Iterative Algorithm Research Articles

Research on robot tracking force control algorithm based on neural networks

Purpose This study aims to propose a force control algorithm based on neural networks, which enables a robot to follow a changing reference force trajectory when in contact with human skin while maintaining a stable tracking force. Design/methodology/approach Aiming at the challenge of robots having difficulty tracking changing force trajectories in skin contact scenarios, a single neuron algorithm adaptive proportional – integral – derivative online compensation is used based on traditional impedance control. At the same time, to better adapt to changes in the skin contact environment, a gated recurrent unit (GRU) network is used to model and predict skin elasticity coefficients, thus adjusting to the uncertainty of skin environments. Findings In two robot–skin interaction experiments, compared with the traditional impedance control and robot force control algorithm based on the radial basis function model and iterative algorithm, the maximum absolute force error, the average absolute force error and the standard deviation of the force error are all decreased. Research limitations/implications As the training process of the GRU network is currently conducted offline, the focus in the subsequent phase is to refine the network to facilitate real-time computation of the algorithm. Practical implications This algorithm can be applied to robot massage, robot B-ultrasound and other robot-assisted treatment scenarios. Originality/value As the proposed approach obtains effective force tracking during robot–skin contact and is verified by the experiment, this approach can be used in robot–skin contact scenarios to enhance the accuracy of force application by a robot.

Attention-Guided Low-Rank Tensor Completion.

Low-rank tensor completion (LRTC) aims to recover missing data of high-dimensional structures from a limited set of observed entries. Despite recent significant successes, the original structures of data tensors are still not effectively preserved in LRTC algorithms, yielding less accurate restoration results. Moreover, LRTC algorithms often incur high computational costs, which hinder their applicability. In this work, we propose an attention-guided low-rank tensor completion (AGTC) algorithm, which can faithfully restore the original structures of data tensors using deep unfolding attention-guided tensor factorization. First, we formulate the LRTC task as a robust factorization problem based on low-rank and sparse error assumptions. Low-rank tensor recovery is guided by an attention mechanism to better preserve the structures of the original data. We also develop implicit regularizers to compensate for modeling inaccuracies. Then, we solve the optimization problem by employing an iterative technique. Finally, we design a multistage deep network by unfolding the iterative algorithm, where each stage corresponds to an iteration of the algorithm; at each stage, the optimization variables and regularizers are updated by closed-form solutions and learned deep networks, respectively. Experimental results for high dynamic range imaging and hyperspectral image restoration show that the proposed algorithm outperforms state-of-the-art algorithms.

Iterative Stress Reconstruction Algorithm to Estimate Three-Dimensional Residual Stress Fields in Manufactured Components

Abstract Residual stress (RS) significantly impacts the mechanical performance of components. Measurement of RS often provides incomplete data in terms of components of stress and spatial density. Employing such fields in finite element simulations results in significant modification of the field to achieve equilibrium and compatibility among strains. To overcome this, an iterative stress reconstruction algorithm (ISRA) is developed to estimate 3D RS fields that satisfy equilibrium, are stress component-wise complete, and represent the characterized data sampled. An Al 7075-T651 plate and an additively manufactured (AM) A36 steel wall are considered for RS reconstruction using measurement data from the literature. A maximum variation of ∼2.5 MPa in the Al plate, and ∼10 MPa in the steel wall are observed between the reconstructed and measured stresses. Furthermore, unknown stress components emerge and reach significant magnitudes (upto ∼2.3 MPa in the Al plate and ∼45 MPa in the AM wall) during ISRA. Indeed, it is found that minor errors in measurement or data processing are eliminated through the physical requirements during ISRA. Employing a reconstructed RS field is hence not just more accurate given its compatibility, but it additionally corrects for minor errors in measurement. Furthermore, it is found that spatially dense measurement data result in convergence with fewer iterations. Finally, although ISRA yields a nonunique solution dependent on boundary conditions, measurement errors, fitting errors, and mesh density, it accommodates for uncertainties and inaccuracies in measurement, as opposed to failing to reach a physically realistic converged solution.

