Engineering Design Optimization Problems Research Articles

Boosting engineering optimization with a novel recursive transfer bi-fidelity surrogate modeling

Abstract In the engineering optimization, there often exist the multiple sources of information with different fidelity levels. In general, low-fidelity (LF) information is usually more accessible than high-fidelity (HF) information, while the latter is usually more accurate than the former. Thus, to capitalize on the advantages of this information, this study proposes a novel recursive transfer bi-fidelity surrogate modeling to fuse information from HF and LF levels. Firstly, the selection method of optimal scale factor is proposed for constructing bi-fidelity surrogate model. Then, a recursive method is developed to further improve its performance. The efficacy of the proposed model is comprehensively evaluated using numerical problems and an engineering example. Comparative analysis with some surrogate models (five multi-fidelity and a single-fidelity surrogate models) demonstrates the superior prediction accuracy and robustness of the proposed model. Additionally, the impact of varying cost ratios and combinations of HF and LF samples on the performance of the proposed model is also investigated, yielding consistent results. Overall, the proposed model has superior performance and holds potential for practical applications in engineering design optimization problems.

An improved Coati Optimization Algorithm with multiple strategies for engineering design optimization problems

Aiming at the problems of insufficient ability of artificial COA in the late optimization search period, loss of population diversity, easy to fall into local extreme value, resulting in slow convergence and lack of exploration ability; In this paper, an improved COA algorithm based on chaotic sequence, nonlinear inertia weight, adaptive T-distribution variation strategy and alert updating strategy is proposed to enhance the performance of COA (shorted as TNTWCOA). The algorithm introduces chaotic sequence mechanism to initialize the position. The position distribution of the initial solution is more uniform, the high quality initial solution is generated, the population richness is increased, and the problem of poor quality and uneven initial solution of the Coati Optimization Algorithm is solved. In exploration phase, the nonlinear inertial weight factor is introduced to coordinate the local optimization ability and global search ability of the algorithm. In the exploitation phase, adaptive T-distribution variation is introduced to increase the diversity of individual population under low fitness value and improve the ability of the algorithm to jump out of the local optimal value. At the same time, the alert update mechanism is proposed to improve the alert ability of COA algorithm, so that it can search within the optional range. When Coati is aware of the danger, Coati on the edge of the population will quickly move to the safe area to obtain a better position, while Coati in the middle of the population will randomly move to get closer to other Coatis. IEEE CEC2017 with 29 classic test functions were used to evaluate the convergence speed, convergence accuracy and other indicators of TNTWCOA algorithm. Meanwhile, TNTWCOA was used to verify 4 engineering design optimization problems, such as pressure vessel optimization design and welding beam design. The results of IEEE CEC2017 and engineering design Optimization problems are compared with Improved Coati Optimization Algorithm (ICOA), Coati Optimization Algorithm (COA), Golden Jackal Optimization Algorithm (GJO), Osprey Optimization Algorithm (OOA), Sand Cat Swarm Optimization Algorithm (SCSO), Subtraction-Average-Based Optimizer (SABO). The experimental results show that the improved TNTWCOA algorithm significantly improves the convergence speed and optimization accuracy, and has good robustness. Three‑bar truss design problem, The Gear Train Design Problem, Speed reducer design problem shows a strong solution advantage. The superior optimization ability and engineering practicability of TNTWCOA algorithm are verified.

Many-Objective Whale Optimization Algorithm for Engineering Design and Large-Scale Many-Objective Optimization Problems

In this paper, a novel Many-Objective Whale Optimization Algorithm (MaOWOA) is proposed to overcome the challenges of large-scale many-objective optimization problems (LSMOPs) encountered in diverse fields such as engineering. Existing algorithms suffer from curse of dimensionality i.e., they are unable to balance convergence with diversity in extensive decision-making scenarios. MaOWOA introduces strategies to accelerate convergence, balance convergence and diversity in solutions and enhance diversity in high-dimensional spaces. The prime contributions of this paper are—development of MaOWOA, incorporation an Information Feedback Mechanism (IFM) for rapid convergence, a Reference Point-based Selection (RPS) to balance convergence and diversity and a Niche Preservation Strategy (NPS) to improve diversity and prevent overcrowding. A comprehensive evaluation demonstrates MaOWOA superior performance over existing algorithms (MaOPSO, MOEA/DD, MaOABC, NSGA-III) across LSMOP1-LSMOP9 benchmarks and RWMaOP1-RWMaOP5 problems. Results validated using Wilcoxon rank sum tests, highlight MaOWOA excellence in key metrics such as generational distance, spread, spacing, runtime, inverse generational distance and hypervolume, outperforming in 71.8% of tested scenarios. Thus, MaOWOA represents a significant advancement in many-objective optimization, offering new avenues for addressing LSMOPs and RWMaOPs’ inherent challenges. This paper details MaOWOA development, theoretical basis and effectiveness, marking a promising direction for future research in optimization strategies amidst growing problem complexity.

