Computational Performance Research Articles

A binary particle swarm optimization-based pruning approach for environmentally sustainable and robust CNNs

Deep Convolutional Neural Networks (CNNs), continue to demonstrate remarkable performance across various tasks. However, their computational demands and energy consumption present significant drawbacks, restricting their practical deployment and contributing to a substantial carbon footprint. This paper addresses this challenge by proposing a novel method named Binary Particle Swarm Optimization Layer Pruner (BPSO-LPruner), aimed at achieving substantial computational reduction and mitigating environmental impact during CNN inference. BPSO-LPruner utilizes a constrained Binary Particle Swarm Optimization for CNN layer pruning, integrating a masked-bit strategy and a new population initialization strategy to enhance search performance. We illustrate the effectiveness of our method in reducing model computational costs and carbon footprint emissions while improving performance across multiple models (VGG16, VGG19, DenseNet-40, ResNet18, ResNet20, ResNet34, ResNet44, ResNet56, ResNet110, ResNet50, and MobileNetv2) and diverse datasets (CIFAR-10, CIFAR-100, Tiny-ImageNet, COVID-19 X-ray dataset). Promising results underscore the performance of the proposed method. Additionally, we demonstrate that layer pruning yields benefits beyond enhanced computational performance. Our experimentation reveals that BPSO-LPruner enhances the model’s reliability and robustness by effectively addressing variations in input data, inherent ambiguity in model parameters, and adversarial images.

QRCODE: Massively parallelized real-time time-dependent density functional theory for periodic systems

We present a new software module, QRCODE (Quantum Research for Calculating Optically Driven Excitations), for massively parallelized real-time time-dependent density functional theory (RT-TDDFT) calculations of periodic systems in the open-source Qbox software package. Our approach utilizes a custom implementation of a fast Fourier transformation scheme that significantly reduces inter-node message passing interface (MPI) communication of the major computational kernel and shows impressive scaling up to 16,344 CPU cores. In addition to improving computational performance, QRCODE contains a suite of various time propagators for accurate RT-TDDFT calculations. As benchmark applications of QRCODE, we calculate the current density and optical absorption spectra of hexagonal boron nitride (h-BN) and photo-driven reaction dynamics of the ozone-oxygen reaction. We also calculate the second and higher harmonic generation of monolayer and multi-layer boron nitride structures as examples of large material systems. Our optimized implementation of RT-TDDFT in QRCODE enables large-scale calculations of real-time electron dynamics of chemical and material systems with enhanced computational performance and impressive scaling across several thousand CPU cores.

Real-time fault-tolerant guidance for launch vehicle ascending flight under thrust drop failure

This paper presents a real-time fault-tolerant guidance method, which solves the autonomous rescue problem in the event of thrust drop failure during the final stage flight of launch vehicles. The core of the method is the online and optimal reconstruction of both the degraded target orbit and the subsequent flight trajectory. Aiming at achieving satisfied onboard computing performance and making the best use of the launcher’s residual energy, a unique relaxation-penalization model transformation method for the nonlinear orbit injection conditions is proposed, and a successive convexification algorithm is developed to solve the problem. Furthermore, both the two classic thrust drop failure situations, that is the mass flow rate drop and the specific impulse drop problems, can be resolved by the proposed algorithm. The average run-time of this orbit-trajectory joint optimization algorithm is below 150ms in an embedded ARM processor @1.5 GHz, which is adequate for onboard use. Using the above algorithm as a central infrastructure, a receding-horizon-strategy-based fault-tolerant guidance method is proposed. By performing the optimization repeatedly at a high frequency, the effects of parameter deviations and external disturbances can be absorbed for the most part, for example, the guidance algorithm is verified to be capable of tolerating at least ±5% thrust deviations. Comprehensive numerical and hardware-in-the-loop simulations are performed to demonstrate the computational performance, accuracy, and reliability of the proposed algorithms.