Incoherent frequency-selective multiplexing holographic encryption by using a triple-beam setup

Inspired by the wavefront masking of the scattering medium, we proposed a multiplexed coded aperture holographic encryption method. The incoherent multiplexed phase mask encryption experiments involved in the method are realized for what we believe to be the first time. From the holograms, we extracted three images using the frequency-selective phase iterative coding algorithm we purposely put forward. Through the theoretical analysis of frequency-selective phase coding, the constructed linear system can recover the original image well. We verified the security of the cryptography using structural similarity index measurements, key space, key sensitivity, and axial multiplexing. Through the theoretical analysis of frequency-selective phase coding, we think the present triple-multiplexed cryptography can be directly extended to multiple-multiplexed cases and applied to multi-image encryption. It may cause a paradigm shift in applications such as incoherent image encryption, wavefront acquisition in scattering, information hiding, and fast target identification.

A novel treatment planning method via scissor beams for uniform-target-dose proton GRID with peak-valley-dose-ratio optimization.

Proton spatially fractionated RT (SFRT) can potentially synergize the unique advantages of using proton Bragg peak and SFRT peak-valley dose ratio (PVDR) to reduce the radiation-induced damage for normal tissues. Uniform-target-dose (UTD) proton GRID is a proton SFRT modality that can be clinically desirable and conveniently adopted since its UTD resembles target dose distribution in conventional proton RT (CONV). However, UTD proton GRID is not used clinically, which is likely due to the lack of an effective treatment planning method. This work will develop a novel treatment planning method using scissor beams (SB) for UTD proton GRID, with the joint optimization of PVDR and dose objectives. The SB method for spatial dose modulation in normal tissues with UTD has two steps: (1) a primary beam (PB) is halved with interleaved beamlets, to generate spatial dose modulation in normal tissues; (2) a complementary beam (CB) is added to fill in previously valley-dose positions in the target to generate UTD, while the CB is angled slightly from the PB, to maintain spatial dose modulation in normal tissues. A treatment planning method with PVDR optimization via the joint total variation and L1 (TVL1) regularization is developed to jointly optimize PVDR and dose objectives. The plan optimization solution is obtained using an iterative convex relaxation algorithm. The new methods SB and SB-TVL1 were validated in comparison with CONV. Compared to CONV of relatively homogeneous dose distribution, SB had modulated spatial dose pattern in normal tissues with UTD and comparable plan quality. Compared to SB, SB-TVL1 further maximized PVDR, with comparable dose-volume parameters. A novel SB method is proposed that can generate modulated spatial dose pattern in normal tissues to achieve UTD proton GRID. A treatment planning method with PVDR optimization capability via TVL1 regularization is developed that can jointly optimize PVDR and dose objectives for proton GRID.

Energy transfer, conversion and mechanical regulation in graded piezoelectric semiconductor bipolar junction transistor

While the effective regulation of carrier redistribution in piezoelectric semiconductor devices by mechanical loads through piezoelectric polarized electric fields is well-studied, there is a scarcity of reported research on the influence of energy transfer and conversion characteristics in a non-thermal equilibrium state of these devices. This paper establishes a nonlinear multi-field coupling model for piezoelectric semiconductor graded bipolar junction transistor (PS-GBJT) and proposes a corresponding multi-gradient iterative algorithm. We regard the product of current and built-in electric field as the work done by electric field force on carriers. By incorporating the energy absorbed/released during carrier recombination/generation process, we observe that non-equilibrium carriers act as a medium that facilitates energy conversion between these two mechanisms. Additionally, the non-uniformly distributed doping extends the influence of space charge region throughout entire transistor. In terms of external input electrical energy, the emitter, base, and collector regions play roles of input energy, transfer energy, and output energy, respectively. The study concludes by demonstrating the regulation of energy transfer or conversion efficiency in emitter, base, and collector regions through mechanical loads, thereby altering the heating behavior of entire GBJT and reshaping its energy transfer path. This leads to the significant finding that distinct energy transfer paths fundamentally define the various operational states of GBJT. The novel insights gained from this research hold reference value for thermal design and energy management of electronic devices.

