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With the rapid development of the economy, the disparity between supply and demand of resources is becoming increasingly prominent in engineering design. In this paper, an improved gray wolf optimization algorithm is proposed (IGWO) to optimize engineering design problems. First, a tent map is used to generate the initial location of the gray wolf population, which evenly distributes the gray wolf population and lays the foundation for a diversified global search process. Second, Gaussian mutation perturbation is used to perform various operations on the current optimal solution to avoid the algorithm falling into local optima. Finally, a cosine control factor is introduced to balance the global and local exploration capabilities of the algorithm and to improve the convergence speed. The IGWO algorithm is applied to four engineering optimization problems with different typical complexity, including a pressure vessel design, a tension spring design, a welding beam design and a three-truss design. The experimental results show that the IGWO algorithm is superior to other comparison algorithms in terms of optimal performance, solution stability, applicability and effectiveness; and can better solve the problem of resource waste in engineering design. The IGWO also optimizes 23 different types of function problems and uses Wilcoxon rank-sum test and Friedman test to verify the 23 test problems. The results show that the IGWO algorithm has higher convergence speed, convergence precision and robustness compared with other algorithms.

As a newly proposed optimization algorithm based on the social hierarchy and hunting behavior of gray wolves, grey wolf algorithm (GWO) has gradually become a popular method for solving the optimization problems in various engineering fields. In order to further improve the convergence speed, solution accuracy, and local minima escaping ability of the traditional GWO algorithm, this work proposes a multi-strategy fusion improved gray wolf optimization (IGWO) algorithm. First, the initial population is optimized using the lens imaging reverse learning algorithm for laying the foundation for global search. Second, a nonlinear control parameter convergence strategy based on cosine variation is proposed to coordinate the global exploration and local exploitation ability of the algorithm. Finally, inspired by the tunicate swarm algorithm (TSA) and the particle swarm algorithm (PSO), a nonlinear tuning strategy for the parameters, and a correction based on the individual historical optimal positions and the global optimal positions are added in the position update equations to speed up the convergence of the algorithm. The proposed algorithm is assessed using 23 benchmark test problems, 15 CEC2014 test problems, and 2 well-known constraint engineering problems. The results show that the proposed IGWO has a balanced E&P capability in coping with global optimization as analyzed by the Wilcoxon rank sum and Friedman tests, and has a clear advantage over other state-of-the-art algorithms.

Bayesian Optimization (BO) is a foundational strategy in engineering design optimization for efficiently handling black-box functions with many constraints and expensive evaluations. This paper introduces a novel constraint-handling framework for Bayesian Optimization (BO) using Prior-data Fitted Networks (PFNs), a foundation transformer model. Unlike traditional approaches requiring separate Gaussian Process (GP) models for each constraint, our framework leverages PFN’s transformer architecture to evaluate objectives and constraints simultaneously in a single forward pass using in-context learning. Through comprehensive benchmarking across 15 test problems spanning synthetic, structural, and engineering design challenges, we demonstrate an order of magnitude speedup while maintaining or improving solution quality compared to conventional GP-based methods with constrained expected improvement (CEI). Our approach particularly excels at engineering problems by rapidly finding feasible, optimal solutions. This benchmark framework for evaluating new BO algorithms in engineering design will be published at https://github.com/rosenyu304/BOEngineeringBenchmark .

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.

Purpose The purpose of this paper is to investigate the performance of chaotic gravitational search algorithm (CGSA) in solving mechanical engineering design frameworks including welded beam design (WBD), compression spring design (CSD) and pressure vessel design (PVD). Design/methodology/approach In this study, ten chaotic maps were combined with gravitational constant to increase the exploitation power of gravitational search algorithm (GSA). Also, CGSA has been used for maintaining the adaptive capability of gravitational constant. Furthermore, chaotic maps were used for overcoming premature convergence and stagnation in local minima problems of standard GSA. Findings The chaotic maps have shown efficient performance for WBD and PVD problems. Further, they have depicted competitive results for CSD framework. Moreover, the experimental results indicate that CGSA shows efficient performance in terms of convergence speed, cost function minimization, design variable optimization and successful constraint handling as compared to other participating algorithms. Research limitations/implications The use of chaotic maps in standard GSA is a new beginning for research in GSA particularly convergence and time complexity analysis. Moreover, CGSA can be used for solving the infinite impulsive response (IIR) parameter tuning and economic load dispatch problems in electrical sciences. Originality/value The hybridization of chaotic maps and evolutionary algorithms for solving practical engineering problems is an emerging topic in metaheuristics. In the literature, it can be seen that researchers have used some chaotic maps such as a logistic map, Gauss map and a sinusoidal map more rigorously than other maps. However, this work uses ten different chaotic maps for engineering design optimization. In addition, non-parametric statistical test, namely, Wilcoxon rank-sum test, was carried out at 5% significance level to statistically validate the simulation results. Besides, 11 state-of-the-art metaheuristic algorithms were used for comparative analysis of the experimental results to further raise the authenticity of the experimental setup.