Surrogate gradient methods for data-driven foundry energy consumption optimization

In many industrial applications, data-driven models are more and more commonly employed as an alternative to classical analytical descriptions or simulations. In particular, such models are often used to predict the outcome of an industrial process with respect to specific quality characteristics from both observed process parameters and control variables. A major step in proceeding from purely predictive to prescriptive analytics, i.e., towards leveraging data-driven models for process optimization, consists of, for given process parameters, determining control variable values such that the output quality improves according to the process model. This task naturally leads to a constrained optimization problem for data-driven prediction algorithms. In many cases, however, the best available models suffer from a lack of regularity: methods such as gradient boosting or random forests are generally non-differentiable and might even exhibit discontinuities. The optimization of these models would therefore require the use of derivative-free techniques. Here, we discuss the use of alternative, independently trained differentiable machine learning models as a surrogate during the optimization procedure. While these alternatives are generally less accurate representations of the actual process, the possibility of employing derivative-based optimization methods provides major advantages in terms of computational performance. Using classical benchmarks as well as a real-world dataset obtained from an industrial environment, we demonstrate that these advantages can outweigh the additional model error, especially in real-time applications.

A theoretical study on Krauklis wave characteristics

Abstract The Krauklis wave is a special seismic phenomenon in fluid saturated fracture medium. The wave can prompt a unique resonance effect and enhance the amplitude at special frequencies. These frequencies have a quantitative relationship with the fracture geometry parameters and can be used for quantitative interpretation of geometry parameters. Such frequency information can be transmitted to body waves by the transformation between the Krauklis wave and the body wave. Both P- and S-waves become frequency dependent. In this study, an original numerical method is brought out to solve the equation of the Krauklis wave dispersion relation. The method has fine computational performance, and the frequency band for numerical solution is extended to the megahertz level. The dispersion, resonance, and attenuation of the Krauklis wave can be analyzed within the entire frequency range for Krauklis wave existence. What is more, the formation mechanism, existence, and observability are illuminated. The analysis shows that there are upper limits of frequency and fracture aperture for Krauklis wave existence, but within the frequency band for artificial seismic and micro-seismic exploration, the Krauklis wave exists widely. For experimental research, the frequency and fracture aperture should be well designed to ensure the generation of the Krauklis wave. The attenuation of the Krauklis wave can suppress the resonance effect. The influence of the attenuation should be taken into account, when the wave is used for seismic characterization of fracture reservoirs or micro-seismic monitoring of hydraulic fracturing.

A learning optimization for resilience enhancement of risk-informed traffic control system with hazardous materials transportation under uncertainty

A learning optimization is proposed to enhance overall resilience of interdependent traffic systems with hazardous materials (hazmat) transportation under uncertainty. To this end, three interconnected systems are proposed against traffic dynamics and congestion in a complex environment of regular traffic and hazmat carriers incurred with time-varying travel cost. In order to increase control resilience against traffic instability, a reinforcement learning hazmat network is proposed. In order to efficiently improve computation resilience against disruption of risk uncertainty, a resilience-aware learning optimization is proposed to obtain optimal solutions. In order to demonstrate computational performance of proposed approach, numerical experiments are performed at a real-world city under various kinds of traffic conditions. Computational comparisons are numerically made with stochastic and robust optimization at large-scale traffic control systems. As it reported, the proposed learning-based optimization can better greatly enhance overall traffic system resilience, control resilience and computation resilience compared to other models under mixed risk of hazmat transportation and uncertain demand.

Advancing scanning probe microscopy simulations: A decade of development in probe-particle models

The Probe-Particle Model combine theories designed for the simulation of scanning probe microscopy experiments, employing non-reactive, flexible tip apices to achieve sub-molecular resolution. In the article we present the latest version of the Probe-Particle Model implemented in the open-source ppafm package, highlighting substantial advancements in accuracy, computational performance, and user-friendliness. To demonstrate this we provide a comprehensive review of approaches for simulating non-contact Atomic Force Microscopy. They vary in complexity from simple Lennard-Jones potential to the latest full density-based model. We compared those approaches with ab initio calculated references, showcasing their respective merits. All parts of the ppafm package have undergone acceleration by 1-2 orders of magnitude using OpenMP and OpenCL technologies. The updated package includes an interactive graphical user interface and seamless integration into the Python ecosystem via pip, facilitating advanced scripting and interoperability with other software. This adaptability positions ppafm as an ideal tool for high-throughput applications, including the training of machine learning models for the automatic recovery of atomic structures from nc-AFM measurements. We envision significant potential for this application in future single-molecule analysis, synthesis, and advancements in surface science in general. Additionally, we discuss simulations of other sub-molecular scanning-probe imaging techniques, such as bond-resolved scanning tunneling microscopy and kelvin probe force microscopy, all built on the robust foundation of the Probe-Particle Model. Altogether this demonstrates the broad impact of the model across diverse domains of on-surface science and molecular chemistry.