An Improved Multi-Strategy Crayfish Optimization Algorithm for Solving Numerical Optimization Problems.

The crayfish optimization algorithm (COA), proposed in 2023, is a metaheuristic optimization algorithm that is based on crayfish's summer escape behavior, competitive behavior, and foraging behavior. COA has a good optimization performance, but it still suffers from the problems of slow convergence speed and sensitivity to the local optimum. To solve these problems, an improved multi-strategy crayfish optimization algorithm for solving numerical optimization problems, called IMCOA, is proposed to address the shortcomings of the original crayfish optimization algorithm for each behavioral strategy. Aiming at the imbalance between local exploitation and global exploration in the summer heat avoidance and competition phases, this paper proposes a cave candidacy strategy and a fitness-distance balanced competition strategy, respectively, so that these two behaviors can better coordinate the global and local optimization capabilities and escape from falling into the local optimum prematurely. The directly foraging formula is modified during the foraging phase. The food covariance learning strategy is utilized to enhance the population diversity and improve the convergence accuracy and convergence speed. Finally, the introduction of an optimal non-monopoly search strategy to perturb the optimal solution for updates improves the algorithm's ability to obtain a global best solution. We evaluated the effectiveness of IMCOA using the CEC2017 and CEC2022 test suites and compared it with eight algorithms. Experiments were conducted using different dimensions of CEC2017 and CEC2022 by performing numerical analyses, convergence analyses, stability analyses, Wilcoxon rank-sum tests and Friedman tests. Experiments on the CEC2017 and CEC2022 test suites show that IMCOA can strike a good balance between exploration and exploitation and outperforms the traditional COA and other optimization algorithms in terms of its convergence speed, optimization accuracy, and ability to avoid premature convergence. Statistical analysis shows that there is a significant difference between the performance of the IMCOA algorithm and other algorithms. Additionally, three engineering design optimization problems confirm the practicality of IMCOA and its potential to solve real-world problems.

Improved marine predators algorithm for engineering design optimization problems

The Marine Predator Algorithm (MPA) has unique advantages as an important branch of population-based algorithms. However, it emerges more disadvantages gradually, such as traps to local optima, insufficient diversity, and premature convergence, when dealing with complex problems in practical industrial engineering design applications. In response to these limitations, this paper proposes a novel Improved Marine Predator Algorithm (IMPA). By introducing an adaptive weight adjustment strategy and a dynamic social learning mechanism, this study significantly improves the encounter frequency and efficiency between predators and preys in marine ecosystems. The performance of the IMPA was evaluated through benchmark functions, CEC2021 suite problems, and engineering design problems, including welded beam design, tension/compression spring design, pressure vessel design, and three-bar design. The results indicate that the IMPA has achieved significant success in the optimization process over other methods, exhibiting excellent performance in both solving optimal parameter solutions and optimizing objective function values. The IMPA performs well in terms of accuracy and robustness, which also proves its efficiency in successfully solving complex industrial engineering design problems.

Hunger games search algorithm based on stochastic individual information for engineering design optimization problems

Abstract The hunger games search algorithm (HGS) is a newly proposed meta-heuristic algorithm that emulates hunger-driven foraging behaviors in a population. It combines fitness values to determine individual weights and updates them based on fitness value size, resulting in high adaptability and effective optimization. However, HGS faces issues like low convergence accuracy and susceptibility to local optima in complex optimization problems. To address these problems, an improved version called BDFXHGS is introduced. BDFXHGS incorporates a collaborative feeding strategy based on HGS's design advantages. Individuals approach others based on hunger degree, facilitating information exchange and resolving convergence and accuracy issues. BDFXHGS combines a disperse foraging strategy and a directional crossover strategy to enhance exploration and convergence speed. The paper conducts qualitative analysis and ablation experiments to examine the effectiveness of the strategies. Comparative experiments are performed using IEEE CEC 2017 benchmark functions to compare BDFXHGS with competitive algorithms, including previous champion algorithms in different dimensions. Additionally, BDFXHGS is evaluated on 25 constrained optimization problems from the IEEE CEC 2020 competition and 5 real engineering optimization problems. Experimental results show that BDFXHGS performs well on benchmarks and outperforms other algorithms in real-world applications.

