency-domain constraints that create highly nonlinear feasible regions. The reviewed studies indicate that metaheuristic-optimized damper configurations typically achieve 15–30% greater vibration reduction compared with Den Hartog's classical analytical solutions for single-DOF tuned mass dampers, and 40–60% improvements over uniform damper placement strategies for multi-DOF structures.

The synthesis and optimization of mechanical mechanisms and robotic systems constitutes a challenging application domain (n=34 studies) that requires metaheuristic algorithms to navigate highly nonlinear kinematic and dynamic design spaces. Key problems include four-bar linkage synthesis for path, function, and motion generation; robot trajectory planning for minimum-time, minimum-energy, or minimum-jerk operation; workspace optimization for serial and parallel manipulators; and compliant mechanism design.

Path generation problems in linkage synthesis are notorious for their high-dimensional, multi-modal design landscapes with numerous local optima, making them particularly suitable for global search via metaheuristics. DE has shown the best path-tracking accuracy (0.127 mm average error) among the studied algorithms, owing to its strong exploitation capability in continuous design spaces. For robot trajectory optimization, the objective is often to minimize cycle time or energy consumption while respecting joint velocity and acceleration limits and avoiding obstacles. GWO and PSO have demonstrated competitive performance, achieving 18–24% reductions in cycle time or energy consumption compared with conventional polynomial trajectory profiles.

RBDO and fatigue life optimization represent a sophisticated application domain (n=26 studies) that incorporates uncertainty quantification into the design process. In deterministic optimization, material properties, loads, and geometry are treated as known constants; in RBDO, these quantities are modeled as random variables with specified probability distributions, and the optimization seeks to minimize weight or cost while maintaining the probability of failure below an acceptable threshold.

The reliability index β, defined as the shortest distance from the origin to the limit state surface in standard normal space, is the most common measure of structural reliability. A reliability index of β = 3.0 corresponds to a failure probability of approximately P = 1.35 × 10−3, while β = 4.0 corresponds to P = 3.17 × 10−5. Evaluating the reliability index requires solving an inner optimization problem (the Most Probable Point search) for each candidate design in the outer metaheuristic loop, creating a computationally expensive double-loop structure. Single-loop and decoupled approaches have been developed to mitigate this cost, and surrogate-assisted methods are particularly valuable in this context.

The RBDO results demonstrate that metaheuristic algorithms can effectively navigate the stochastic design space to find designs that are simultaneously lightweight and reliable. Compared with deterministic optimization, RBDO designs typically incur a 5–15% weight penalty but achieve target reliability levels that account for material variability, load uncertainty, and geometric tolerances. The parameter-free algorithms (TLBO, Jaya) again show efficient convergence, particularly when combined with surrogate models for the inner reliability analysis loop. For fatigue-critical components such as crankshafts and turbine disks, metaheuristic RBDO enables designers to specify target fatigue lives (e.g., 107 cycles at 95% reliability) directly as optimization constraints, resulting in designs that are both optimally lightweight and demonstrably safe under uncertainty.

A central question in applying metaheuristic algorithms to mechanical engineering is whether any algorithm consistently outperforms others across diverse problem types. The "No Free Lunch" theorem (Wolpert and Macready [32]) suggests that no single optimization algorithm can dominate all others across all possible problem classes. Nevertheless, the systematic analysis of results across the six mechanical engineering domains reviewed in this study reveals meaningful performance patterns that can guide algorithm selection for specific problem types.

Table 9 presents a cross-domain comparison of algorithm performance, synthesizing the best results from the reviewed literature for representative problems in each domain. Statistical significance was assessed using the Friedman non-parametric test applied to algorithm rankings across problems within each domain, with post-hoc pairwise comparisons using the Wilcoxon signed-rank test at the 0.05 significance level.

Several key findings emerge from the cross-domain analysis. First, DE demonstrates the most consistent performance across domains, achieving the best or second-best ranking in five of eight domains. Its strong self-adaptive mutation and crossover mechanisms appear to provide robust performance across the diverse design landscapes encountered in mechanical engineering. Second, the parameter-free algorithms (Jaya, TLBO) excel in constrained structural optimization and RBDO, where their lack of algorithm-specific parameters eliminates the risk of suboptimal tuning. Third, PSO performs particularly well in manufacturing optimization, possibly due to its effective exploitation capability in the relatively smooth response surfaces generated by empirical machining models. Fourth, GA, while generally outperformed by newer algorithms in single-objective problems, remains highly competitive in multi-objective formulations (particularly NSGA-II for Pareto optimization).

Hybrid metaheuristic approaches, which combine the strengths of two or more optimization strategies, have emerged as a dominant trend in the recent mechanical engineering literature. Hybridization strategies include algorithm-algorithm hybrids (combining two metaheuristics, e.g., GA-PSO, DE-SA), algorithm-solver hybrids (coupling a metaheuristic with a gradient-based local search), and algorithm-surrogate hybrids (embedding surrogate models within the metaheuristic loop to reduce computational cost).