A Σ-Δ ADC with a DPOQ system and a new multi-Stage digital filter

This paper proposes a high-precision Sigma Delta ADC for automotive electronic sensors and delves into methods for optimizing quantizers and filters, with a focus on DPOQ quantizers and hybrid CIC filters. This ADC features a Dual-path One-bit Quantization (DPOQ) System, which improves the accuracy of Sigma-Delta ADCs while reducing hardware consumption. Meanwhile, this paper presents a new multistage digital filter. The filter uses a cascade of multiple filters, including cosine-like (CL), cascaded integral comb (CIC), interpolated second-order polynomial (ISOP), and half-band (HB) filters, to enhance the ADC’s accuracy. The filter are designed using canonical signed digit (CSD) and common subexpression (CSE) optimized the design algorithm of the filter, to reduce hardware resource consumption and improve computational performance. The ADC is synthesized using 180 nm CMOS technology, achieving an output SNDR of 96.26 dB, ENOB of 15.73 bits, and total power of 518.35 uW.

Exchange-correlation kernel for perturbation dependent auxiliary functions in auxiliary density perturbation theory

ContextAnalytic exchange-correlation kernel formulations are of the outermost importance for density functional theory (DFT) perturbation calculations. In this paper, the working equation for the exchange-correlation kernel of the generalized gradient approximation (GGA) for perturbation dependent auxiliary functions is derived and discussed in the framework of auxiliary density functional theory (ADFT). The presented new formulation is extended to the unrestricted approach, too. A comprehensive discussion of the implementation of the GGA ADFT kernel, using either the native exchange-correlation functional implementations in deMon2k or the ones from the LibXC library, is given. Calculations with analytic exchange-correlation kernels are compared to their finite difference counterparts. The obtained results are in quantitative agreement. Nevertheless, analytic GGA ADFT kernel implementations show substantial improvement in the computational performance. Similar results are reported for analytic second derivatives of effective core potential (ECP) and model core potential (MCP) matrix elements when compared to their finite difference counterparts in molecular frequency analyses.MethodAll calculations are performed in the framework of ADFT as implemented in deMon2k. In the ADFT analytic frequency calculations, auxiliary density perturbation theory was used. The underlying two-center exchange-correlation kernel matrix elements are calculated by numerical integration either with analytic or finite difference kernel expressions. Validation calculations are performed with the VWN and PBE functionals employing DFT-optimized DZVP basis sets in conjunction with automatically generated GEN-A2 auxiliary density function sets. In the (Pt3Cu)n cluster benchmark calculations, the RPBE functional was used. For Pt atoms, the quasi-relativistic LANL2DZ effective core potential with the corresponding valence basis set was employed, whereas for Cu atoms, the all-electron DFT-optimized TZVP basis was applied. The auxiliary density was expanded by the automatically generated GEN-A2* auxiliary function set. We run all benchmark calculations in parallel on 24 cores.

Multi-objective multi-population simplified swarm optimization for container loading optimization with practical constraints

The container loading problem (CLP) holds significant importance in logistics and supply chain management due to its direct influence on transportation costs and times, thereby impacting the competitive advantages of enterprises across industries. Although there are existing studies for CLP, there remains a gap in addressing the optimization of multiple objectives while satisfying practical constraints. Moreover, container loading methods must also meet performance requirements such as high computational speed, explainability, and implementation capability. Although meta-heuristic-based algorithms have shown effective computational capabilities and performance, such algorithms often being trapped in the local optima especially when searching in the vast solution space of the CLP, particularly as the quantity and diversity of cargo sizes and shapes increase. Motivated by realistic needs, this study aims to develop a UNISON-based framework that integrates the merging spaces algorithm, a novel simple but effective hybrid simplified swarm optimization genetic algorithm (SSO-GA), and a multi-populations co-evolution strategy to determine the loading sequence of parcels to maximize space utilization and weight balance while satisfying to practical constraints. Specifically, the merging spaces algorithm merges fragmented small spaces resulting from loaded parcels into larger spaces, thereby facilitating the accommodation of additional parcels. The hybrid SSO-GA splits encoded solutions and updates segment using novel strategies resulting in the rearrangement of a group of parcels and their corresponding layouts for better space utilization. Furthermore, the multi-populations co-evolution strategy enhances the diversity of the search space and stabilizes solution quality by simultaneously exploiting the best solutions and exploring alternative solutions during the solution update process. An empirical study was conducted by using a public benchmark dataset which demonstrated the practical effectiveness of the proposed framework by significantly improving average space utilization while ensuring center balance and satisfying practical constraints. Furthermore, this study can also serve as a digital support system capable of assisting decision-makers in optimizing container loading operations, thereby improving productivity and saving valuable time.

