Owing to their global search capabilities and gradient-free operation,metaheuristic algorithms are widely applied to a wide range of optimization problems.However,their computational demands become prohibitive when ta...Owing to their global search capabilities and gradient-free operation,metaheuristic algorithms are widely applied to a wide range of optimization problems.However,their computational demands become prohibitive when tackling high-dimensional optimization challenges.To effectively address these challenges,this study introduces cooperative metaheuristics integrating dynamic dimension reduction(DR).Building upon particle swarm optimization(PSO)and differential evolution(DE),the proposed cooperative methods C-PSO and C-DE are developed.In the proposed methods,the modified principal components analysis(PCA)is utilized to reduce the dimension of design variables,thereby decreasing computational costs.The dynamic DR strategy implements periodic execution of modified PCA after a fixed number of iterations,resulting in the important dimensions being dynamically identified.Compared with the static one,the dynamic DR strategy can achieve precise identification of important dimensions,thereby enabling accelerated convergence toward optimal solutions.Furthermore,the influence of cumulative contribution rate thresholds on optimization problems with different dimensions is investigated.Metaheuristic algorithms(PSO,DE)and cooperative metaheuristics(C-PSO,C-DE)are examined by 15 benchmark functions and two engineering design problems(speed reducer and composite pressure vessel).Comparative results demonstrate that the cooperative methods achieve significantly superior performance compared to standard methods in both solution accuracy and computational efficiency.Compared to standard metaheuristic algorithms,cooperative metaheuristics achieve a reduction in computational cost of at least 40%.The cooperative metaheuristics can be effectively used to tackle both high-dimensional unconstrained and constrained optimization problems.展开更多
Formalizing complex processes and phenomena of a real-world problem may require a large number of variables and constraints,resulting in what is termed a large-scale optimization problem.Nowadays,such large-scale opti...Formalizing complex processes and phenomena of a real-world problem may require a large number of variables and constraints,resulting in what is termed a large-scale optimization problem.Nowadays,such large-scale optimization problems are solved using computing machines,leading to an enormous computational time being required,which may delay deriving timely solutions.Decomposition methods,which partition a large-scale optimization problem into lower-dimensional subproblems,represent a key approach to addressing time-efficiency issues.There has been significant progress in both applied mathematics and emerging artificial intelligence approaches on this front.This work aims at providing an overview of the decomposition methods from both the mathematics and computer science points of view.We also remark on the state-of-the-art developments and recent applications of the decomposition methods,and discuss the future research and development perspectives.展开更多
Most material distribution-based topology optimization methods work on a relaxed form of the optimization problem and then push the solution toward the binary limits.However,when benchmarking these methods,researchers...Most material distribution-based topology optimization methods work on a relaxed form of the optimization problem and then push the solution toward the binary limits.However,when benchmarking these methods,researchers use known solutions to only a single form of benchmark problem.This paper proposes a comparison platform for systematic benchmarking of topology optimization methods using both binary and relaxed forms.A greyness measure is implemented to evaluate how far a solution is from the desired binary form.The well-known ZhouRozvany(ZR)problem is selected as the benchmarking problem here,making use of available global solutions for both its relaxed and binary forms.The recently developed non-penalization Smooth-edged Material Distribution for Optimizing Topology(SEMDOT),well-established Solid Isotropic Material with Penalization(SIMP),and continuation methods are studied on this platform.Interestingly,in most cases,the grayscale solutions obtained by SEMDOT demonstrate better performance in dealing with the ZR problem than SIMP.The reasons are investigated and attributed to the usage of two different regularization techniques,namely,the Heaviside smooth function in SEMDOT and the power-law penalty in SIMP.More importantly,a simple-to-use benchmarking graph is proposed for evaluating newly developed topology optimization methods.展开更多
In this paper,we propose a three-term conjugate gradient method for solving unconstrained optimization problems based on the Hestenes-Stiefel(HS)conjugate gradient method and Polak-Ribiere-Polyak(PRP)conjugate gradien...In this paper,we propose a three-term conjugate gradient method for solving unconstrained optimization problems based on the Hestenes-Stiefel(HS)conjugate gradient method and Polak-Ribiere-Polyak(PRP)conjugate gradient method.Under the condition of standard Wolfe line search,the proposed search direction is the descent direction.For general nonlinear functions,the method is globally convergent.Finally,numerical results show that the proposed method is efficient.展开更多
This research presents a novel nature-inspired metaheuristic optimization algorithm,called theNarwhale Optimization Algorithm(NWOA).The algorithm draws inspiration from the foraging and prey-hunting strategies of narw...This research presents a novel nature-inspired metaheuristic optimization algorithm,called theNarwhale Optimization Algorithm(NWOA).The algorithm draws inspiration from the foraging and prey-hunting strategies of narwhals,“unicorns of the sea”,particularly the use of their distinctive spiral tusks,which play significant roles in hunting,searching prey,navigation,echolocation,and complex social interaction.Particularly,the NWOA imitates the foraging strategies and techniques of narwhals when hunting for prey but focuses mainly on the cooperative and exploratory behavior shown during group hunting and in the use of their tusks in sensing and locating prey under the Arctic ice.These functions provide a strong assessment basis for investigating the algorithm’s prowess at balancing exploration and exploitation,convergence speed,and solution accuracy.The performance of the NWOA is evaluated on 30 benchmark test functions.A comparison study using the Grey Wolf Optimizer(GWO),Whale Optimization Algorithm(WOA),Perfumer Optimization Algorithm(POA),Candle Flame Optimization(CFO)Algorithm,Particle Swarm Optimization(PSO)Algorithm,and Genetic Algorithm(GA)validates the results.As evidenced in the experimental results,NWOA is capable of yielding competitive outcomes among these well-known optimizers,whereas in several instances.These results suggest thatNWOAhas proven to be an effective and robust optimization tool suitable for solving many different complex optimization problems from the real world.展开更多
