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
In this paper, both Fritz John and Karush-Kuhn-Tucker necessary optimality conditions are established for a （weakly） LU-efficient solution in the considered nonsmooth multiobjective programming problem with the mult...In this paper, both Fritz John and Karush-Kuhn-Tucker necessary optimality conditions are established for a （weakly） LU-efficient solution in the considered nonsmooth multiobjective programming problem with the multiple interval-objective function. Further, the sufficient optimality conditions for a （weakly） LU-efficient solution and several duality results in Mond-Weir sense are proved under assumptions that the functions constituting the considered nondifferentiable multiobjective programming problem with the multiple interval- objective function are convex.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
Artificial rabbits optimization(ARO)is a recently proposed biology-based optimization algorithm inspired by the detour foraging and random hiding behavior of rabbits in nature.However,for solving optimization problems...Artificial rabbits optimization(ARO)is a recently proposed biology-based optimization algorithm inspired by the detour foraging and random hiding behavior of rabbits in nature.However,for solving optimization problems,the ARO algorithm shows slow convergence speed and can fall into local minima.To overcome these drawbacks,this paper proposes chaotic opposition-based learning ARO(COARO),an improved version of the ARO algorithm that incorporates opposition-based learning(OBL)and chaotic local search(CLS)techniques.By adding OBL to ARO,the convergence speed of the algorithm increases and it explores the search space better.Chaotic maps in CLS provide rapid convergence by scanning the search space efficiently,since their ergodicity and non-repetitive properties.The proposed COARO algorithm has been tested using thirty-three distinct benchmark functions.The outcomes have been compared with the most recent optimization algorithms.Additionally,the COARO algorithm’s problem-solving capabilities have been evaluated using six different engineering design problems and compared with various other algorithms.This study also introduces a binary variant of the continuous COARO algorithm,named BCOARO.The performance of BCOARO was evaluated on the breast cancer dataset.The effectiveness of BCOARO has been compared with different feature selection algorithms.The proposed BCOARO outperforms alternative algorithms,according to the findings obtained for real applications in terms of accuracy performance,and fitness value.Extensive experiments show that the COARO and BCOARO algorithms achieve promising results compared to other metaheuristic algorithms.展开更多
We introduce Quafu-Qcover,an open-source cloud-based software package developed for solving combinatorial optimization problems using quantum simulators and hardware backends.Quafu-Qcover provides a standardized and c...We introduce Quafu-Qcover,an open-source cloud-based software package developed for solving combinatorial optimization problems using quantum simulators and hardware backends.Quafu-Qcover provides a standardized and comprehensive workflow that utilizes the quantum approximate optimization algorithm(QAOA).It facilitates the automatic conversion of the original problem into a quadratic unconstrained binary optimization(QUBO)model and its corresponding Ising model,which can be subsequently transformed into a weight graph.The core of Qcover relies on a graph decomposition-based classical algorithm,which efficiently derives the optimal parameters for the shallow QAOA circuit.Quafu-Qcover incorporates a dedicated compiler capable of translating QAOA circuits into physical quantum circuits that can be executed on Quafu cloud quantum computers.Compared to a general-purpose compiler,our compiler demonstrates the ability to generate shorter circuit depths,while also exhibiting superior speed performance.Additionally,the Qcover compiler has the capability to dynamically create a library of qubits coupling substructures in real-time,utilizing the most recent calibration data from the superconducting quantum devices.This ensures that computational tasks can be assigned to connected physical qubits with the highest fidelity.The Quafu-Qcover allows us to retrieve quantum computing sampling results using a task ID at any time,enabling asynchronous processing.Moreover,it incorporates modules for results preprocessing and visualization,facilitating an intuitive display of solutions for combinatorial optimization problems.We hope that Quafu-Qcover can serve as an instructive illustration for how to explore application problems on the Quafu cloud quantum computers.展开更多
Real-world engineering design problems with complex objective functions under some constraints are relatively difficult problems to solve.Such design problems are widely experienced in many engineering fields,such as ...Real-world engineering design problems with complex objective functions under some constraints are relatively difficult problems to solve.Such design problems are widely experienced in many engineering fields,such as industry,automotive,construction,machinery,and interdisciplinary research.However,there are established optimization techniques that have shown effectiveness in addressing these types of issues.This research paper gives a comparative study of the implementation of seventeen new metaheuristic methods in order to optimize twelve distinct engineering design issues.The algorithms used in the study are listed as:transient search optimization(TSO),equilibrium optimizer(EO),grey wolf optimizer(GWO),moth-flame optimization(MFO),whale optimization algorithm(WOA),slimemould algorithm(SMA),harris hawks optimization(HHO),chimp optimization algorithm(COA),coot optimization algorithm(COOT),multi-verse optimization(MVO),arithmetic optimization algorithm(AOA),aquila optimizer(AO),sine cosine algorithm(SCA),smell agent optimization(SAO),and seagull optimization algorithm(SOA),pelican optimization algorithm(POA),and coati optimization algorithm(CA).As far as we know,there is no comparative analysis of recent and popular methods against the concrete conditions of real-world engineering problems.Hence,a remarkable research guideline is presented in the study for researchersworking in the fields of engineering and artificial intelligence,especiallywhen applying the optimization methods that have emerged recently.Future research can rely on this work for a literature search on comparisons of metaheuristic optimization methods in real-world problems under similar conditions.展开更多