An efficient improved exponential distribution optimizer: application to the global, engineering and combinatorial optimization problems

Population-based meta-heuristic optimization algorithms play a vital role in addressing optimization problems. Nowadays, exponential distribution optimizer (EDO) can be considered to be one of the most recent among these algorithms. Although it has achieved many promising results, it has a set of shortcomings, for example, the decelerated convergence, and provides local optima solution as it cannot escape from local regions in addition to imbalance between diversification and intensification. Therefore, in this study, an enhanced variant of EDO called mEDO was proposed to address these shortcomings by combining two efficient search mechanisms named orthogonal learning (OL) and local escaping operator (LEO). In mEDO, the LEO has been exploited to escape local optima and improve the convergence behavior of the EDO by employing random operators to maximize the search process and to effectively discover the globally optima solution. Then the OL has been combined to keep the two phases (i.e., exploration and exploitation) balanced. To validate the effectiveness and performance of the mEDO algorithm, the proposed method has been evaluated over ten functions of the IEEE CEC’2020 test suite as well as eight real-world applications (engineering design optimization problems), Furthermore we test the applicability of the proposed algorithm by tackling 21 instance of the quadratic assignment problem (QAP). The experimental and statistical results of the proposed algorithm have been compared against seven other common metaheuristic algorithms (MAs), including the basic EDO. The results show the supremacy of the mEDO algorithm over the other algorithms and reveal the applicability and effectiveness of the mEDO algorithm compared to well-established metaheuristic algorithms. The experimental results and different statistical measures revealed the reliability and applicability of the mEDO method in solving the global, engineering design, and combinatorial optimization problems by achieving a reasonable solution in terms of scoring a global optima solutions and avoiding premature convergence by increasing the population’s diversity.

Gorilla optimization algorithm combining sine cosine and cauchy variations and its engineering applications

To address the issues of lacking ability, loss of population diversity, and tendency to fall into the local extreme value in the later stage of optimization searching, resulting in slow convergence and lack of exploration ability of the artificial gorilla troops optimizer algorithm (AGTO), this paper proposes a gorilla search algorithm that integrates the positive cosine and Cauchy's variance (SCAGTO). Firstly, the population is initialized using the refractive reverse learning mechanism to increase species diversity. A positive cosine strategy and nonlinearly decreasing search and weight factors are introduced into the finder position update to coordinate the global and local optimization ability of the algorithm. The follower position is updated by introducing Cauchy variation to perturb the optimal solution, thereby improving the algorithm's ability to obtain the global optimal solution. The SCAGTO algorithm is evaluated using 30 classical test functions of Test Functions 2018 in terms of convergence speed, convergence accuracy, average absolute error, and other indexes, and two engineering design optimization problems, namely, the pressure vessel optimization design problem and the welded beam design problem, are introduced for verification. The experimental results demonstrate that the improved gorilla search algorithm significantly enhances convergence speed and optimization accuracy, and exhibits good robustness. The SCAGTO algorithm demonstrates certain solution advantages in optimizing the pressure vessel design problem and welded beam design problem, verifying the superior optimization ability and engineering practicality of the SCAGTO algorithm.

PERFORMANCE EVALUATIONS OF THE MANTA RAY FORAGING OPTIMIZATION ALGORITHM IN REAL-WORLD CONSTRAINED OPTIMIZATION PROBLEMS

Metaheuristic algorithms are often preferred for solving constrained engineering design optimization problems. The most important reason for choosing these algorithms is that they guarantee a satisfactory response within a reasonable time. The swarm intelligence-based manta ray foraging optimization algorithm (MRFO) is a metaheuristic algorithm proposed to solve engineering applications. In this study, the performance of MRFO is evaluated on 19 mechanical engineering optimization problems in the CEC2020 real-world constrained optimization problem suite. In order to increase the MRFO performance, three modifications are made to the algorithm; in this way, the enhanced manta ray foraging optimization (EMRFO) algorithm is proposed. The effects of the modifications made are analyzed and interpreted separately. Its performance has been compared with the algorithms in the literature, and it has been shown that EMRFO is a successful and preferable algorithm for this problem suite.