This paper introduces a hybrid multi-objective optimization algorithm,designated HMODESFO,which amalgamates the exploratory prowess of Differential Evolution(DE)with the rapid convergence attributes of the Sailfish Op...This paper introduces a hybrid multi-objective optimization algorithm,designated HMODESFO,which amalgamates the exploratory prowess of Differential Evolution(DE)with the rapid convergence attributes of the Sailfish Optimization(SFO)algorithm.The primary objective is to address multi-objective optimization challenges within mechanical engineering,with a specific emphasis on planetary gearbox optimization.The algorithm is equipped with the ability to dynamically select the optimal mutation operator,contingent upon an adaptive normalized population spacing parameter.The efficacy of HMODESFO has been substantiated through rigorous validation against estab-lished industry benchmarks,including a suite of Zitzler-Deb-Thiele(ZDT)and Zeb-Thiele-Laumanns-Zitzler(DTLZ)problems,where it exhibited superior performance.The outcomes underscore the algorithm’s markedly enhanced optimization capabilities relative to existing methods,particularly in tackling highly intricate multi-objective planetary gearbox optimization problems.Additionally,the performance of HMODESFO is evaluated against selected well-known mechanical engineering test problems,further accentuating its adeptness in resolving complex optimization challenges within this domain.展开更多
Addressing the complex issue of emergency resource distribution center site selection in uncertain environments, this study was conducted to comprehensively consider factors such as uncertainty parameters and the urge...Addressing the complex issue of emergency resource distribution center site selection in uncertain environments, this study was conducted to comprehensively consider factors such as uncertainty parameters and the urgency of demand at disaster-affected sites. Firstly, urgency cost, economic cost, and transportation distance cost were identified as key objectives. The study applied fuzzy theory integration to construct a triangular fuzzy multi-objective site selection decision model. Next, the defuzzification theory transformed the fuzzy decision model into a precise one. Subsequently, an improved Chaotic Quantum Multi-Objective Harris Hawks Optimization (CQ-MOHHO) algorithm was proposed to solve the model. The CQ-MOHHO algorithm was shown to rapidly produce high-quality Pareto front solutions and identify optimal site selection schemes for emergency resource distribution centers through case studies. This outcome verified the feasibility and efficacy of the site selection decision model and the CQ-MOHHO algorithm. To further assess CQ-MOHHO’s performance, Zitzler-Deb-Thiele (ZDT) test functions, commonly used in multi-objective optimization, were employed. Comparisons with Multi-Objective Harris Hawks Optimization (MOHHO), Non-dominated Sorting Genetic Algorithm II (NSGA-II), and Multi-Objective Grey Wolf Optimizer (MOGWO) using Generational Distance (GD), Hypervolume (HV), and Inverted Generational Distance (IGD) metrics showed that CQ-MOHHO achieved superior global search ability, faster convergence, and higher solution quality. The CQ-MOHHO algorithm efficiently achieved a balance between multiple objectives, providing decision-makers with satisfactory solutions and a valuable reference for researching and applying emergency site selection problems.展开更多
The dung beetle optimizer(DBO)is a metaheuristic algorithm with fast convergence and powerful search capabilities,which has shown excellent performance in solving various optimization problems.However,it suffers from ...The dung beetle optimizer(DBO)is a metaheuristic algorithm with fast convergence and powerful search capabilities,which has shown excellent performance in solving various optimization problems.However,it suffers from the problems of easily falling into local optimal solutions and poor convergence accuracy when dealing with large-scale complex optimization problems.Therefore,we propose an adaptive DBO(ADBO)based on an elastic annealing mechanism to address these issues.First,the convergence factor is adjusted in a nonlinear decreasing manner to balance the requirements of global exploration and local exploitation,thus improving the convergence speed and search quality.Second,a greedy difference optimization strategy is introduced to increase population diversity,improve the global search capability,and avoid premature convergence.Finally,the elastic annealing mechanism is used to perturb the randomly selected individuals,helping the algorithm escape local optima and thereby improve solution quality and algorithm stability.The experimental results on the CEC 2017 and CEC 2022 benchmark function sets and MCNC benchmark circuits verify the effectiveness,superiority,and universality of ADBO.展开更多
Multi-objective optimization is critical for problem-solving in engineering,economics,and AI.This study introduces the Multi-Objective Chef-Based Optimization Algorithm(MOCBOA),an upgraded version of the Chef-Based Op...Multi-objective optimization is critical for problem-solving in engineering,economics,and AI.This study introduces the Multi-Objective Chef-Based Optimization Algorithm(MOCBOA),an upgraded version of the Chef-Based Optimization Algorithm(CBOA)that addresses distinct objectives.Our approach is unique in systematically examining four dominance relations—Pareto,Epsilon,Cone-epsilon,and Strengthened dominance—to evaluate their influence on sustaining solution variety and driving convergence toward the Pareto front.Our comparison investigation,which was conducted on fifty test problems from the CEC 2021 benchmark and applied to areas such as chemical engineering,mechanical design,and power systems,reveals that the dominance approach used has a considerable impact on the key optimization measures such as the hypervolume metric.This paper provides a solid foundation for determining themost effective dominance approach and significant insights for both theoretical research and practical applications in multi-objective optimization.展开更多
In this study,a completely different approach to optimization is introduced through the development of a novel metaheuristic algorithm called the Barber Optimization Algorithm(BaOA).Inspired by the human interactions ...In this study,a completely different approach to optimization is introduced through the development of a novel metaheuristic algorithm called the Barber Optimization Algorithm(BaOA).Inspired by the human interactions between barbers and customers,BaOA captures two key processes:the customer’s selection of a hairstyle and the detailed refinement during the haircut.These processes are translated into a mathematical framework that forms the foundation of BaOA,consisting of two critical phases:exploration,representing the creative selection process,and exploitation,which focuses on refining details for optimization.The performance of BaOA is evaluated using 52 standard benchmark functions,including unimodal,high-dimensional multimodal,fixed-dimensional multimodal,and the Congress on Evolutionary Computation(CEC)2017 test suite.This comprehensive assessment highlights BaOA’s ability to balance exploration and exploitation effectively,resulting in high-quality solutions.A comparative analysis against twelve widely known metaheuristic algorithms further demonstrates BaOA’s superior performance,as it consistently delivers better results across most benchmark functions.To validate its real-world applicability,BaOA is tested on four engineering design problems,illustrating its capability to address practical challenges with remarkable efficiency.The results confirm BaOA’s versatility and reliability as an optimization tool.This study not only introduces an innovative algorithm but also establishes its effectiveness in solving complex problems,providing a foundation for future research and applications in diverse scientific and engineering domains.展开更多