In practical engineering,multi-objective optimization often encounters situations where multiple Pareto sets(PS)in the decision space correspond to the same Pareto front(PF)in the objective space,known as Multi-Modal ...In practical engineering,multi-objective optimization often encounters situations where multiple Pareto sets(PS)in the decision space correspond to the same Pareto front(PF)in the objective space,known as Multi-Modal Multi-Objective Optimization Problems(MMOP).Locating multiple equivalent global PSs poses a significant challenge in real-world applications,especially considering the existence of local PSs.Effectively identifying and locating both global and local PSs is a major challenge.To tackle this issue,we introduce an immune-inspired reproduction strategy designed to produce more offspring in less crowded,promising regions and regulate the number of offspring in areas that have been thoroughly explored.This approach achieves a balanced trade-off between exploration and exploitation.Furthermore,we present an interval allocation strategy that adaptively assigns fitness levels to each antibody.This strategy ensures a broader survival margin for solutions in their initial stages and progressively amplifies the differences in individual fitness values as the population matures,thus fostering better population convergence.Additionally,we incorporate a multi-population mechanism that precisely manages each subpopulation through the interval allocation strategy,ensuring the preservation of both global and local PSs.Experimental results on 21 test problems,encompassing both global and local PSs,are compared with eight state-of-the-art multimodal multi-objective optimization algorithms.The results demonstrate the effectiveness of our proposed algorithm in simultaneously identifying global Pareto sets and locally high-quality PSs.展开更多
Sparse large-scale multi-objective optimization problems(SLMOPs)are common in science and engineering.However,the large-scale problem represents the high dimensionality of the decision space,requiring algorithms to tr...Sparse large-scale multi-objective optimization problems(SLMOPs)are common in science and engineering.However,the large-scale problem represents the high dimensionality of the decision space,requiring algorithms to traverse vast expanse with limited computational resources.Furthermore,in the context of sparse,most variables in Pareto optimal solutions are zero,making it difficult for algorithms to identify non-zero variables efficiently.This paper is dedicated to addressing the challenges posed by SLMOPs.To start,we introduce innovative objective functions customized to mine maximum and minimum candidate sets.This substantial enhancement dramatically improves the efficacy of frequent pattern mining.In this way,selecting candidate sets is no longer based on the quantity of nonzero variables they contain but on a higher proportion of nonzero variables within specific dimensions.Additionally,we unveil a novel approach to association rule mining,which delves into the intricate relationships between non-zero variables.This novel methodology aids in identifying sparse distributions that can potentially expedite reductions in the objective function value.We extensively tested our algorithm across eight benchmark problems and four real-world SLMOPs.The results demonstrate that our approach achieves competitive solutions across various challenges.展开更多
Drone logistics is a novel method of distribution that will become prevalent.The advantageous location of the logistics hub enables quicker customer deliveries and lower fuel consumption,resulting in cost savings for ...Drone logistics is a novel method of distribution that will become prevalent.The advantageous location of the logistics hub enables quicker customer deliveries and lower fuel consumption,resulting in cost savings for the company’s transportation operations.Logistics firms must discern the ideal location for establishing a logistics hub,which is challenging due to the simplicity of existing models and the intricate delivery factors.To simulate the drone logistics environment,this study presents a new mathematical model.The model not only retains the aspects of the current models,but also considers the degree of transportation difficulty from the logistics hub to the village,the capacity of drones for transportation,and the distribution of logistics hub locations.Moreover,this paper proposes an improved particle swarm optimization(PSO)algorithm which is a diversity-based hybrid PSO(DHPSO)algorithm to solve this model.In DHPSO,the Gaussian random walk can enhance global search in the model space,while the bubble-net attacking strategy can speed convergence.Besides,Archimedes spiral strategy is employed to overcome the local optima trap in the model and improve the exploitation of the algorithm.DHPSO maintains a balance between exploration and exploitation while better defining the distribution of logistics hub locations Numerical experiments show that the newly proposed model always achieves better locations than the current model.Comparing DHPSO with other state-of-the-art intelligent algorithms,the efficiency of the scheme can be improved by 42.58%.This means that logistics companies can reduce distribution costs and consumers can enjoy a more enjoyable shopping experience by using DHPSO’s location selection.All the results show the location of the drone logistics hub is solved by DHPSO effectively.展开更多