A Formulation of Structural Design Optimization Problems for Quantum Annealing

We present a novel formulation of structural design optimization problems specifically tailored to be solved by qa. Structural design optimization aims to find the best, i.e., material-efficient yet high-performance, configuration of a structure. To this end, computational optimization strategies can be employed, where a recently evolving strategy based on quantum mechanical effects is qa. This approach requires the optimization problem to be present, e.g., as a qubo model. Thus, we develop a novel formulation of the optimization problem. The latter typically involves an analysis model for the component. Here, we use energy minimization principles that govern the behavior of structures under applied loads. This allows us to state the optimization problem as one overall minimization problem. Next, we map this to a qubo problem that can be immediately solved by qa. We validate the proposed approach using a size optimization problem of a compound rod under self-weight loading. To this end, we develop strategies to account for the limitations of currently available hardware. Remarkably, for small-scale problems, our approach showcases functionality on today’s hardware such that this study can lay the groundwork for continued exploration of qa’s impact on engineering design optimization problems.

An effective theoretical and experimental analysis method for the improved slime mould algorithm

Metaheuristic intelligent optimization algorithms are effective methods for solving high-dimensional nonlinear complex optimization problems. The slime mould algorithm is a novel intelligent optimization algorithm proposed in 2020. However, the basic slime mould algorithm still has some shortcomings, such as slow convergence rate, easy to fall into local extremum, and unbalanced exploration and development capability. To further improve and expand the optimization ability and application scope of the slime mould algorithm, and enhance its performance in solving large-scale complex optimization problems, this paper proposes a slime mould algorithm (PPMSMA) based on Gaussian perturbation and phased position update, positive variation, and multi-strategy greedy selection. Firstly, Gaussian perturbation and phased position update mechanism are introduced to avoid the difficulty of the algorithm to jump out of the local extrema and also to speed up the convergence of the algorithm. Then, a positive variation strategy based on the sine cosine mechanism is introduced to move the variation of the population towards a better direction. Finally, a multi-strategy greedy selection mechanism is introduced, which effectively improves the search ability of the algorithm. The analysis and research on the optimization ability and performance of metaheuristic algorithms mainly include two aspects: theoretical analysis and experimental testing. Theoretical analysis has always been a relatively weak link in the research of metaheuristic algorithms, and there is currently no clear and effective method formed. For experimental testing, although there are more methods, they often lack systematization and adequacy. In this paper, a more complete, fine-grained and systematic approach to theoretical and experimental analysis is proposed. In the theoretical analysis part, the time complexity and spatial complexity of the PPMSMA algorithm are analytically proved to be the same as the basic slime mould algorithm, and the probability measure method is used to prove that PPMSMA algorithm can converge to the global optimal solution. In the simulation experiment section, the PPMSMA algorithm is compared with multiple sets of 10 representative comparison algorithms on the CEC2017 complex test function set suite for optimization accuracy analysis, Friedman comprehensive ranking analysis, average optimization rate analysis of PPMSMA relative to other algorithms, convergence curve analysis, and Wilcoxon rank-sum test analysis. To further examine the scalability of the improved algorithm in solving large-scale optimization problems, PPMSMA is compared with the above 10 comparative algorithms under 1000 dimensional conditions in the large-scale global optimization test set CEC2010, and the solution stability of each algorithm is analyzed through violin plots. The results show that the PPMSMA algorithm has significantly improved convergence performance, optimization accuracy, and solution stability in both high-dimensional and large-scale complex problems, and has significant advantages compared to multiple sets of 10 representative comparative algorithms. Finally, PPMSMA and 10 other comparative algorithms are used to solve engineering design optimization problems with different complexities. The experimental results validate the universality, reliability, and superiority of PPMSMA in handling engineering design constraint optimization problems.