This paper introduces dynamic boundary updating-surrogate model-based(DBU-SMB),a novel evolutionary framework for global optimization that integrates dynamic boundary updating(DBU)within a surrogate model-based(SMB)ap...This paper introduces dynamic boundary updating-surrogate model-based(DBU-SMB),a novel evolutionary framework for global optimization that integrates dynamic boundary updating(DBU)within a surrogate model-based(SMB)approach.The method operates in three progressive stages:adaptive sampling,DBU,and refinement.In the first stage,adaptive sampling strategically explores the design space to gather critical information for improving the surrogate model.The second stage incorporates DBU to guide the optimization toward promising regions in the parameter space,enhancing consistency and efficiency.Finally,the refinement stage iteratively improves the optimization results,ensuring a comprehensive exploration of the design space.The proposed DBU-SMB framework is algorithm-agnostic,meaning it does not rely on any specific machine learning model or meta-heuristic algorithm.To demonstrate its effectiveness,we applied DBU-SMB to four highly nonlinear and non-convex optimization problems.The results show a reduction of over 90%in the number of function evaluations compared to traditional methods,while avoiding entrapment in local optima and discovering superior solutions.These findings highlight the efficiency and robustness of DBU-SMB in achieving optimal designs,particularly for large-scale and complex optimization problems.展开更多
Variable-fidelity(VF)surrogate models have received increasing attention in engineering design optimization as they can approximate expensive high-fidelity(HF)simulations with reduced computational power.A key challen...Variable-fidelity(VF)surrogate models have received increasing attention in engineering design optimization as they can approximate expensive high-fidelity(HF)simulations with reduced computational power.A key challenge to building a VF model is devising an adaptive model updating strategy that jointly selects additional low-fidelity(LF)and/or HF samples.The additional samples must enhance the model accuracy while maximizing the computational efficiency.We propose ISMA-VFEEI,a global optimization framework that integrates an Improved Slime-Mould Algorithm(ISMA)and a Variable-Fidelity Expected Extension Improvement(VFEEI)learning function to construct a VF surrogate model efficiently.First,A cost-aware VFEEI function guides the adaptive LF/HF sampling by explicitly incorporating evaluation cost and existing sample proximity.Second,ISMA is employed to solve the resulting non-convex optimization problem and identify global optimal infill points for model enhancement.The efficacy of ISMA-VFEEI is demonstrated through six numerical benchmarks and one real-world engineering case study.The engineering case study of a high-speed railway Electric Multiple Unit(EMU),the optimization objective of a sanding device attained a minimum value of 1.546 using only 20 HF evaluations,outperforming all the compared methods.展开更多
The shop scheduling problem with limited buffers has broad applications in real-world production scenarios,so this research direction is of great practical significance.However,there is currently little research on th...The shop scheduling problem with limited buffers has broad applications in real-world production scenarios,so this research direction is of great practical significance.However,there is currently little research on the hybrid flow shop scheduling problem with limited buffers(LBHFSP).This paper deeply investigates the LBHFSP to optimize the goal of the total completion time.To better solve the LBHFSP,a multi-level subpopulation-based particle swarm optimization algorithm(MLPSO)is proposed,which is founded on the attributes of the LBHFSP and the shortcomings of the basic PSO(particle swarm optimization)algorithm.In MLPSO,firstly,considering the impact of the limited buffers on the process of subsequent operations,a specific circular decoding strategy is developed to accommodate the characteristics of limited buffers.Secondly,an initialization strategy based on blocking time is designed to enhance the quality and diversity of the initial population.Afterward,a multi-level subpopulation collaborative search is developed to prevent being trapped in a local optimum and improve the global exploration capability.Additionally,a local search strategy based on the first blocked job is designed to enhance the MLPSO algorithm’s exploitation capability.Lastly,numerous experiments are carried out to test the performance of the proposed MLPSO by comparing it with classical intelligent optimization and popular algorithms in recent years.The results confirm that the proposed MLPSO has an outstanding performance when compared to other algorithms when solving LBHFSP.展开更多
This paper addresses the Multi-Vehicle Routing Problem with Time Windows and Simultaneous Pickup and Delivery(MVRPTWSPD),aiming to optimize logistics distribution routes and minimize total costs.A vehicle routing opti...This paper addresses the Multi-Vehicle Routing Problem with Time Windows and Simultaneous Pickup and Delivery(MVRPTWSPD),aiming to optimize logistics distribution routes and minimize total costs.A vehicle routing optimization model is developed based on the operational requirements of the KS Logistics Center,focusing on minimizing vehicle dispatch,loading and unloading,operating,and time window penalty costs.The model incorporates constraints such as vehicle capacity,time windows,and travel distance,and is solved using a genetic algorithm to ensure optimal route planning.Through MATLAB simulations,34 customer points are analyzed,demonstrating that the simultaneous pickup and delivery model reduces total costs by 30.13%,increases vehicle loading rates by 20.04%,and decreases travel distance compared to delivery-only or pickup-only models.The results demonstrate the significant advantages of the simultaneous pickup and delivery mode in reducing logistics costs and improving vehicle utilization,offering valuable insights for enhancing the operational efficiency of the KS Logistics Center.展开更多
This paper addresses the distributed nonconvex optimization problem, where both the global cost function and local inequality constraint function are nonconvex. To tackle this issue, the p-power transformation and pen...This paper addresses the distributed nonconvex optimization problem, where both the global cost function and local inequality constraint function are nonconvex. To tackle this issue, the p-power transformation and penalty function techniques are introduced to reframe the nonconvex optimization problem. This ensures that the Hessian matrix of the augmented Lagrangian function becomes local positive definite by choosing appropriate control parameters. A multi-timescale primal-dual method is then devised based on the Karush-Kuhn-Tucker(KKT) point of the reformulated nonconvex problem to attain convergence. The Lyapunov theory guarantees the model's stability in the presence of an undirected and connected communication network. Finally, two nonconvex optimization problems are presented to demonstrate the efficacy of the previously developed method.展开更多