Coordinative dispatching of shared and public transportation under passenger flow outburst

In the passenger flow outburst area (e.g., metro emergency, dispersal of sporting events, and concerts), passengers put forward large demand for ride-sourcing services. Insufficient ride-sourcing supply of the area induces increasing matching time, and the ride-sourcing influx from outside picking up passengers leads to heavier road traffic congestion in the flow outburst area. To solve this problem, we propose a novel coordinative dispatching method of ride-sourcing and multi-modal transit, in which subsidies and buses are provided for passengers in flow outburst areas to encourage taking other public transportation to low passenger flow areas first and then taking ride-sourcing to their destinations. In this paper, there are two options for passengers: (a) wait for ride-sourcing to pick them up; (b) take other public transportation first and then take ride-sourcing. To obtain the optimal dispatching and subsidy schemes, we develop a bi-level mixed integer programming model based on network flow theory and design the corresponding iterative algorithm to solve it. Considering the high uncertainty of ride-sourcing demand in the area, we further develop a robust optimization model to obtain more reliable schemes. Case studies based on a real-problem-scale dataset are conducted. The results demonstrate that our approach can be carried out in real time, and encouraging passengers to take multi-modal transit shows great potential in reducing affected users’ delays. The robust optimization model offers a more reliable and competitive solution when demand varies widely. Our method offers a win–win–win way for passengers, ride-sourcing service providers, and public transportation systems.

One step inversion free iterative algorithm for computing generalised bisymmetric solution for nonlinear matrix equations

In this paper, we investigate one step inversion free iterative algorithm for computing generalised bisymmetric solution to the nonlinear matrix equations (NLME) X + A T X − q A + B T X − q B = H ( q ≥ 2 ) , where A , B , H are given matrices, while X is a generalised bisymmetric matrix to be computed. The necessary conditions for the existence of a generalised bisymmetric solution and the convergence of the suggested iterative method are derived. Some lemmas and theorems are provided and proved where the iterative solutions are obtained. Four numerical examples are presented to exhibit the effectiveness of the suggested method and to verify the theoretical findings of this paper.

Cayley Rotation Averaging: Multiple Camera Averaging Under the Cayley Framework.

Rotation averaging, which aims to calculate the absolute rotations of a set of cameras from a redundant set of their relative rotations, is an important and challenging topic arising in the study of structure from motion. A central problem in rotation averaging is how to alleviate the influence of noise and outliers. Addressing this problem, we investigate rotation averaging under the Cayley framework in this paper, inspired by the extra-constraint-free nature of the Cayley rotation representation. Firstly, for the relative rotation of an arbitrary pair of cameras regardless of whether it is corrupted by noise/outliers or not, a general Cayley rotation constraint equation is derived for reflecting the relationship between this relative rotation and the absolute rotations of the two cameras, according to the Cayley rotation representation. Then based on such a set of Cayley rotation constraint equations, a Cayley-based approach for Rotation Averaging is proposed, called CRA, where an adaptive regularizer is designed for further alleviating the influence of outliers. Finally, a unified iterative algorithm for minimizing some commonly-used loss functions is proposed under this approach. Experimental results on 16 real-world datasets and multiple synthetic datasets demonstrate that the proposed CRA approach achieves a better accuracy in comparison to several typical rotation averaging approaches in most cases.

Trustful double auction design for Peer-to-Peer energy trading between interconnected micro-grids with supply–demand imbalance

Peer-to-Peer (P2P) energy trading between Interconnected Micro-Grids (IMGs) presents a promising approach for enhancing the economic advantages for prosumers while mitigating supply–demand imbalances within individual Micro-Grids (MGs). This paper proposes a trustful double auction mechanism for P2P energy trading among prosumers in IMGs, structured into two distinct stages. Initially, concurrent auctions are conducted within each MG to facilitate intra-grid trading, followed by subsequent auctions facilitating inter-grid trading across IMGs. We figure out the allocation and pricing rules that satisfy the required properties in mechanism design even when the auction consists of two stages. Given that energy transactions across IMGs entail non-negligible power losses, equitable allocation of these losses among prosumers is paramount. To address this, we integrate a fair cost distribution methodology into our auction mechanism, implemented by an iterative algorithm. Rigorous analysis substantiates our proposed auction mechanism’s incentive compatibility, individual rationality, and budget balance, thereby fostering truthful and voluntary prosumer participation while averting potential market deficits. Numerical analysis underscores the efficacy of our approach, showcasing a significant improvement in P2P transactions and supply–demand balance enhancement compared to trading solely within individual MGs.