Multi-objective constrained robust design of a metamaterial vibration isolator with a limited budget

Many real-world engineering design optimisation problems encounter input uncertainties, which may introduce undesired fluctuations in design performance or even make the design solution infeasible. Robust design optimisation (RDO) is widely studied due to its ability to deal with uncertainties. RDO methods require many evaluations generally, which is prohibitive when relying on expensive simulations. Surrogate-assisted optimisation can help to reduce the number of simulation calls. An improved constrained multi-objective efficient robust global optimisation method (CMO-ERGO) is proposed in this work, which combines the robust expected improvement of ERGO with the probability of feasibility. CMO-ERGO improves the ERGO framework and quantifies the robustness of the objective and the constraint functions using an analytical uncertainty quantification based on the Kriging surrogate. The proposed method is tested on three numerical benchmark functions and applied to the robust design of a metamaterial vibration isolator with a honeycomb structure to explore its performance in solving engineering applications. The robustness of optimal solutions is demonstrated using the Monte Carlo Method. Moreover, comparisons between CMO-ERGO and several existing RDO methods illustrate the effectiveness and efficiency of CMO-ERGO.

Optimization based on performance of lungs in body: Lungs performance-based optimization (LPO)

The development of efficient optimization algorithms is crucial across various scientific disciplines. As the complexity and diversity of optimization problems continue to grow, researchers seek faster and stronger algorithms capable of optimizing a wide range of functions. This paper introduces Lung performance-based optimization (LPO), a novel and efficient algorithm inspired by the regular and intelligent performance of lungs in the human body. LPO draws inspiration from the intricate mechanisms and adaptability of the respiratory system. The lungs exhibit remarkable efficiency in oxygen exchange, demonstrating a high level of optimization in their function. The forced oscillation technique measures air pressure and airflow rate to evaluate the respiratory system as an electrical impedance. The impedance curves have two distinct components, respiratory resistance (ZR) and respiratory reactance (ZX), which can be analyzed clinically and from an engineering perspective to gain insights into the respiratory system's workings. LPO aims to provide an innovative approach to solving complex optimization problems by emulating and harnessing this natural efficiency. To evaluate the effectiveness of LPO, experiments were conducted using the unconstrained optimization functions CEC2005 and CEC2014, as well as engineering design optimization problems. These problems were compared against numerous contemporary algorithms proposed in the literature. The results demonstrate that LPO excels in handling these optimization problems and exhibits the potential to tackle a wide range of modern optimization challenges. The findings highlight the power and effectiveness of LPO as a new optimization algorithm. With its inspiration rooted in the sophisticated performance of the lungs, LPO offers a unique perspective in the optimization landscape. Its ability to handle diverse optimization problems and its potential for application in various domains make LPO a promising algorithm for future research and practical implementation. Note that the source code of the LPO is publicly available at https://www.optim-app.com/projects/lpo.

An efficient manta ray foraging optimization algorithm with individual information interaction and fractional derivative mutation for solving complex function extremum and engineering design problems

The manta ray foraging optimization algorithm (MRFO) is a recently proposed meta-heuristic algorithm that mimics the foraging process of manta rays. It has yielded good outcomes in solving some optimization problems because its mechanism is clear, no additional parameters need to be set, and the balance between global and local search is good. Nonetheless, while dealing with high-dimensional global optimization and complex engineering optimization problems, there are also issues such as premature convergence, low optimization-seeking accuracy, or unstable solutions. To this end, this article proposes an efficient manta ray foraging optimization algorithm (NIFMRFO) by incorporating individual information interaction and fractional derivative mutation. First, to prevent premature convergence of the algorithm, a nonlinear cosine adjustment parameter is presented, which is intended to make the demand relationship between global exploration and local development more reasonable. Then, an information interaction strategy among random individuals is employed to expedite the rate at which the algorithm converges. Finally, a fractional derivative mutation strategy is utilized to continually enhance individuals’ quality in each iteration, which not only increases the population diversity but also helps to improve the precision and stability of the search results. Theoretical analysis indicates that the improved NIFMRFO algorithm and basic MRFO algorithm have the same time complexity. In simulation experiments, the CEC2017 suite is used to conduct comparison tests with six superior-performance representative comparison algorithms in several dimensions. In terms of the optimization-seeking accuracy, convergence curve, violin plot, and Friedman average ranking, the analysis of these graphs and data shows that the NIFMRFO algorithm’s ameliorated strategy improves superiority-seeking power, convergence speed, and steadiness. Meanwhile, the Wilcoxon rank-sum test result illustrates significant differences between NIFMRFO and other compared algorithms. Finally, these algorithms are utilized to tackle seven realistic engineering design optimization problems. The result makes it clear that NIFMRFO is distinctly superior to the other six algorithms, showing that its solving ability is superior and has broad application prospects.