Satellite Component Layout Optimization(SCLO) is crucial in satellite system design.This paper proposes a novel Satellite Three-Dimensional Component Assignment and Layout Optimization(3D-SCALO) problem tailored to en...Satellite Component Layout Optimization(SCLO) is crucial in satellite system design.This paper proposes a novel Satellite Three-Dimensional Component Assignment and Layout Optimization(3D-SCALO) problem tailored to engineering requirements, aiming to optimize satellite heat dissipation while considering constraints on static stability, 3D geometric relationships between components, and special component positions. The 3D-SCALO problem is a challenging bilevel combinatorial optimization task, involving the optimization of discrete component assignment variables in the outer layer and continuous component position variables in the inner layer,with both influencing each other. To address this issue, first, a Mixed Integer Programming(MIP) model is proposed, which reformulates the original bilevel problem into a single-level optimization problem, enabling the exploration of a more comprehensive optimization space while avoiding iterative nested optimization. Then, to model the 3D geometric relationships between components within the MIP framework, a linearized 3D Phi-function method is proposed, which handles non-overlapping and safety distance constraints between cuboid components in an explicit and effective way. Subsequently, the Finite-Rectangle Method(FRM) is proposed to manage 3D geometric constraints for complex-shaped components by approximating them with a finite set of cuboids, extending the applicability of the geometric modeling approach. Finally, the feasibility and effectiveness of the proposed MIP model are demonstrated through two numerical examples"and a real-world engineering case, which confirms its suitability for complex-shaped components and real engineering applications.展开更多
As Internet of Things(IoT)applications expand,Mobile Edge Computing(MEC)has emerged as a promising architecture to overcome the real-time processing limitations of mobile devices.Edge-side computation offloading plays...As Internet of Things(IoT)applications expand,Mobile Edge Computing(MEC)has emerged as a promising architecture to overcome the real-time processing limitations of mobile devices.Edge-side computation offloading plays a pivotal role in MEC performance but remains challenging due to complex task topologies,conflicting objectives,and limited resources.This paper addresses high-dimensional multi-objective offloading for serial heterogeneous tasks in MEC.We jointly consider task heterogeneity,high-dimensional objectives,and flexible resource scheduling,modeling the problem as a Many-objective optimization.To solve it,we propose a flexible framework integrating an improved cooperative co-evolutionary algorithm based on decomposition(MOCC/D)and a flexible scheduling strategy.Experimental results on benchmark functions and simulation scenarios show that the proposed method outperforms existing approaches in both convergence and solution quality.展开更多
The moving morphable component(MMC)topology optimization method,as a typical explicit topology optimization method,has been widely concerned.In the MMC topology optimization framework,the surrogate material model is m...The moving morphable component(MMC)topology optimization method,as a typical explicit topology optimization method,has been widely concerned.In the MMC topology optimization framework,the surrogate material model is mainly used for finite element analysis at present,and the effectiveness of the surrogate material model has been fully confirmed.However,there are some accuracy problems when dealing with boundary elements using the surrogate material model,which will affect the topology optimization results.In this study,a boundary element reconstruction(BER)model is proposed based on the surrogate material model under the MMC topology optimization framework to improve the accuracy of topology optimization.The proposed BER model can reconstruct the boundary elements by refining the local meshes and obtaining new nodes in boundary elements.Then the density of boundary elements is recalculated using the new node information,which is more accurate than the original model.Based on the new density of boundary elements,the material properties and volume information of the boundary elements are updated.Compared with other finite element analysis methods,the BER model is simple and feasible and can improve computational accuracy.Finally,the effectiveness and superiority of the proposed method are verified by comparing it with the optimization results of the original surrogate material model through several numerical examples.展开更多
Due to the digital transformation tendency among cultural institutions and the substantial influence of the social media platform,the demands of visual communication keep increasing for promoting traditional cultural ...Due to the digital transformation tendency among cultural institutions and the substantial influence of the social media platform,the demands of visual communication keep increasing for promoting traditional cultural artifacts online.As an effective medium,posters serve to attract public attention and facilitate broader engagement with cultural artifacts.However,existing poster generation methods mainly rely on fixed templates and manual design,which limits their scalability and adaptability to the diverse visual and semantic features of the artifacts.Therefore,we propose CAPGen,an automated aesthetic Cultural Artifacts Poster Generation framework built on a Multimodal Large Language Model(MLLM)with integrated iterative optimization.During our research,we collaborated with designers to define principles of graphic design for cultural artifact posters,to guide the MLLM in generating layout parameters.Later,we generated these parameters into posters.Finally,we refined the posters using an MLLM integrated with a multi-round iterative optimization mechanism.Qualitative results show that CAPGen consistently outperforms baseline methods in both visual quality and aesthetic performance.Furthermore,ablation studies indicate that the prompt,iterative optimization mechanism,and design principles significantly enhance the effectiveness of poster generation.展开更多
Automated essay scoring(AES)systems have gained significant importance in educational settings,offering a scalable,efficient,and objective method for evaluating student essays.However,developing AES systems for Arabic...Automated essay scoring(AES)systems have gained significant importance in educational settings,offering a scalable,efficient,and objective method for evaluating student essays.However,developing AES systems for Arabic poses distinct challenges due to the language’s complex morphology,diglossia,and the scarcity of annotated datasets.This paper presents a hybrid approach to Arabic AES by combining text-based,vector-based,and embeddingbased similarity measures to improve essay scoring accuracy while minimizing the training data required.Using a large Arabic essay dataset categorized into thematic groups,the study conducted four experiments to evaluate the impact of feature selection,data size,and model performance.Experiment 1 established a baseline using a non-machine learning approach,selecting top-N correlated features to predict essay scores.The subsequent experiments employed 5-fold cross-validation.Experiment 2 showed that combining embedding-based,text-based,and vector-based features in a Random Forest(RF)model achieved an R2 of 88.92%and an accuracy of 83.3%within a 0.5-point tolerance.Experiment 3 further refined the feature selection process,demonstrating that 19 correlated features yielded optimal results,improving R2 to 88.95%.In Experiment 4,an optimal data efficiency training approach was introduced,where training data portions increased from 5%to 50%.The study found that using just 10%of the data achieved near-peak performance,with an R2 of 85.49%,emphasizing an effective trade-off between performance and computational costs.These findings highlight the potential of the hybrid approach for developing scalable Arabic AES systems,especially in low-resource environments,addressing linguistic challenges while ensuring efficient data usage.展开更多
基金funded by National Natural Science Foundation of China(Nos.12402142,11832013 and 11572134)Natural Science Foundation of Hubei Province(No.2024AFB235)+1 种基金Hubei Provincial Department of Education Science and Technology Research Project(No.Q20221714)the Opening Foundation of Hubei Key Laboratory of Digital Textile Equipment(Nos.DTL2023019 and DTL2022012).