A Gramian matrix approach to synthesizing finite-frequency H2 controller

This paper studies the H2 control problem for linear continuous-time systems over a finite-frequency range. Using the finite-frequency Gramian matrix approach, a necessary and sufficient condition is obtained for the characterization of the finite-frequency H2 performance of a Hurwitz stability system. With such a characterization, a sufficient condition for the solvability of the finite-frequency H2 control problem is derived. An iterative algorithm is then constructed to solve the corresponding controller gain numerically. Finally, a numerical example of a two-cart-one-spring system is given to illustrate the effectiveness of the proposed scheme.

Dynamic Flow Algorithm with Intermediate Storage for Emergency Evacuation Allowing Lane Reversal based on Incomplete Intuitionistic Fuzzy Preference Relation

Background Evacuation in case of disasters is of the greatest importance because of significant occurrences of natural and artificial disasters worldwide, which is why a reliable evacuation plan is always needed. However, evacuation models are difficult to develop due to various uncertain aspects that need to be considered, multiple and often conflicting criteria for evaluation and as lack of expertise regarding a specific preference of alternatives. Objective This study aims to transport the maximum number of evacuees in a dynamic network with lane reversal by a safe pattern of transportation, i.e., allowing storage at intermediate nodes. The optimal order of shelters and intermediate nodes for a reliable evacuation plan will be defined by incomplete intuitionistic fuzzy preference relation. Methods The illustrated method incorporates multiple and often conflicting criteria into a process of emergency decision-making. When evaluating evacuation alternatives, a decision-maker may hesitate and be unsure which alternative is better or not have sufficient expertise to evaluate a pair of alternatives. To model uncertainty and hesitation, intuitionistic fuzzy values are used to describe alternatives in more detail. This study relies on flow models and graph theory to simulate the movement of evacuees to safe destinations. Furthermore, fuzzy methods and their recent modifications are applied to determine the effective priority order of shelters. A case study which simulates the evacuation of aggrieved to safe destinations is presented. Results A method of evaluating the shelters and intermediate nodes for evacuation based on incomplete intuitionistic fuzzy preference relation is proposed. The method allows the missed values of experts’ assessments to be filled in regarding the evacuation alternatives and deals with intuitionistic fuzzy values, which describe experts’ hesitation. The dynamic character of flow distribution enables transit arc capacities and time factors to be processed. The contraflow technique, which is a powerful tool to decrease traffic jams and congestion on roads by reversing the movement along the unused segments, is applied to maximize the number of survivors. Conclusion The results of the method were compared to those of existing methods, and their consistency was proved. In the future, we intend to apply interval-valued intuitionistic preference relations and iterative algorithms to improve the consistency of intuitionistic preference relations to the tasks of transporting the maximum possible number of aggrieved to safe locations.

Fluid–Structure Interaction Analysis of Manta-Bots with Self-Induced Vertical Undulations during Fin-Based Locomotion

Driven by the demands of ocean exploration, an increasing number of manta ray-inspired robots have been designed and manufactured, primarily utilizing flexible skeletons combined with motor-driven mechanisms. However, the mechanical analysis of these designs remains underdeveloped, often relying on simplistic imitation of biological prototypes and typically neglecting the vertical motion induced by pectoral fin flapping. This paper presents a fluid–structure interaction analysis framework that couples rigid body motion with elastic deformation using flexible multibody dynamics and the vortex particle method. An implicit iterative algorithm with Aitken relaxation is employed to address added-mass instability, and the framework has been validated against experimental data. An analysis of a representative manta-bot model shows that self-induced vertical undulations reduce the thrust coefficient by approximately 40% compared to fixed vertical degrees of freedom, while slightly improving overall propulsive efficiency. The study also highlights the critical role of mass distribution in manta-bots, noting that excessive focus on complex pectoral fin movements and large fin mass can significantly reduce thrust by increasing vertical displacement, ultimately proving counterproductive.

Joint mining of fluid knowledge and multi-sensor data for gas–water two-phase flow status monitoring and evolution analysis

Gas-water two-phase flow process widely exists in petroleum, chemical and other industrial processes, which is intricate, manifested by dynamic evolution of fluid structures and real-time fluctuation of flow parameters. Detailed description and real-time monitoring of flow status are of great significance to safe operation of industry processes. In this paper, a monitoring framework jointly mining the fluid knowledge and latent property behind multi-sensor data is proposed to address the issues of uncertainty and sample scarcity in transitional flow statuses, which enables real-time monitoring on structural evolution and parameter change of flow process. Firstly, the shared iterative algorithm with multi-task weight discovery is proposed to establish the relative semantic description system to characterize flow process knowledge by mining the relationship between multi-sensor data and different fluid semantic properties, which is helpful for interpretable monitoring of flow status structure and parameter information. Secondly, latent properties mined from multi-sensor data by sparse exponential discriminant analysis contribute to flow characterization completeness and discrimination. Thirdly, the process knowledge and latent information of flow status is transformed into different degrees of describable semantic and latent properties, which obtain relative representations of flow status in the joint description space realized by rank support vector machine. The results demonstrate that the method enables precise monitoring and detailed description of typical and uncertain flow statuses in the absence of transitional flow status modeling samples.

