The hybrid flow shop scheduling problem (HFSP), as a realistic extension of the classical flow shop scheduling problem, widely exists in real-world industrial production systems. In practice, the fact that machines are unrelated is important and cannot be neglected. This study focuses on the HFSP with unrelated parallel machines (HFSP-UPM) to minimize the makespan. To address this problem, a hybrid representation that combines single-sequence coding and full-sequence coding is developed to search for solution space that is not covered by common encoding methods. An initialization block integrating random heuristic strategies is proposed for improving the quality of the initial sparrow swarm. To improve the diversity of a sparrow swarm further, a perturbation block embedded with a set of historical best positions and an enhancement strategy are developed. A critical set based local search block is designed for high-intensity local exploitation of promising regions when necessary. Several benchmark cases from the literature as well as some randomly generated instances characterized by the distribution of real data from factory studies are employed to participate in the test. The test results reveal the effectiveness of the proposed perturbation block and local search block. Compared to state-of-the-art metaheuristic algorithms, the enhanced sparrow search algorithm (ESSA) demonstrates higher convergence accuracy when handling instances. The value of the gap between a solution found by the ESSA and a feasible solution found by the mixed-integer programming (MIP) model can reach 0.6%.

Renewable energy sources, such as wind power, face challenges owing to their erratic construction and intermittent nature, leading to the emergence of energy storage strategies to achieve grid stability and reliable electricity supplies. Determination of the correct size of energy storage devices for wind power plants is complicated. In this study, the ant colony optimization (ACO) algorithm is proposed for the best distribution/sizing of wind-generated hybrid storage capacity. Ants’ foraging habits motivate the development of wind turbines with high dependability, high efficiency and low energy storage costs. A study is conducted to confirm the practicality of the proposed method, using real data from a wind power plant to calculate the contrast between wind energy production and load consumption features, to influence the appropriate quantity for energy storage organization. The study demonstrates that the ACO approach provides precise and efficient solutions for determining the optimal energy distribution in wind power plants.

In this article, a fuzzy rough-interval linear programming (FRILP) approach is proposed to deal with the uncertainty expressed by the fuzzy rough set in the optimization of booster cost under uncertainty. The FRILP model was applied to two cases to verify its effectiveness in booster optimization under uncertainty. The optimal upper and lower approximation intervals of the injection mass and booster cost in the fuzzy rough set were obtained and the effects of booster number and location were analysed. The results indicated that with an increase in booster number, the injection mass generally decreased, and booster cost decreased or increased. The nodal chlorine concentration also decreased and was distributed uniformly under a scenario with more boosters. Locating the booster far from the source resulted in more uniform chlorine distribution. The results could help managers design booster schemes with consideration of technical and economic factors comprehensively under uncertainty.

Topology optimization is a technique used in engineering to determine the optimal distribution of material within a defined design domain. This technique has been applied to the design of cellular materials to create an efficient microstructural arrangement that meets the necessary performance criteria and minimizes the weight of the material. This article presents an innovative approach that combines topology optimization, a homogenization method based on the unit cell concept and finite-volume theory to design highly efficient periodic cellular materials with optimized macroscopic elastic properties. To determine the optimal microstructural topology, specific linear combinations of components of the homogenized elastic matrix are considered to obtain optimized elastic properties, such as maximum shear/bulk moduli, considering a prescribed volume fraction constraint of solid material. Numerical examples are analysed, and the results demonstrate the exceptional performance of this approach in achieving optimal designs of cellular materials characterized by chequerboard-free patterns without filtering techniques.

Metaheuristic algorithms play a crucial role in engineering optimization, as they can find the optimal parameter configuration in engineering systems. This article proposes a multi-strategy improved seagull optimization algorithm (OPSOA) to solve engineering application problems. Aiming to solve the problems of slow search speed and low convergence accuracy of the standard seagull optimization algorithm (SOA), four strategies, including Lévy flight and Cauchy mutation, were introduced to improve its performance. Comparison shows that OPSOA and its incomplete algorithms are better than SOA, indicating that each improvement is effective. By testing the benchmark functions of CEC 2017 and CEC 2022, it is shown that OPSOA has a strong ability to find the optimal solution and is superior to other algorithms in terms of convergence accuracy and search speed. The application of this algorithm in practical engineering problems proves that it has significant advantages in solving complex problems.