The optimization of polymer structures aims to determine an optimal sequence or topology that achieves a given target property or structural performance.This inverse design problem involves searching within a vast com...The optimization of polymer structures aims to determine an optimal sequence or topology that achieves a given target property or structural performance.This inverse design problem involves searching within a vast combinatorial phase space defined by components,se-quences,and topologies,and is often computationally intractable due to its NP-hard nature.At the core of this challenge lies the need to evalu-ate complex correlations among structural variables,a classical problem in both statistical physics and combinatorial optimization.To address this,we adopt a mean-field approach that decouples direct variable-variable interactions into effective interactions between each variable and an auxiliary field.The simulated bifurcation(SB)algorithm is employed as a mean-field-based optimization framework.It constructs a Hamiltonian dynamical system by introducing generalized momentum fields,enabling efficient decoupling and dynamic evolution of strongly coupled struc-tural variables.Using the sequence optimization of a linear copolymer adsorbing on a solid surface as a case study,we demonstrate the applica-bility of the SB algorithm to high-dimensional,non-differentiable combinatorial optimization problems.Our results show that SB can efficiently discover polymer sequences with excellent adsorption performance within a reasonable computational time.Furthermore,it exhibits robust con-vergence and high parallel scalability across large design spaces.The approach developed in this work offers a new computational pathway for polymer structure optimization.It also lays a theoretical foundation for future extensions to topological design problems,such as optimizing the number and placement of side chains,as well as the co-optimization of sequence and topology.展开更多
Feature selection(FS)is essential in machine learning(ML)and data mapping by its ability to preprocess high-dimensional data.By selecting a subset of relevant features,feature selection cuts down on the dimension of t...Feature selection(FS)is essential in machine learning(ML)and data mapping by its ability to preprocess high-dimensional data.By selecting a subset of relevant features,feature selection cuts down on the dimension of the data.It excludes irrelevant or surplus features,thus boosting the performance and efficiency of the model.Particle Swarm Optimization(PSO)boasts a streamlined algorithmic framework and exhibits rapid convergence traits.Compared with other algorithms,it incurs reduced computational expenses when tackling high-dimensional datasets.However,PSO faces challenges like inadequate convergence precision.Therefore,regarding FS problems,this paper presents a binary version enhanced PSO based on the Support Vector Machines(SVM)classifier.First,the Sand Cat Swarm Optimization(SCSO)is added to enhance the global search capability of PSO and improve the accuracy of the solution.Secondly,the Latin hypercube sampling strategy initializes populations more uniformly and helps to increase population diversity.The last is the roundup search strategy introducing the grey wolf hierarchy idea to help improve convergence speed.To verify the capability of Self-adaptive Cooperative Particle Swarm Optimization(SCPSO),the CEC2020 test suite and CEC2022 test suite are selected for experiments and applied to three engineering problems.Compared with the standard PSO algorithm,SCPSO converges faster,and the convergence accuracy is significantly improved.Moreover,SCPSO’s comprehensive performance far exceeds that of other algorithms.Six datasets from the University of California,Irvine(UCI)database were selected to evaluate SCPSO’s effectiveness in solving feature selection problems.The results indicate that SCPSO has significant potential for addressing these problems.展开更多
Hybrid renewable energy systems(HRES)offer cost-effectiveness,low-emission power solutions,and reduced dependence on fossil fuels.However,the renewable energy allocation problem remains challenging due to complex syst...Hybrid renewable energy systems(HRES)offer cost-effectiveness,low-emission power solutions,and reduced dependence on fossil fuels.However,the renewable energy allocation problem remains challenging due to complex system interactions and multiple operational constraints.This study develops a novel Multi-Neighborhood Enhanced Harris Hawks Optimization(MNEHHO)algorithm to address the allocation of HRES components.The proposed approach integrates key technical parameters,including charge-discharge efficiency,storage device configurations,and renewable energy fraction.We formulate a comprehensive mathematical model that simultaneously minimizes levelized energy costs and pollutant emissions while maintaining system reliability.The MNEHHO algorithm employs multiple neighborhood structures to enhance solution diversity and exploration capabilities.The model’s effectiveness is validated through case studies across four distinct institutional energy demand profiles.Results demonstrate that our approach successfully generates practically feasible HRES configurations while achieving significant reductions in costs and emissions compared to conventional methods.The enhanced search mechanisms of MNEHHO show superior performance in avoiding local optima and achieving consistent solutions.Experimental results demonstrate concrete improvements in solution quality(up to 46% improvement in objective value)and computational efficiency(average coefficient of variance of 24%-27%)across diverse institutional settings.This confirms the robustness and scalability of our method under various operational scenarios,providing a reliable framework for solving renewable energy allocation problems.展开更多