Maximizing Engagement in Large-Scale Social Networks

Motivated by the importance of user engagement as a crucial element in cascading leaving of users from a social network, we study identifying a largest relaxed variant of a degree-based cohesive subgraph: the maximum anchored k-core problem. Given graph [Formula: see text] and integers k and b, the maximum anchored k-core problem seeks to find a largest subset of vertices [Formula: see text] that induces a subgraph with at least [Formula: see text] vertices of degree at least k. We introduce a new integer programming (IP) formulation for the maximum anchored k-core problem and conduct a polyhedral study on the polytope of the problem. We show the linear programming relaxation of the proposed IP model is at least as strong as that of a naïve formulation. We also identify facet-defining inequalities of the IP formulation. Furthermore, we develop inequalities and fixing procedures to improve the computational performance of our IP model. We use benchmark instances to compare the computational performance of the IP model with (i) the naïve IP formulation and (ii) two existing heuristic algorithms. Our proposed IP model can optimally solve half of the benchmark instances that cannot be solved to optimality either by the naïve model or the existing heuristic approaches. Funding: This work is funded by the National Science Foundation (NSF) [Grant DMS-2318790] titled AMPS: Novel Combinatorial Optimization Techniques for Smartgrids and Power Networks. Supplemental Material: The online appendix is available at https://doi.org/10.1287/ijoo.2022.0024 .

Neural network empowered liquidity pricing in a two-price economy under conic finance settings

In the article at hand neural networks are used to model liquidity in financial markets, under conic finance settings, in two different contexts. That is, on the one hand this paper illustrates how the use of neural networks within a two-price economy allows to obtain accurate pricing and Greeks of financial derivatives, enhancing computational performances compared to classical approaches such as (conic) Monte Carlo. The methodology proposed for this purpose is agnostic of the underlying valuation model, and it easily adapts to all models suitable for pricing in conic financial markets. On the other hand, this article also investigates the possibility of valuing contingent claims under conic assumptions, using local stochastic volatility models, where the local volatility is approximated by means of a (combination of) neural network(s). Moreover, we also show how it is possible to generate hybrid families of distortion functions to better fit the implied liquidity of the market, as well as we introduce a conic version of the SABR model, based on the Wang transform, that still allows for analytical bid and ask pricing formulae.

The evaluation of computational modelling performance within the context of rationality theory: finding the area between two curves

ABSTRACT This study aimed to investigate the development of computational modelling performances of students during the computer-assisted system (CAS) integrated ACODESA method based on Habermas’ construct of rationality. The participants included 22 university students. In the study, in which the embedded design was utilised, the qualitative phase aimed to examine the computational modelling performances of the students during the stages of CAS integrated ACODESA method. It was determined that the students showed improvement in modelling the Riemann sum accurately with CAS, and in choosing to use for loop to determine the area of the rectangles that represented the Riemann sum, and in comprehensibility and acceptability. In the quantitative phase of the study, pre and post-tests were conducted to determine the effect of the CAS-integrated ACODESA method on computational modelling performances of the students. The computational modelling scores were compared with the paired samples t-test. It was found that CAS-integrated ACODESA method made statistically significant effect on computational modelling performances of the students.

LibEMMI_MGFD: A program of marine controlled-source electromagnetic modelling and inversion using frequency-domain multigrid solver

We develop a software package libEMMI_MGFD for 3D frequency-domain marine controlled-source electromagnetic (CSEM) modelling and inversion. It is the first open-source C program tailored for geometrical multigrid (GMG) CSEM simulation. An volumetric anisotropic averaging scheme has been employed to compute effective medium for modelling over uniform and nonuniform grid. The computing coordinate is aligned with acquisition geometry by rotation with the azimuth and dip angles, facilitating the injection of the source and the extraction of data with arbitrary orientations. Efficient nonlinear optimization is achieved using quasi-Newton scheme assisted with bisection backtracking line search. In constructing the modularized Maxwell solver and evaluating the misfit and gradient for 3D CSEM inversion, the reverse communication technique is the key to the compaction of the software while maintaining the computational performance. A number of numeric tests demonstrate the efficiency of the modelling while preserving the solution accuracy. A 3D marine CSEM inversion example has been examined for resistivity imaging. Program summaryProgram Title: libEMMI_MGFDCPC Library link to program files:https://doi.org/10.17632/mpk7xrd38m.1Developer's repository link:https://github.com/yangpl/libEMMI_MGFDLicensing provisions: GNU General Public License v3.0Programming language: C, ShellSoftware dependencies: MPI [1]Nature of problem: 3D Controlled-source electromagnetic modelling and inversion.Solution method: Frequency-domain modelling on staggered grid; Geometrical multigrid (GMG) method as an iterative solver; Quasi-Newton method for nonlinear minimization; Bisection-based backtracking line search.