The traditional optimization approaches suffer from certain problems like getting stuck in local optima, low speed, susceptibility to local optima, and searching unknown search spaces, thus requiring reliance on single-based solutions. Herein, an Improved Aquila Optimizer (IAO) is proposed, which is a unique meta-heuristic optimization method motivated by the hunting behavior of Aquila. An improved version of Aquila optimizer seeks to increase effectiveness and productivity. IAO emulates the hunting behaviors of Aquila, elucidating each step of the hunting process. The IAO algorithm contains innovative elements to boost its optimization capabilities. It combines a combination of low flight with a leisurely descent for exploitation, high-altitude vertical dives, contour flying with brief gliding attacks for exploration, and controlled swooping maneuvers for effective prey capture. To assess the effectiveness of IAO, Herein, numerous experiments were carried out. Firstly, IAO was compared using 23 classical optimization functions. The achieved results demonstrate that the proposed model outperforms various champion algorithms. Secondly, the proposed algorithm is applied to five real-world engineering problems. The achieved results prove effectiveness in diverse application domains. The key findings of the research work highlight IAO’s resilience and adaptability in solving challenging optimization issues and its importance as a strong optimization tool for real-world engineering applications. Convergence curves compare the speed of proposed algorithms with selected algorithms for 1000 iterations. Time complexity analysis shows that the best time is 0.00015225 which is better as compared to other algorithms also Wilcoxon ranksum test is carried out to calculate the p-value is less than 0.05 rejecting the null hypothesis. The research emphasizes the potential of IAO as a tool for tackling real-world optimization challenges by explaining its efficacy and competitiveness compared to other optimization procedures via comprehensive testing and analysis.

The Hare Escape Optimization (HEO) algorithm is a novel metaheuristic inspired by the evasive movement strategies of hares when pursued by predators. Unlike conventional nature-inspired algorithms, HEO integrates Levy flight dynamics and adaptive directional shifts to enhance the balance between exploration and exploitation, improving its ability to escape local optima and converge efficiently. To validate its effectiveness, HEO was tested against 29 state-of-the-art metaheuristics on 43 benchmark functions from the CEC 2015 and CEC 2020 testbeds, demonstrating superior performance in both unimodal and multimodal landscapes. Beyond benchmark validation, HEO was applied to four complex constrained engineering design problems; spring, welded beam, pressure vessel, and truss optimization where it outperformed leading optimization methods in solution feasibility and computational efficiency. Additionally, HEO was employed to optimize hyperparameters in convolutional neural networks (CNNs) for image classification tasks, significantly enhancing model accuracy and convergence speed. The results indicate that HEO is a robust, adaptable optimization tool with promising applications in both engineering and deep learning. Its unique search mechanism provides a new perspective in metaheuristic optimization, opening pathways for further advancements in intelligent optimization techniques.