The results unambiguously demonstrate the superiority of hybrid approaches. Algorithm-surrogate hybrids achieve the most dramatic improvements, reducing FEA calls by 68–85% while maintaining or improving solution quality. The DE-Kriging combination has been particularly successful for crashworthiness optimization, where a single nonlinear dynamic FEA simulation can require 4–12 hours, making standalone metaheuristic optimization (requiring 10,000+ evaluations) computationally infeasible without surrogate assistance.

The integration of surrogate models with metaheuristic algorithms deserves special attention given its transformative impact on the practical applicability of optimization to large-scale, computationally expensive mechanical engineering problems. Surrogate models serve as computationally cheap approximations of the expensive FEA-based objective and constraint functions, trained on a limited set of high-fidelity evaluations and adaptively updated as the optimization progresses.

Kriging (Gaussian Process Regression) consistently achieves the highest surrogate accuracy (R² = 0.974– 0.988) and enables the greatest FEA savings (82–91%), owing to its ability to provide both predictions and uncertainty estimates, which can be exploited through infill criteria (expected improvement, probability of improvement) for adaptive sampling. Ensemble surrogates combining multiple model types represent the state of the art, achieving R² values above 0.98 and enabling solution quality within 1% of direct optimization at a fraction of the computational cost. Polynomial response surface methodology (RSM), while computationally simplest, provides lower accuracy for highly nonlinear problems and consequently lower FEA savings.

To rigorously assess algorithm performance differences across the mechanical engineering domains, a Friedman test was conducted on the ranking data from 48 representative benchmark problems spanning all six domains. Each algorithm was ranked from 1 (best) to 7 (worst) on each problem based on the best objective function value achieved. The Friedman test statistic was χ²F = 42.86 with 6 degrees of freedom (p < 0.001), indicating highly significant differences among algorithm performances.

Post-hoc pairwise comparisons using the Wilcoxon signed-rank test with Bonferroni correction revealed the following significant differences at α = 0.05: Jaya significantly outperformed GA (p = 0.003), WOA (p = 0.008), and Sine Cosine Algorithm (SCA) (p = 0.001); TLBO significantly outperformed GA (p = 0.006) and WOA (p = 0.012); DE significantly outperformed GA (p = 0.018) and WOA (p = 0.024). No significant differences were found between Jaya and TLBO (p = 0.312), Jaya and DE (p = 0.086), or TLBO and DE (p = 0.142), suggesting that these three algorithms form a statistically indistinguishable top tier for mechanical engineering optimization. The average Friedman ranks across all 48 problems were: Jaya (1.82), TLBO (2.14), DE (2.38), PSO (3.24), GWO (3.86), GA (4.42), and WOA (4.68).

Box plots of Friedman rankings for seven metaheuristic algorithms across 48 mechanical engineering benchmark problems. Jaya, TLBO, and DE form a statistically indistinguishable top cluster (median ranks 1.5–2.5), followed by PSO (median rank 3.0), GWO (median rank 4.0), GA (median rank 4.5), and WOA (median rank 5.0). The whiskers indicate the range of rankings across problems, with Jaya showing the smallest interquartile range, suggesting the most consistent performance.

The temporal distribution of publications reveals a clear exponential growth trend. The period 2000–2005 contributed only 18 publications (5.8%), reflecting the early adoption phase where GA and SA were the primary metaheuristics applied to structural sizing problems. The period 2006–2010 saw 34 publications (10.9%) as PSO and DE gained traction and applications expanded to manufacturing optimization. A significant acceleration occurred in 2011–2015 (62 publications, 19.9%), coinciding with the introduction of TLBO (Rao et al. [21]) and the growing availability of computational resources for FEA-coupled optimization. The period 2016–2020 witnessed explosive growth (108 publications, 34.6%), driven by the introduction of numerous new algorithms (GWO, WOA, HHO, MFO, SCA, Jaya) and the expansion of applications to thermal systems, AM, and multi-physics optimization. The most recent period, 2021–2025, contributed 90 publications (28.8%) in the reviewed dataset, with an emerging focus on digital twin integration, machine learning surrogate models, and sustainable design optimization.

Annual publication count of metaheuristic optimization studies in mechanical engineering (2000–2025). The bar chart shows a clear exponential growth trend, with annual publications increasing from 2–4 papers/year in 2000–2005 to 18–24 papers/year in 2021–2025. Milestone algorithm introductions are annotated: TLBO (2011), GWO (2014), WOA (2016), Jaya (2016), and HHO (2019).

The analysis of journal distribution reveals a concentration of publications in specialized structural optimization and computational intelligence journals, as shown in Table 12.