Physics-Constrained Bayesian Optimization for Optimal Actuators Placement in Composite Structures Assembly

Complex constrained global optimization problems such as optimal actuators placement are extremely challenging. Such challenges, including nonlinearity and nonstationarity of engineering response surfaces, hinder the use of ordinary constrained Bayesian optimization (CBO) techniques with standard Gaussian processes as surrogate models. To overcome those challenges, we propose a physics-constrained Bayesian optimization with multi-layer deep structured Gaussian processes, <i>MGP-CBO</i>. Specifically, we introduce a surrogate model with a multi-layer deep Gaussian process (MGP) mean function. The hierarchical structure of our model enables the applicability of constrained Bayesian optimization to complex nonlinear and nonstationary processes. The deep Gaussian process regression model, <i>MGP</i>, can efficiently and effectively represent the response surface function between actuators and dimensional deformations, thus yielding a better estimated global optimum in a shorter computational time. The proposed <i>MGP-CBO</i> model can realize faster convergence to the global optimum with lower constraint violations. Through extensive evaluations carried out on synthetic problems and a real-world engineering design problem, we show that <i>MGP-CBO</i> outperforms existing benchmarks. Although we use the optimal actuators placement as a demonstration example, the proposed <i>MGP-CBO</i> model can be applied to other complex nonstationary engineering optimization problems. <i>Note to Practitioners</i>&#x2014;Bayesian optimization is a widely used sequential design strategy for engineering optimization because it does not rely on functional forms of response surfaces. This paper helps address two questions in practice: (i) how to incorporate physics constraints into Bayesian optimization. (ii) How to do Bayesian optimization when the systems have hierarchical structures. In practice, the hierarchical system structure is ubiquitous, and the engineering optimization is constrained by physical laws or special requirements. Therefore, the proposed physics-constrained Bayesian optimization with a multi-layer Gaussian process could provide a new tool for engineering design optimization problems. The computational convergence and complexity have been investigated. The proposed method is applicable to broad complex and nonstationary engineering optimization problems.

Resistance–capacitance optimizer: a physics-inspired population-based algorithm for numerical and industrial engineering computation problems

The primary objective of this study is to delve into the application and validation of the Resistance Capacitance Optimization Algorithm (RCOA)—a new, physics-inspired metaheuristic optimization algorithm. The RCOA, intriguingly inspired by the time response of a resistance–capacitance circuit to a sudden voltage fluctuation, has been earmarked for solving complex numerical and engineering design optimization problems. Uniquely, the RCOA operates without any control/tunable parameters. In the first phase of this study, we evaluated the RCOA's credibility and functionality by deploying it on a set of 23 benchmark test functions. This was followed by thoroughly examining its application in eight distinct constrained engineering design optimization scenarios. This methodical approach was undertaken to dissect and understand the algorithm's exploration and exploitation phases, leveraging standard benchmark functions as the yardstick. The principal findings underline the significant effectiveness of the RCOA, especially when contrasted against various state-of-the-art algorithms in the field. Beyond its apparent superiority, the RCOA was put through rigorous statistical non-parametric testing, further endorsing its reliability as an innovative tool for handling complex engineering design problems. The conclusion of this research underscores the RCOA's strong performance in terms of reliability and precision, particularly in tackling constrained engineering design optimization challenges. This statement, derived from the systematic study, strengthens RCOA's position as a potentially transformative tool in the mathematical optimization landscape. It also paves the way for further exploration and adaptation of physics-inspired algorithms in the broader realm of optimization problems.