A distributionally robust approach for the parallel machine scheduling problem with optional machines and job tardiness

This paper investigates a parallel machine scheduling problem with uncertain job processing time, where the job tardiness and optional machines are considered. To address the factor of energy saving, only a subset of all available machines are turned on, which is referred to as not-all-machine (NAM). To depict the uncertain processing time, a mean–mean absolute deviation (MAD) ambiguity set is utilized, and the cost of job tardiness is minimized under the worst-case distribution scenario over the ambiguity set. After building a distributionally robust optimization (DRO) model, theoretical bounds of the optimal number of machines are obtained. Since the model is not computationally scalable, an upper bound on its inner minimization problem is employed, and a mixed integer linear programming (MILP) approximation is obtained based on McCormick inequalities. For the DRO model, tailored speedup techniques are employed, significantly enhancing the computational performance. To evaluate the validity of the proposed DRO model, we compare it with its stochastic programming (SP) counterpart under various parameter settings. Numerical experiments demonstrate that the DRO model exhibits strong performance in the worst-case scenarios. As the problem size increases, the DRO model casts clear advantages over the SP model in terms of computational efficiency and reliability. It is observed that the performance of the DRO model is more stable than that of the nominal sequence, especially with loose due dates. Furthermore, the out-of-sample performance under various decision making preferences shed new lights into the trade-off between energy saving and production efficiency.

Adaptive unified gas-kinetic scheme for diatomic gases with rotational and vibrational nonequilibrium

Multiscale nonequilibrium physics at large variations of local Knudsen number are encountered in applications of aerospace engineering and micro-electro-mechanical systems, such as high-speed flying vehicles and low pressure of the encapsulation. An accurate description of flow physics in all flow regimes within a single computation requires a genuinely multiscale method. The adaptive unified gas-kinetic scheme (AUGKS) is developed for such multiscale flow simulation. The AUGKS applies discretized velocity space to accurately capture the non-equilibrium physics in the multiscale UGKS, and adaptively employs continuous distribution functions following Chapman–Enskog expansion to efficiently recover near-equilibrium flow region in GKS. The UGKS and GKS are dynamically connected at the cell interface through the fluxes from the discretized and continuous gas distribution functions, which avoids any buffer zone between them. In this study, the AUGKS with rotation and vibration non-equilibrium is developed based on a multiple temperature relaxation model. The real gas effect in different flow regimes has been properly captured. To capture aerodynamic heating accurately, the heat flux modifications from the rotation and vibration modes are also included in the current scheme. Unstructured discrete particle velocity space is adopted to further improve the computational performance of the AUGKS. Numerical tests, including Sod tube, normal shock structure, high-speed flow around the two-dimensional cylinder and three-dimensional sphere and space vehicles, and an unsteady nozzle plume flow from the continuum flow to the background vacuum, have been conducted to validate the current scheme. In comparison with the original UGKS, the current scheme speeds up the computation, reduces the memory requirement, and maintains the equivalent accuracy for multiscale flow simulation, which provides an effective tool for nonequilibrium flow simulations, especially for the flows at low and medium speed.

Ultra-Low-Power Sensor Nodes for Real-Time Synchronous and High-Accuracy Timing Wireless Data Acquisition.