文摘Owing to their global search capabilities and gradient-free operation,metaheuristic algorithms are widely applied to a wide range of optimization problems.However,their computational demands become prohibitive when tackling high-dimensional optimization challenges.To effectively address these challenges,this study introduces cooperative metaheuristics integrating dynamic dimension reduction(DR).Building upon particle swarm optimization(PSO)and differential evolution(DE),the proposed cooperative methods C-PSO and C-DE are developed.In the proposed methods,the modified principal components analysis(PCA)is utilized to reduce the dimension of design variables,thereby decreasing computational costs.The dynamic DR strategy implements periodic execution of modified PCA after a fixed number of iterations,resulting in the important dimensions being dynamically identified.Compared with the static one,the dynamic DR strategy can achieve precise identification of important dimensions,thereby enabling accelerated convergence toward optimal solutions.Furthermore,the influence of cumulative contribution rate thresholds on optimization problems with different dimensions is investigated.Metaheuristic algorithms(PSO,DE)and cooperative metaheuristics(C-PSO,C-DE)are examined by 15 benchmark functions and two engineering design problems(speed reducer and composite pressure vessel).Comparative results demonstrate that the cooperative methods achieve significantly superior performance compared to standard methods in both solution accuracy and computational efficiency.Compared to standard metaheuristic algorithms,cooperative metaheuristics achieve a reduction in computational cost of at least 40%.The cooperative metaheuristics can be effectively used to tackle both high-dimensional unconstrained and constrained optimization problems.
基金The Australian Research Council(DP200101197,DP230101107).
文摘Formalizing complex processes and phenomena of a real-world problem may require a large number of variables and constraints,resulting in what is termed a large-scale optimization problem.Nowadays,such large-scale optimization problems are solved using computing machines,leading to an enormous computational time being required,which may delay deriving timely solutions.Decomposition methods,which partition a large-scale optimization problem into lower-dimensional subproblems,represent a key approach to addressing time-efficiency issues.There has been significant progress in both applied mathematics and emerging artificial intelligence approaches on this front.This work aims at providing an overview of the decomposition methods from both the mathematics and computer science points of view.We also remark on the state-of-the-art developments and recent applications of the decomposition methods,and discuss the future research and development perspectives.
文摘Most material distribution-based topology optimization methods work on a relaxed form of the optimization problem and then push the solution toward the binary limits.However,when benchmarking these methods,researchers use known solutions to only a single form of benchmark problem.This paper proposes a comparison platform for systematic benchmarking of topology optimization methods using both binary and relaxed forms.A greyness measure is implemented to evaluate how far a solution is from the desired binary form.The well-known ZhouRozvany(ZR)problem is selected as the benchmarking problem here,making use of available global solutions for both its relaxed and binary forms.The recently developed non-penalization Smooth-edged Material Distribution for Optimizing Topology(SEMDOT),well-established Solid Isotropic Material with Penalization(SIMP),and continuation methods are studied on this platform.Interestingly,in most cases,the grayscale solutions obtained by SEMDOT demonstrate better performance in dealing with the ZR problem than SIMP.The reasons are investigated and attributed to the usage of two different regularization techniques,namely,the Heaviside smooth function in SEMDOT and the power-law penalty in SIMP.More importantly,a simple-to-use benchmarking graph is proposed for evaluating newly developed topology optimization methods.
基金Supported by the Science and Technology Project of Guangxi(Guike AD23023002)。
文摘In this paper,we propose a three-term conjugate gradient method for solving unconstrained optimization problems based on the Hestenes-Stiefel(HS)conjugate gradient method and Polak-Ribiere-Polyak(PRP)conjugate gradient method.Under the condition of standard Wolfe line search,the proposed search direction is the descent direction.For general nonlinear functions,the method is globally convergent.Finally,numerical results show that the proposed method is efficient.
文摘This research presents a novel nature-inspired metaheuristic optimization algorithm,called theNarwhale Optimization Algorithm(NWOA).The algorithm draws inspiration from the foraging and prey-hunting strategies of narwhals,“unicorns of the sea”,particularly the use of their distinctive spiral tusks,which play significant roles in hunting,searching prey,navigation,echolocation,and complex social interaction.Particularly,the NWOA imitates the foraging strategies and techniques of narwhals when hunting for prey but focuses mainly on the cooperative and exploratory behavior shown during group hunting and in the use of their tusks in sensing and locating prey under the Arctic ice.These functions provide a strong assessment basis for investigating the algorithm’s prowess at balancing exploration and exploitation,convergence speed,and solution accuracy.The performance of the NWOA is evaluated on 30 benchmark test functions.A comparison study using the Grey Wolf Optimizer(GWO),Whale Optimization Algorithm(WOA),Perfumer Optimization Algorithm(POA),Candle Flame Optimization(CFO)Algorithm,Particle Swarm Optimization(PSO)Algorithm,and Genetic Algorithm(GA)validates the results.As evidenced in the experimental results,NWOA is capable of yielding competitive outcomes among these well-known optimizers,whereas in several instances.These results suggest thatNWOAhas proven to be an effective and robust optimization tool suitable for solving many different complex optimization problems from the real world.
基金supported by the Serbian Ministry of Education and Science under Grant No.TR35006 and COST Action:CA23155—A Pan-European Network of Ocean Tribology(OTC)The research of B.Rosic and M.Rosic was supported by the Serbian Ministry of Education and Science under Grant TR35029.