Artificial ecosystem optimization by means of fitness distance balance model for engineering design optimization

Optimization techniques have contributed to significant strides in complex real-world engineering problems. However, they must overcome several difficulties, such as the balance between the capacities for exploitation and exploration and avoiding local optimum. An enhanced Artificial Ecosystem Optimization (AEO) is proposed incorporating Fitness Distance Balance Model (FDB) for handling various engineering design optimization problems. In the proposed optimizer, the combined FDB design aids in selecting individuals who successfully contribute to population-level searches. Therefore, the FDB model is integrated with the AEO algorithm to increase the solution quality in nonlinear and multidimensional optimization situations. The FDBAEO is developed for handling six well-studied engineering optimization tasks considering the welded beam, the rolling element bearing, the pressure vessel, the speed reducer, the planetary gear train, and the hydrostatic thrust bearing design problems. The simulation outcomes were evaluated compared to the systemic AEO algorithm and other recent meta-heuristic approaches. The findings demonstrated that the FDBAEO reached the global optimal point more successfully. It has demonstrated promising abilities. Also, the proposed FDBAEO shows greater outperformance compared to several recent algorithms of Atomic Orbital Search, Arithmetic-Trigonometric, Beluga whale, Chef-Based, and Artificial Ecosystem Optimizers. Moreover, it declares great superiority compared to various reported optimizers.

Letter: Application of optimization algorithms to engineering design problems and discrepancies in mathematical formulas

Engineering design optimization problems have attracted the attention of researchers since they appeared. Those who work on developing optimization algorithms, in particular, apply their developed algorithms to these problems in order to test their new algorithms’ capabilities. The mathematical discrepancy emerges during the implementation of equations and constraints related to these engineering problems. This is due to an error occurring in writing or transmitting these equations from one paper to another. Maintaining these discrepancies will have a negative impact on the assessment and model performance verification of the newly developed algorithms, as well as the decision-making process. To address this issue, this study investigates the mathematical discrepancies occurred by researchers in four well-known engineering design optimization problems (Welded Beam Design WBD, Speed Reducer Design SRD, Cantilever Beam Design CBD, and Multiple Disk Clutch Brake Design MDCBD). We have investigated some of the recently published papers in the literature, identifying discrepancies in their mathematical formulas, and fixing them appropriately by referring and comparing them to the original problem. Furthermore, all mathematical discrepancies , references, parameters, cost functions, constraints, and constraint errors are highlighted, arranged and organized in tables. As a result, this work can help readers and researchers avoid being confused and wasting time when working on these engineering design optimization problems.

A multi-strategy enhanced African vultures optimization algorithm for global optimization problems

Abstract The African vultures optimization algorithm (AVOA) is a recently proposed metaheuristic inspired by the African vultures’ behaviors. Though the basic AVOA performs very well for most optimization problems, it still suffers from the shortcomings of slow convergence rate and local optimal stagnation when solving complex optimization tasks. Therefore, this study introduces a modified version named enhanced AVOA (EAVOA). The proposed EAVOA uses three different techniques namely representative vulture selection strategy, rotating flight strategy, and selecting accumulation mechanism, respectively, which are developed based on the basic AVOA. The representative vulture selection strategy strikes a good balance between global and local searches. The rotating flight strategy and selecting accumulation mechanism are utilized to improve the quality of the solution. The performance of EAVOA is validated on 23 classical benchmark functions with various types and dimensions and compared to those of nine other state-of-the-art methods according to numerical results and convergence curves. In addition, three real-world engineering design optimization problems are adopted to evaluate the practical applicability of EAVOA. Furthermore, EAVOA has been applied to classify multi-layer perception using XOR and cancer datasets. The experimental results clearly show that the EAVOA has superiority over other methods.

Al-Biruni Earth Radius (BER) Metaheuristic Search Optimization Algorithm

Metaheuristic optimization algorithms present an effective method for solving several optimization problems from various types of applications and fields. Several metaheuristics and evolutionary optimization algorithms have been emerged recently in the literature and gained widespread attention, such as particle swarm optimization (PSO), whale optimization algorithm (WOA), grey wolf optimization algorithm (GWO), genetic algorithm (GA), and gravitational search algorithm (GSA). According to the literature, no one metaheuristic optimization algorithm can handle all present optimization problems. Hence novel optimization methodologies are still needed. The Al-Biruni earth radius (BER) search optimization algorithm is proposed in this paper. The proposed algorithm was motivated by the behavior of swarm members in achieving their global goals. The search space around local solutions to be explored is determined by Al-Biruni earth radius calculation method. A comparative analysis with existing state-of-the-art optimization algorithms corroborated the findings of BER’s validation and testing against seven mathematical optimization problems. The results show that BER can both explore and avoid local optima. BER has also been tested on an engineering design optimization problem. The results reveal that, in terms of performance and capability, BER outperforms the performance of state-of-the-art metaheuristic optimization algorithms.