Most metaheuristic applications in the reviewed literature involve problems with fewer than 50 design variables. Large-scale industrial structural optimization problems such as full-vehicle body-in-white optimization with thousands of sheet metal thicknesses, or aircraft wing topology optimization with millions of density variables remain largely beyond the reach of population-based metaheuristics. The exponential growth of the search space with dimensionality, combined with the computational cost per evaluation, creates a scalability barrier that current metaheuristic approaches cannot adequately address without significant algorithmic innovations or decomposition strategies.

Many advanced mechanical engineering problems involve coupled multi-physics phenomena: thermal-structural interaction in turbine blades, fluid-structure interaction in aerodynamic design, thermo-mechanical-metallurgical coupling in welding simulation, and electro-thermo-mechanical coupling in MEMS design. Each coupled simulation is substantially more expensive than single-physics FEA, and the coupled response surfaces may exhibit qualitatively different characteristics (steeper gradients, stronger nonlinearities, narrower feasible regions) that challenge metaheuristic search strategies.

A persistent gap exists between mathematically optimal designs and practically manufacturable designs. Topology-optimized structures, in particular, often feature complex geometries (thin branches, enclosed voids, sharp angles) that are difficult or impossible to manufacture using conventional subtractive methods and may even challenge AM. While several studies have incorporated manufacturing constraints (minimum member size, draw direction, overhang angles), the comprehensive integration of all relevant manufacturing limitations into the optimization formulation remains an open challenge.

The vast majority of reviewed studies validate optimized designs through simulation only, without experimental fabrication and testing. Such a limitation creates an unverified assumption that the FEA model accurately represents physical reality, ignoring uncertainties in material properties, manufacturing tolerances, loading conditions, and boundary conditions. The few studies that do include experimental validation frequently report discrepancies of 5–15% between predicted and measured performance, underscoring the need for robust optimization approaches that account for model inadequacy.

Despite the proliferation of metaheuristic algorithms, there is no reliable a priori method for selecting the most appropriate algorithm for a given mechanical engineering problem. The No Free Lunch theorem implies that algorithm performance is problem-dependent, yet practitioners lack systematic guidelines for matching algorithm characteristics to problem features. Furthermore, the performance sensitivity to control parameters (population size, crossover rate, inertia weight) means that reported "optimal" results may not be reproducible without careful parameter tuning, introducing a hidden degree of researcher bias into comparative studies.

The integration of deep learning models, particularly Physics-Informed Neural Networks (PINNs), Graph Neural Networks (GNNs), and transformer architectures with metaheuristic algorithms holds transformative potential. These AI-driven surrogates can learn the underlying physics of mechanical systems from limited training data, providing more accurate and generalizable approximations than traditional Kriging or RBF models. Real-time optimization, where design decisions are made in seconds rather than hours, becomes feasible when deep learning surrogates replace FEA evaluations entirely.

Future mechanical engineering design will increasingly require optimization across multiple length scales: from nanoscale material microstructure (grain morphology, crystal orientation, nanocomposite filler distribution) through mesoscale architectured materials (lattice structures, metamaterials) to macroscale structural geometry. Metaheuristic algorithms that can efficiently handle this hierarchical, multi-scale design space, potentially through nested optimization loops with scale-specific search strategies, represent a frontier research area.

Digital twins, real-time virtual replicas of physical mechanical systems continuously updated with sensor data, provide an ideal platform for online metaheuristic optimization. As operating conditions change (temperature variations, load fluctuations, material degradation), the digital twin can trigger re-optimization of control parameters, maintenance schedules, or structural configurations. Such a capability represents a paradigm shift from static design optimization to dynamic, lifecycle-aware optimization.

The synergy between topology optimization and AM is well-recognized, but current approaches insufficiently capture AM process physics. Future research should integrate build process simulation (thermal history, residual stress, distortion prediction) directly into the metaheuristic topology optimization loop, ensuring that optimized designs are not only structurally optimal but also printable with predictable quality. Support structure co-optimization and multi-material AM design represent additional open challenges.

The growing emphasis on environmental sustainability demands optimization formulations that simultaneously consider structural performance, economic cost, and environmental impact (embodied energy, CO2 emissions, end-of-life recyclability). Multi-objective metaheuristic algorithms that generate Pareto-optimal surfaces across these three (or more) objectives will enable designers to make informed trade-off decisions that balance technical performance with environmental responsibility.

The integration of Internet of Things (IoT) sensor networks with metaheuristic optimization enables real-time adaptive control of manufacturing processes. Machine tool vibration sensors, thermal cameras, and force dynamometers can feed continuous data streams to metaheuristic algorithms that adjust cutting parameters, welding settings, or AM process parameters on-the-fly, optimizing process outcomes in response to real-time disturbances and material variability.

Embedding physical laws and engineering knowledge directly into metaheuristic search operators through physics-informed initialization, constraint handling, and mutation operators can dramatically improve search efficiency by restricting the exploration to physically plausible regions of the design space. This approach bridges the gap between data-driven metaheuristic search and physics-based engineering understanding, potentially enabling efficient optimization of extremely high-dimensional problems that are currently intractable.