文摘This paper introduces a hybrid multi-objective optimization algorithm,designated HMODESFO,which amalgamates the exploratory prowess of Differential Evolution(DE)with the rapid convergence attributes of the Sailfish Optimization(SFO)algorithm.The primary objective is to address multi-objective optimization challenges within mechanical engineering,with a specific emphasis on planetary gearbox optimization.The algorithm is equipped with the ability to dynamically select the optimal mutation operator,contingent upon an adaptive normalized population spacing parameter.The efficacy of HMODESFO has been substantiated through rigorous validation against estab-lished industry benchmarks,including a suite of Zitzler-Deb-Thiele(ZDT)and Zeb-Thiele-Laumanns-Zitzler(DTLZ)problems,where it exhibited superior performance.The outcomes underscore the algorithm’s markedly enhanced optimization capabilities relative to existing methods,particularly in tackling highly intricate multi-objective planetary gearbox optimization problems.Additionally,the performance of HMODESFO is evaluated against selected well-known mechanical engineering test problems,further accentuating its adeptness in resolving complex optimization challenges within this domain.
文摘Addressing the complex issue of emergency resource distribution center site selection in uncertain environments, this study was conducted to comprehensively consider factors such as uncertainty parameters and the urgency of demand at disaster-affected sites. Firstly, urgency cost, economic cost, and transportation distance cost were identified as key objectives. The study applied fuzzy theory integration to construct a triangular fuzzy multi-objective site selection decision model. Next, the defuzzification theory transformed the fuzzy decision model into a precise one. Subsequently, an improved Chaotic Quantum Multi-Objective Harris Hawks Optimization (CQ-MOHHO) algorithm was proposed to solve the model. The CQ-MOHHO algorithm was shown to rapidly produce high-quality Pareto front solutions and identify optimal site selection schemes for emergency resource distribution centers through case studies. This outcome verified the feasibility and efficacy of the site selection decision model and the CQ-MOHHO algorithm. To further assess CQ-MOHHO’s performance, Zitzler-Deb-Thiele (ZDT) test functions, commonly used in multi-objective optimization, were employed. Comparisons with Multi-Objective Harris Hawks Optimization (MOHHO), Non-dominated Sorting Genetic Algorithm II (NSGA-II), and Multi-Objective Grey Wolf Optimizer (MOGWO) using Generational Distance (GD), Hypervolume (HV), and Inverted Generational Distance (IGD) metrics showed that CQ-MOHHO achieved superior global search ability, faster convergence, and higher solution quality. The CQ-MOHHO algorithm efficiently achieved a balance between multiple objectives, providing decision-makers with satisfactory solutions and a valuable reference for researching and applying emergency site selection problems.
基金Project supported by the National Natural Science Foundation of China(No.62102130)the Central Government Guides Local Science and Technology Development Fund Project of China(No.226Z0201G)+4 种基金the Natural Science Foundation of Hebei Province of China(Nos.F2020204003 and F2024204001)the Hebei Youth Talents Support Project of China(No.BJ2019008)the Science and Technology Research Projects of Higher Education Institutions in Hebei Province of China(No.QN2024138)the Basic Scientific Research Funds Research Project of Hebei Provincial Colleges and Universities of China(No.KY2022073)the Hebei Province Higher Education Institution Scientific Research Project of China(No.QN2025192)。
文摘The dung beetle optimizer(DBO)is a metaheuristic algorithm with fast convergence and powerful search capabilities,which has shown excellent performance in solving various optimization problems.However,it suffers from the problems of easily falling into local optimal solutions and poor convergence accuracy when dealing with large-scale complex optimization problems.Therefore,we propose an adaptive DBO(ADBO)based on an elastic annealing mechanism to address these issues.First,the convergence factor is adjusted in a nonlinear decreasing manner to balance the requirements of global exploration and local exploitation,thus improving the convergence speed and search quality.Second,a greedy difference optimization strategy is introduced to increase population diversity,improve the global search capability,and avoid premature convergence.Finally,the elastic annealing mechanism is used to perturb the randomly selected individuals,helping the algorithm escape local optima and thereby improve solution quality and algorithm stability.The experimental results on the CEC 2017 and CEC 2022 benchmark function sets and MCNC benchmark circuits verify the effectiveness,superiority,and universality of ADBO.
基金funded by Researchers Supporting Programnumber(RSPD2024R809),King Saud University,Riyadh,Saudi Arabia.
文摘Multi-objective optimization is critical for problem-solving in engineering,economics,and AI.This study introduces the Multi-Objective Chef-Based Optimization Algorithm(MOCBOA),an upgraded version of the Chef-Based Optimization Algorithm(CBOA)that addresses distinct objectives.Our approach is unique in systematically examining four dominance relations—Pareto,Epsilon,Cone-epsilon,and Strengthened dominance—to evaluate their influence on sustaining solution variety and driving convergence toward the Pareto front.Our comparison investigation,which was conducted on fifty test problems from the CEC 2021 benchmark and applied to areas such as chemical engineering,mechanical design,and power systems,reveals that the dominance approach used has a considerable impact on the key optimization measures such as the hypervolume metric.This paper provides a solid foundation for determining themost effective dominance approach and significant insights for both theoretical research and practical applications in multi-objective optimization.
文摘In this study,a completely different approach to optimization is introduced through the development of a novel metaheuristic algorithm called the Barber Optimization Algorithm(BaOA).Inspired by the human interactions between barbers and customers,BaOA captures two key processes:the customer’s selection of a hairstyle and the detailed refinement during the haircut.These processes are translated into a mathematical framework that forms the foundation of BaOA,consisting of two critical phases:exploration,representing the creative selection process,and exploitation,which focuses on refining details for optimization.The performance of BaOA is evaluated using 52 standard benchmark functions,including unimodal,high-dimensional multimodal,fixed-dimensional multimodal,and the Congress on Evolutionary Computation(CEC)2017 test suite.This comprehensive assessment highlights BaOA’s ability to balance exploration and exploitation effectively,resulting in high-quality solutions.A comparative analysis against twelve widely known metaheuristic algorithms further demonstrates BaOA’s superior performance,as it consistently delivers better results across most benchmark functions.To validate its real-world applicability,BaOA is tested on four engineering design problems,illustrating its capability to address practical challenges with remarkable efficiency.The results confirm BaOA’s versatility and reliability as an optimization tool.This study not only introduces an innovative algorithm but also establishes its effectiveness in solving complex problems,providing a foundation for future research and applications in diverse scientific and engineering domains.