A Data and Model-Driven Clutter Suppression Method for Airborne Bistatic Radar Based on Deep Unfolding

Space–time adaptive processing (STAP) based on sparse recovery achieves excellent clutter suppression and target detection performance, even with a limited number of available training samples. However, most of these methods face performance degradation due to grid mismatch, which impedes their application in bistatic clutter suppression. Some gridless methods, such as atomic norm minimization (ANM), can effectively address grid mismatch issues, yet they are sensitive to parameter settings and array errors. In this article, the authors propose a data and model-driven algorithm that unfolds the iterative process of atomic norm minimization into a deep network. This approach establishes a concrete and systematic link between iterative algorithms, extensively utilized in signal processing, and deep neural networks. This methodology not only addresses the challenges associated with parameter settings in traditional optimization algorithms, but also mitigates the lack of interpretability issues commonly found in deep neural networks. Moreover, due to more rational parameter settings, the proposed algorithm achieves effective clutter suppression with fewer iterations, thereby reducing computational time. Finally, extensive simulation experiments demonstrate the effectiveness of the proposed algorithm in clutter suppression for airborne bistatic radar.

A Data and Model-Driven Clutter Suppression Method for Airborne Bistatic Radar Based on Deep Unfolding

Space–time adaptive processing (STAP) based on sparse recovery achieves excellent clutter suppression and target detection performance, even with a limited number of available training samples. However, most of these methods face performance degradation due to grid mismatch, which impedes their application in bistatic clutter suppression. Some gridless methods, such as atomic norm minimization (ANM), can effectively address grid mismatch issues, yet they are sensitive to parameter settings and array errors. In this article, the authors propose a data and model-driven algorithm that unfolds the iterative process of atomic norm minimization into a deep network. This approach establishes a concrete and systematic link between iterative algorithms, extensively utilized in signal processing, and deep neural networks. This methodology not only addresses the challenges associated with parameter settings in traditional optimization algorithms, but also mitigates the lack of interpretability issues commonly found in deep neural networks. Moreover, due to more rational parameter settings, the proposed algorithm achieves effective clutter suppression with fewer iterations, thereby reducing computational time. Finally, extensive simulation experiments demonstrate the effectiveness of the proposed algorithm in clutter suppression for airborne bistatic radar.

Adaptive Fuzzy Fault-Tolerant Attitude Control for a Hypersonic Gliding Vehicle: A Policy-Iteration Approach

In this paper, adaptive fuzzy fault-tolerant control (AFFTC) for the attitude control system of a hypersonic gliding vehicle (HGV) experiencing an actuator fault is proposed. Actuator faults of the HGV are considered with respect to its actual structure and actuator characteristics. The HGV’s attitude system is firstly represented by a T–S fuzzy model, and then a normal T–S fuzzy controller is designed. A reinforcement learning (RL)-based policy iterative solution algorithm is proposed for the solving of the T-S fuzzy controller. Then, based on the normal T–S controller, a fuzzy FTC controller is proposed in which the control matrices can improve themselves according to the special fault. An integral reinforcement learning (IRL)-based solving algorithm is proposed to reduce the dependence of the design methods on the HGV model. Simulations on three different kinds of actuator faults show that the designed IRL-based FTC can ensure a reliable flight by the HGV.