This paper presents an energy-efficient and high-accuracy sampling synchronization approach for real-time synchronous data acquisition in wireless sensor networks (saWSNs). A proprietary protocol based on time-division multiple access (TDMA) and deep energy-efficient coding in sensor firmware is proposed. A real saWSN model based on 2.4 GHz nRF52832 system-on-chip (SoC) sensors was designed and experimentally tested. The obtained results confirmed significant improvements in data synchronization accuracy (even by several times) and power consumption (even by a hundred times) compared to other recently reported studies. The results demonstrated a sampling synchronization accuracy of 0.8 μs and ultra-low power consumption of 15 μW per 1 kb/s throughput for data. The protocol was well designed, stable, and importantly, lightweight. The complexity and computational performance of the proposed scheme were small. The CPU load for the proposed solution was <2% for a sampling event handler below 200 Hz. Furthermore, the transmission reliability was high with a packet error rate (PER) not exceeding 0.18% for TXPWR ≥ -4 dBm and 0.03% for TXPWR ≥ 3 dBm. The efficiency of the proposed protocol was compared with other solutions presented in the manuscript. While the number of new proposals is large, the technical advantage of our solution is significant.

Semantic Tree Based PPDP Technique for Multiple Sensitive Attributes in Inter Cloud

Digital devices and information systems have made data privacy essential. The collected data contains sensitive attributes such as salary, marital status and health history that need to be protected. Such data is exchanged or published to a third party using cloud infrastructure to perform various analyses, conduct research, and make critical decisions. Unauthorized users of the published data may violate privacy, notwithstanding the benefits. Data anonymization is one of the technique for achieving data privacy. Existing techniques consider single sensitive attribute and data is anonymized using generalization or suppression approaches. On observation, it is found that these techniques are less efficient since the collected data contains multiple sensitive attributes when anonymized using the same approaches leads to higher information loss and residue records. In this paper, multiple sensitive attributes are considered and the dataset is anonymized by constructing a semantic hierarchical tree it is further partitioned using the anatomy approach. Later, the partitions are stored in interclouds to achieve better privacy protection. Experiments are conducted to observe and analyze the computational performance, residue records and diversity percentage. The results obtained prove that the proposed technique is efficient when compared to the existing ones.

Navigation Based on Hybrid Decentralized and Centralized Training and Execution Strategy for Multiple Mobile Robots Reinforcement Learning

In addressing the complex challenges of path planning in multi-robot systems, this paper proposes a novel Hybrid Decentralized and Centralized Training and Execution (DCTE) Strategy, aimed at optimizing computational efficiency and system performance. The strategy solves the prevalent issues of collision and coordination through a tiered optimization process. The DCTE strategy commences with an initial decentralized path planning step based on Deep Q-Network (DQN), where each robot independently formulates its path. This is followed by a centralized collision detection the analysis of which serves to identify potential intersections or collision risks. Paths confirmed as non-intersecting are used for execution, while those in collision areas prompt a dynamic re-planning step using DQN. Robots treat each other as dynamic obstacles to circumnavigate, ensuring continuous operation without disruptions. The final step involves linking the newly optimized paths with the original safe paths to form a complete and secure execution route. This paper demonstrates how this structured strategy not only mitigates collision risks but also significantly improves the computational efficiency of multi-robot systems. The reinforcement learning time was significantly shorter, with the DCTE strategy requiring only 3 min and 36 s compared to 5 min and 33 s in the comparison results of the simulation section. The improvement underscores the advantages of the proposed method in enhancing the effectiveness and efficiency of multi-robot systems.

A genetic algorithm and particle swarm optimization for redundancy allocation problem in systems with limited number of non-cooperating repairmen

This article considered the redundancy allocation problem (RAP) in repairable heterogeneous systems composed of k-out-of-n: G subsystems with a limited number of repairmen. The unit costs of the binary-state components within the subsystems remain constant over time. Exponential characteristics of independent failure and repair processes were assumed. To evaluate subsystem and system availability, a Continuous Time Markov Chain (CTMC) adapted to three standby modes (cold, warm, and hot) was developed. The characteristics of the redundant system and the assumption of a limited number of repairmen contribute to the existing scientific literature on RAP. Two nature-inspired metaheuristic approaches were developed to maximize the availability of the coherent system as an objective function to optimize redundancy with a cost constraint on component purchase. The proposed approaches were tested on a 15-unit large-scale system. The effectiveness and performance of the algorithms was evaluated as a function of the number of generations/iterations and population/swarm size. The genetic algorithm (GA) proved to be highly effective in finding the global optimum and outperformed particle swarm optimization (PSO) in terms of computational performance. Analysis of metaheuristic algorithms can offer valuable insights into future research on redundancy optimization. The sensitivity analysis of the large-scale system clearly demonstrates that the number of repairmen and cost constraints (up to three times the sum of the value of active components) have a significant impact on the system’s availability. Above this level, increasing spending on system building, regardless of the number of repairmen, is not justified by considerations of system availability.