文摘This paper introduces dynamic boundary updating-surrogate model-based(DBU-SMB),a novel evolutionary framework for global optimization that integrates dynamic boundary updating(DBU)within a surrogate model-based(SMB)approach.The method operates in three progressive stages:adaptive sampling,DBU,and refinement.In the first stage,adaptive sampling strategically explores the design space to gather critical information for improving the surrogate model.The second stage incorporates DBU to guide the optimization toward promising regions in the parameter space,enhancing consistency and efficiency.Finally,the refinement stage iteratively improves the optimization results,ensuring a comprehensive exploration of the design space.The proposed DBU-SMB framework is algorithm-agnostic,meaning it does not rely on any specific machine learning model or meta-heuristic algorithm.To demonstrate its effectiveness,we applied DBU-SMB to four highly nonlinear and non-convex optimization problems.The results show a reduction of over 90%in the number of function evaluations compared to traditional methods,while avoiding entrapment in local optima and discovering superior solutions.These findings highlight the efficiency and robustness of DBU-SMB in achieving optimal designs,particularly for large-scale and complex optimization problems.
基金funded by National Natural Science Foundation of China(grant No.52405255)Special Program of Huzhou(grant No.2023GZ05)+1 种基金Projects of Huzhou Science and Technology Correspondent(grant No.2023KT76)Guangdong Basic and Applied Basic Research Foundation(grant No.2025A1515010487)。
文摘Variable-fidelity(VF)surrogate models have received increasing attention in engineering design optimization as they can approximate expensive high-fidelity(HF)simulations with reduced computational power.A key challenge to building a VF model is devising an adaptive model updating strategy that jointly selects additional low-fidelity(LF)and/or HF samples.The additional samples must enhance the model accuracy while maximizing the computational efficiency.We propose ISMA-VFEEI,a global optimization framework that integrates an Improved Slime-Mould Algorithm(ISMA)and a Variable-Fidelity Expected Extension Improvement(VFEEI)learning function to construct a VF surrogate model efficiently.First,A cost-aware VFEEI function guides the adaptive LF/HF sampling by explicitly incorporating evaluation cost and existing sample proximity.Second,ISMA is employed to solve the resulting non-convex optimization problem and identify global optimal infill points for model enhancement.The efficacy of ISMA-VFEEI is demonstrated through six numerical benchmarks and one real-world engineering case study.The engineering case study of a high-speed railway Electric Multiple Unit(EMU),the optimization objective of a sanding device attained a minimum value of 1.546 using only 20 HF evaluations,outperforming all the compared methods.
基金supported in part by the National Natural Science Foundation of China under Grant No.52175490.
文摘The shop scheduling problem with limited buffers has broad applications in real-world production scenarios,so this research direction is of great practical significance.However,there is currently little research on the hybrid flow shop scheduling problem with limited buffers(LBHFSP).This paper deeply investigates the LBHFSP to optimize the goal of the total completion time.To better solve the LBHFSP,a multi-level subpopulation-based particle swarm optimization algorithm(MLPSO)is proposed,which is founded on the attributes of the LBHFSP and the shortcomings of the basic PSO(particle swarm optimization)algorithm.In MLPSO,firstly,considering the impact of the limited buffers on the process of subsequent operations,a specific circular decoding strategy is developed to accommodate the characteristics of limited buffers.Secondly,an initialization strategy based on blocking time is designed to enhance the quality and diversity of the initial population.Afterward,a multi-level subpopulation collaborative search is developed to prevent being trapped in a local optimum and improve the global exploration capability.Additionally,a local search strategy based on the first blocked job is designed to enhance the MLPSO algorithm’s exploitation capability.Lastly,numerous experiments are carried out to test the performance of the proposed MLPSO by comparing it with classical intelligent optimization and popular algorithms in recent years.The results confirm that the proposed MLPSO has an outstanding performance when compared to other algorithms when solving LBHFSP.
文摘This paper addresses the Multi-Vehicle Routing Problem with Time Windows and Simultaneous Pickup and Delivery(MVRPTWSPD),aiming to optimize logistics distribution routes and minimize total costs.A vehicle routing optimization model is developed based on the operational requirements of the KS Logistics Center,focusing on minimizing vehicle dispatch,loading and unloading,operating,and time window penalty costs.The model incorporates constraints such as vehicle capacity,time windows,and travel distance,and is solved using a genetic algorithm to ensure optimal route planning.Through MATLAB simulations,34 customer points are analyzed,demonstrating that the simultaneous pickup and delivery model reduces total costs by 30.13%,increases vehicle loading rates by 20.04%,and decreases travel distance compared to delivery-only or pickup-only models.The results demonstrate the significant advantages of the simultaneous pickup and delivery mode in reducing logistics costs and improving vehicle utilization,offering valuable insights for enhancing the operational efficiency of the KS Logistics Center.
基金supported in part by the National Natural Science Foundation of China(62236002,62403004,62203001,62303009,62136008)the Open Project of Anhui Key Laboratory of Industrial Energy-Saving and Safety,Anhui University(KFKT202405)
文摘This paper addresses the distributed nonconvex optimization problem, where both the global cost function and local inequality constraint function are nonconvex. To tackle this issue, the p-power transformation and penalty function techniques are introduced to reframe the nonconvex optimization problem. This ensures that the Hessian matrix of the augmented Lagrangian function becomes local positive definite by choosing appropriate control parameters. A multi-timescale primal-dual method is then devised based on the Karush-Kuhn-Tucker(KKT) point of the reformulated nonconvex problem to attain convergence. The Lyapunov theory guarantees the model's stability in the presence of an undirected and connected communication network. Finally, two nonconvex optimization problems are presented to demonstrate the efficacy of the previously developed method.
基金supported by the National Natural Science Foundation of China(No.92371206)the Postgraduate Scientific Research Innovation Project of Hunan Province,China(No.CX2023063).