Salp swarm algorithm (SSA) is a relatively new and straightforward swarm-based meta-heuristic optimization algorithm, which is inspired by the flocking behavior of salps when foraging and navigating in oceans. Although SSA is very competitive, it suffers from some limitations including unbalanced exploration and exploitation operation, slow convergence. Therefore, this study presents an improved version of SSA, called OOSSA, to enhance the comprehensive performance of the basic method. In preference, a new opposition-based learning strategy based on optical lens imaging principle is proposed, and combined with the orthogonal experimental design, an orthogonal lens opposition-based learning technique is designed to help the population jump out of a local optimum. Next, the scheme of adaptively adjusting the number of leaders is embraced to boost the global exploration capability and improve the convergence speed. Also, a dynamic learning strategy is applied to the canonical methodology to improve the exploitation capability. To confirm the efficacy of the proposed OOSSA, this paper uses 26 standard mathematical optimization functions with various features to test the method. Alongside, the performance of the proposed methodology is validated by Wilcoxon signed-rank and Friedman statistical tests. Additionally, three well-known engineering optimization problems and unknown parameters extraction issue of photovoltaic model are applied to check the ability of the OOSA algorithm to obtain solutions to intractable real-world problems. The experimental results reveal that the developed OOSSA is significantly superior to the standard SSA, currently popular SSA-based algorithms, and other state-of-the-artmeta-heuristic algorithms for solving numerical optimization, real-world engineering optimization, and photovoltaic model parameter extraction problems. Finally, an OOSSA-based path planning approach is developed for creating the shortest obstacle-free route for autonomous mobile robots. Our introduced method is compared with several successful swarm-based metaheuristic techniques in five maps, and the comparative results indicate that the suggested approach can generate the shortest collision-free trajectory as compared to other peers.

The study proposes an enhanced, high-caliber Population Evolution Polar Lights Optimization (IPLO) algorithm to address the shortcomings of the existing Polar Lights Optimization (PLO) method. These include issues like insufficient diversity in the population, a lack of speed in convergence, and an uneven balance between local optimization and global search. In the IPLO, a pseudo-random lens SPM chaos initialization (PRLS-CI) strategy is proposed for population initialization, aiming to enhance the quality and diversity of the initial population. To strike a successful balance between global exploration and local search, a reinforcement learning approach is suggested that combines adaptive dynamics with a reward loss function centered on exploration. Furthermore, the adaptive t-distribution mutation strategy is employed to enhance population diversity, accelerating the convergence speed of IPLO. In addition, the simplex method is used to construct diversified geometric search paths, improving the utilization efficiency of the population’s peripheral individuals. A comparison between the proposed IPLO and well-known optimization algorithms, as well as their improved versions, shows that IPLO outperforms other algorithms and their improved versions on multiple benchmark functions, specifically in terms of faster convergence speed and higher solution accuracy. The validation outcomes on the CEC2017, CEC 2019, and CEC 2022 benchmark functions, along with four engineering design issues, further substantiate the efficacy of the IPLO algorithm in tackling intricate real-world optimization tasks. Compared to PLO, IPLO improves convergence accuracy by 66.7%, increases convergence speed by 69.6%, and enhances stability by 99.9%.

The Blended-Wing-Body (BWB) layout represents an innovative subsonic transport aircraft design. Drawing inspiration from the Pultruded Rod Stitched Efficient Unitized Structure (PRSEUS) proposed by National Aeronautics and Space Administration (NASA), this study focuses on a design optimization for the entire structure of a BWB civil aircraft. A PRSEUS-based finite element model was established and subjected to a static analysis. The results indicate a considerable structural strength margin, suggesting potential for lightweight design advancements. Meanwhile, the structural region division techniques were adopted to analyze the sensitivity of the BWB aircraft structure and to sort the parameters affecting its mass. Subsequently, seven surrogate modeling techniques were employed to train a surrogate model for the BWB aircraft structure to analyze the primary factors affecting its prediction accuracy. Among various modeling approaches, the optimal heuristic computation (ES) method demonstrates superior prediction accuracy and enhances the efficiency of optimal solution searches, resulting in a 18.45% mass reduction in the optimized BWB civil aircraft structure. Based on the optimization results of the ES model, a dual-loop optimization strategy was proposed by considering the vibration effects on the BWB aircraft. This strategy facilitates the optimization of the dimensional parameters of the BWB aircraft structure, resulting in substantial 17.83% increase in the first-order natural frequency of the optimized structure. After two rounds of optimization, the mass of the optimized BWB aircraft structure accounted for only 25% of the maximum takeoff mass. Consequently, the proposed optimization strategies present robust applicability and high efficiency, providing a valuable reference for designers and researchers in related fields.