Quadrature based innovative techniques concerning nonlinear equations having unknown multiplicity

Solution of nonlinear equations is one of the most frequently encountered issue in engineering and applied sciences. Most of the intricateed engineering problems are modeled in the frame work of nonlinear equation f(x)=0. The significance of iterative algorithms executed by computers in resolving such functions is of paramount importance and undeniable in contemporary times. If we study the simple roots and the roots having multiplicity greater of any nonlinear equations we come to the point that finding the roots of nonlinear equations having multiplicity greater than one is not trivialvia classical iterative methods. Instability or slow convergence rate is faced by these methods, and also sometimes these methods diverge. In this article, we give some innovative and robust iterative techniques for obtaining the approximate solution of nonlinear equations having multiplicity m>1. Quadrature formulas are implemented to obtain iterative techniques for finding roots of nonlinear equations having unknown multiplicity. The derived methods are the variants of modified Newton method with high order of convergence and better accuracy. The convergence criteria of the new techniques are studied by using Taylor series method. Some examples are tested for the sack of implementations of these techniques. Numerical and graphical comparison shows the performance and efficiency of these new techniques.

Optimization of Large-Scale Sparse Matrix-Vector Multiplication on Multi-GPU Systems

Sparse matrix-vector multiplication (SpMV) is one of the important kernels of many iterative algorithms for solving sparse linear systems. The limited storage and computational resources of individual GPUs restrict both the scale and speed of SpMV computing in problem-solving. As real-world engineering problems continue to increase in complexity, the imperative for collaborative execution of iterative solving algorithms across multiple GPUs is increasingly apparent. Although the multi-GPU-based SpMV takes less kernel execution time, it also introduces additional data transmission overhead, which diminishes the performance gains derived from parallelization across multi-GPUs. Based on the non-zero elements distribution characteristics of sparse matrices and the trade-off between redundant computations and data transfer overhead, this paper introduces a series of SpMV optimization techniques tailored for multi-GPU environments and effectively enhances the execution efficiency of iterative algorithms on multiple GPUs. Firstly, we propose a two-level non-zero elements-based matrix partitioning method to increase the overlap of kernel execution and data transmission. Then, considering the irregular non-zero elements distribution in sparse matrices, a long-row-aware matrix partitioning method is proposed to hide more data transmissions. Finally, an optimization using redundant and inexpensive short-row execution to exchange costly data transmission is proposed. Our experimental evaluation demonstrates that, compared with the SpMV on a single GPU, the proposed method achieves an average speedup of 2.00x and 1.85x on platforms equipped with two RTX 3090 and two Tesla V100-SXM2, respectively. The average speedup of 2.65x is achieved on a platform equipped with four Tesla V100-SXM2.

Multi-objective energy management in a renewable and EV-integrated microgrid using an iterative map-based self-adaptive crystal structure algorithm

The use of plug-in hybrid electric vehicles (PHEVs) provides a way to address energy and environmental issues. Integrating a large number of PHEVs with advanced control and storage capabilities can enhance the flexibility of the distribution grid. This study proposes an innovative energy management strategy (EMS) using an Iterative map-based self-adaptive crystal structure algorithm (SaCryStAl) specifically designed for microgrids with renewable energy sources (RESs) and PHEVs. The goal is to optimize multi-objective scheduling for a microgrid with wind turbines, micro-turbines, fuel cells, solar photovoltaic systems, and batteries to balance power and store excess energy. The aim is to minimize microgrid operating costs while considering environmental impacts. The optimization problem is framed as a multi-objective problem with nonlinear constraints, using fuzzy logic to aid decision-making. In the first scenario, the microgrid is optimized with all RESs installed within predetermined boundaries, in addition to grid connection. In the second scenario, the microgrid operates with a wind turbine at rated power. The third case study involves integrating plug-in hybrid electric vehicles (PHEVs) into the microgrid in three charging modes: coordinated, smart, and uncoordinated, utilizing standard and rated RES power. The SaCryStAl algorithm showed superior performance in operation cost, emissions, and execution time compared to traditional CryStAl and other recent optimization methods. The proposed SaCryStAl algorithm achieved optimal solutions in the first scenario for cost and emissions at 177.29 €ct and 469.92 kg, respectively, within a reasonable time frame. In the second scenario, it yielded optimal cost and emissions values of 112.02 €ct and 196.15 kg, respectively. Lastly, in the third scenario, the SaCryStAl algorithm achieves optimal cost values of 319.9301 €ct, 160.9827 €ct and 128.2815 €ct for uncoordinated charging, coordinated charging and smart charging modes respectively. Optimization results reveal that the proposed SaCryStAl outperformed other evolutionary optimization algorithms, such as differential evolution, CryStAl, Grey Wolf Optimizer, particle swarm optimization, and genetic algorithm, as confirmed through test cases.