文摘Satellite Component Layout Optimization(SCLO) is crucial in satellite system design.This paper proposes a novel Satellite Three-Dimensional Component Assignment and Layout Optimization(3D-SCALO) problem tailored to engineering requirements, aiming to optimize satellite heat dissipation while considering constraints on static stability, 3D geometric relationships between components, and special component positions. The 3D-SCALO problem is a challenging bilevel combinatorial optimization task, involving the optimization of discrete component assignment variables in the outer layer and continuous component position variables in the inner layer,with both influencing each other. To address this issue, first, a Mixed Integer Programming(MIP) model is proposed, which reformulates the original bilevel problem into a single-level optimization problem, enabling the exploration of a more comprehensive optimization space while avoiding iterative nested optimization. Then, to model the 3D geometric relationships between components within the MIP framework, a linearized 3D Phi-function method is proposed, which handles non-overlapping and safety distance constraints between cuboid components in an explicit and effective way. Subsequently, the Finite-Rectangle Method(FRM) is proposed to manage 3D geometric constraints for complex-shaped components by approximating them with a finite set of cuboids, extending the applicability of the geometric modeling approach. Finally, the feasibility and effectiveness of the proposed MIP model are demonstrated through two numerical examples"and a real-world engineering case, which confirms its suitability for complex-shaped components and real engineering applications.
基金supported by Youth Talent Project of Scientific Research Program of Hubei Provincial Department of Education under Grant Q20241809Doctoral Scientific Research Foundation of Hubei University of Automotive Technology under Grant 202404.
文摘As Internet of Things(IoT)applications expand,Mobile Edge Computing(MEC)has emerged as a promising architecture to overcome the real-time processing limitations of mobile devices.Edge-side computation offloading plays a pivotal role in MEC performance but remains challenging due to complex task topologies,conflicting objectives,and limited resources.This paper addresses high-dimensional multi-objective offloading for serial heterogeneous tasks in MEC.We jointly consider task heterogeneity,high-dimensional objectives,and flexible resource scheduling,modeling the problem as a Many-objective optimization.To solve it,we propose a flexible framework integrating an improved cooperative co-evolutionary algorithm based on decomposition(MOCC/D)and a flexible scheduling strategy.Experimental results on benchmark functions and simulation scenarios show that the proposed method outperforms existing approaches in both convergence and solution quality.
基金supported by the Science and Technology Research Project of Henan Province(242102241055)the Industry-University-Research Collaborative Innovation Base on Automobile Lightweight of“Science and Technology Innovation in Central Plains”(2024KCZY315)the Opening Fund of State Key Laboratory of Structural Analysis,Optimization and CAE Software for Industrial Equipment(GZ2024A03-ZZU).
文摘The moving morphable component(MMC)topology optimization method,as a typical explicit topology optimization method,has been widely concerned.In the MMC topology optimization framework,the surrogate material model is mainly used for finite element analysis at present,and the effectiveness of the surrogate material model has been fully confirmed.However,there are some accuracy problems when dealing with boundary elements using the surrogate material model,which will affect the topology optimization results.In this study,a boundary element reconstruction(BER)model is proposed based on the surrogate material model under the MMC topology optimization framework to improve the accuracy of topology optimization.The proposed BER model can reconstruct the boundary elements by refining the local meshes and obtaining new nodes in boundary elements.Then the density of boundary elements is recalculated using the new node information,which is more accurate than the original model.Based on the new density of boundary elements,the material properties and volume information of the boundary elements are updated.Compared with other finite element analysis methods,the BER model is simple and feasible and can improve computational accuracy.Finally,the effectiveness and superiority of the proposed method are verified by comparing it with the optimization results of the original surrogate material model through several numerical examples.
基金supported by the National Key Research and Development Program of China(2023YFF0906502)the Postgraduate Research and Innovation Project of Hunan Province under Grant(CX20240473).
文摘Due to the digital transformation tendency among cultural institutions and the substantial influence of the social media platform,the demands of visual communication keep increasing for promoting traditional cultural artifacts online.As an effective medium,posters serve to attract public attention and facilitate broader engagement with cultural artifacts.However,existing poster generation methods mainly rely on fixed templates and manual design,which limits their scalability and adaptability to the diverse visual and semantic features of the artifacts.Therefore,we propose CAPGen,an automated aesthetic Cultural Artifacts Poster Generation framework built on a Multimodal Large Language Model(MLLM)with integrated iterative optimization.During our research,we collaborated with designers to define principles of graphic design for cultural artifact posters,to guide the MLLM in generating layout parameters.Later,we generated these parameters into posters.Finally,we refined the posters using an MLLM integrated with a multi-round iterative optimization mechanism.Qualitative results show that CAPGen consistently outperforms baseline methods in both visual quality and aesthetic performance.Furthermore,ablation studies indicate that the prompt,iterative optimization mechanism,and design principles significantly enhance the effectiveness of poster generation.
基金funded by Deanship of Graduate studies and Scientific Research at Jouf University under grant No.(DGSSR-2024-02-01264).
文摘Automated essay scoring(AES)systems have gained significant importance in educational settings,offering a scalable,efficient,and objective method for evaluating student essays.However,developing AES systems for Arabic poses distinct challenges due to the language’s complex morphology,diglossia,and the scarcity of annotated datasets.This paper presents a hybrid approach to Arabic AES by combining text-based,vector-based,and embeddingbased similarity measures to improve essay scoring accuracy while minimizing the training data required.Using a large Arabic essay dataset categorized into thematic groups,the study conducted four experiments to evaluate the impact of feature selection,data size,and model performance.Experiment 1 established a baseline using a non-machine learning approach,selecting top-N correlated features to predict essay scores.The subsequent experiments employed 5-fold cross-validation.Experiment 2 showed that combining embedding-based,text-based,and vector-based features in a Random Forest(RF)model achieved an R2 of 88.92%and an accuracy of 83.3%within a 0.5-point tolerance.Experiment 3 further refined the feature selection process,demonstrating that 19 correlated features yielded optimal results,improving R2 to 88.95%.In Experiment 4,an optimal data efficiency training approach was introduced,where training data portions increased from 5%to 50%.The study found that using just 10%of the data achieved near-peak performance,with an R2 of 85.49%,emphasizing an effective trade-off between performance and computational costs.These findings highlight the potential of the hybrid approach for developing scalable Arabic AES systems,especially in low-resource environments,addressing linguistic challenges while ensuring efficient data usage.