The continuous fixed-radius disc cover (CFDC) problem is a location model to cover the given demand points by finding the minimum number of fixed-radius discs in the plane. It is an NP-hard problem, and only a few approximate algorithms have been proposed over the past three decades. In the article, a new heuristic called dynamic reduction (DR) is introduced. The heuristic works by initiating an upper bound on the number of discs, and then reducing the number by removing redundant discs during updates to the disc centres. Experimental results, using different radius settings on some datasets of a travelling salesman problem library (TSP-Lib), show that the proposed heuristic greatly outperforms the recent approximation algorithm in accuracy. Notably, an enhancement of the heuristic is also provided.

This study proposes an improved adaptive kriging model-based FE model updating framework to increase the updated FE model’s accuracy and reduce computational costs. The proposed adaptive kriging model uses an efficient hybrid expected improvement and minimizing surrogate prediction sampling strategy to generate new training samples. The k-fold cross-validation is introduced to assess the kriging model’s accuracy. Benchmark functions and model updating of a full-scale bridge structure validated the proposed adaptive kriging model. The results demonstrate that the hybrid sampling strategy balances the global and local exploration of the design space and provides reasonable training samples, increasing the accuracy of the adaptive kriging model. The cross-validation significantly saves computational costs. After model updating, the frequency relative errors of the continuous bridge are under 2%, and the modal assurance criterion values are over 0.96. The updated FE model can serve as the baseline FE model of the bridge.

Optimization techniques necessitate a diverse focus to overcome green supply chain practice (GSCP) challenges, to address a variety of conflicting problems and uncertain challenges. This study aims to review the literature on optimization techniques for GSCP challenges, revealing the intricate interrelationship among attributes under uncertainty for hierarchical structure construction, and presenting insights and priorities for future research. Data were collected from the Scopus database, resulting in a total of 465 publications. An integrated method of systematic review was used to review and validate the GSCP optimization techniques. Hence, assessments of multi-objective optimization and uncertainty are pivotal for enhancing GSCP. The challenges posed by GSCP underscore the need to use heuristic algorithms, mixed integer programming, goal programming, stochastic programming and the non-dominated sorting genetic algorithm II in practical applications. This study offers a contribution to the literature on GSCP and provides valuable information to assist researchers and practitioners using optimization techniques.

This article proposes a deep learning model based on a multi-scale convolutional attention mechanism network SegNext for improving Topology Optimization (TO-Next), aimed at addressing the computational challenges associated with finite element iterations in traditional density-based methods. TO-Next is trained on diverse topology structures with varying loads, constraints and enriched physical information after initial iterations to enhance its generalization. Following training on three distinct decoder architectures, the optimal encoder–decoder network structure is determined. This study also investigates the algorithm's generalization capability under both single and multiple load constraints. The results indicate the superior performance and efficiency of the proposed method compared with the Solid Isotropic Material with Penalization (SIMP) method, enabling real-time generation of near-optimal topology structures within a short timeframe.

This article proposes a deep learning model based on a multi-scale convolutional attention mechanism network SegNext for improving Topology Optimization (TO-Next), aimed at addressing the computational challenges associated with finite element iterations in traditional density-based methods. TO-Next is trained on diverse topology structures with varying loads, constraints and enriched physical information after initial iterations to enhance its generalization. Following training on three distinct decoder architectures, the optimal encoder–decoder network structure is determined. This study also investigates the algorithm's generalization capability under both single and multiple load constraints. The results indicate the superior performance and efficiency of the proposed method compared with the Solid Isotropic Material with Penalization (SIMP) method, enabling real-time generation of near-optimal topology structures within a short timeframe.