In recent years,surrogate models derived from genuine data samples have proven to be efficient in addressing optimization challenges that are costly or time⁃intensive.However,the individuals in the population become i...In recent years,surrogate models derived from genuine data samples have proven to be efficient in addressing optimization challenges that are costly or time⁃intensive.However,the individuals in the population become indistinguishable as the curse of dimensionality increases in the objective space and the accumulation of surrogate approximated errors.Therefore,in this paper,each objective function is modeled using a radial basis function approach,and the optimal solution set of the surrogate model is located by the multi⁃objective evolutionary algorithm of strengthened dominance relation.The original objective function values of the true evaluations are converted to two indicator values,and then the surrogate models are set up for the two performance indicators.Finally,an adaptive infill sampling strategy that relies on approximate performance indicators is proposed to assist in selecting individuals for real evaluations from the potential optimal solution set.The algorithm is contrasted against several advanced surrogate⁃assisted evolutionary algorithms on two suites of test cases,and the experimental findings prove that the approach is competitive in solving expensive many⁃objective optimization problems.展开更多
In this study,we construct a bi-level optimization model based on the Stackelberg game and propose a robust optimization algorithm for solving the bi-level model,assuming an actual situation with several participants ...In this study,we construct a bi-level optimization model based on the Stackelberg game and propose a robust optimization algorithm for solving the bi-level model,assuming an actual situation with several participants in energy trading.Firstly,the energy trading process is analyzed between each subject based on the establishment of the operation framework of multi-agent participation in energy trading.Secondly,the optimal operation model of each energy trading agent is established to develop a bi-level game model including each energy participant.Finally,a combination algorithm of improved robust optimization over time(ROOT)and CPLEX is proposed to solve the established game model.The experimental results indicate that under different fitness thresholds,the robust optimization results of the proposed algorithm are increased by 56.91%and 68.54%,respectively.The established bi-level game model effectively balances the benefits of different energy trading entities.The proposed algorithm proposed can increase the income of each participant in the game by an average of 8.59%.展开更多
Efficient warehouse management is critical for modern supply chain systems,particularly in the era of e-commerce and automation.The Multi-Picker Robot Routing Problem(MPRRP)presents a complex challenge involving the o...Efficient warehouse management is critical for modern supply chain systems,particularly in the era of e-commerce and automation.The Multi-Picker Robot Routing Problem(MPRRP)presents a complex challenge involving the optimization of routes for multiple robots assigned to retrieve items from distinct locations within a warehouse.This study introduces optimized metaheuristic strategies to address MPRRP,with the aim of minimizing travel distances,energy consumption,and order fulfillment time while ensuring operational efficiency.Advanced algorithms,including an enhanced Particle Swarm Optimization(PSO-MPRRP)and a tailored Genetic Algorithm(GA-MPRRP),are specifically designed with customized evolutionary operators to effectively solve the MPRRP.Comparative experiments are conducted to evaluate the proposed strategies against benchmark approaches,demonstrating significant improvements in solution quality and computational efficiency.The findings contribute to the development of intelligent,scalable,and environmentally friendly warehouse systems,paving the way for future advances in robotics and automated logistics management.展开更多
In a world where supply chains are increasingly complex and unpredictable,finding the optimal way to move goods through transshipment networks is more important and challenging than ever.In addition to addressing the ...In a world where supply chains are increasingly complex and unpredictable,finding the optimal way to move goods through transshipment networks is more important and challenging than ever.In addition to addressing the complexity of transportation costs and demand,this study presents a novel method that offers flexible routing alternatives to manage these complexities.When real-world variables such as fluctuating costs,variable capacity,and unpredictable demand are considered,traditional transshipment models often prove inadequate.To overcome these challenges,we propose an innovative fully fuzzy-based framework using LR flat fuzzy numbers.This framework allows for more adaptable and flexible decision-making in multi-objective transshipment situations by effectively capturing uncertain parameters.To overcome these challenges,we develop an innovative,fully fuzzy-based framework using LR flat fuzzy numbers to effectively capture uncertainty in key parameters,offering more flexible and adaptive decision-making in multi-objective transshipment problems.The proposed model also presents alternative route options,giving decisionmakers a range of choices to satisfy multiple requirements,including reducing costs,improving service quality,and expediting delivery.Through extensive numerical experiments,we demonstrate that the model can achieve greater adaptability,efficiency,and flexibility than standard approaches.This multi-path structure provides additional flexibility to adapt to dynamic network conditions.Using ranking strategies,we compared our multi-objective transshipment model with existing methods.The results indicate that,while traditional methods such as goal and fuzzy programming generate results close to the anti-ideal value,thus reducing their efficiency,our model produces solutions close to the ideal value,thereby facilitating better decision making.By combining dynamic routing alternatives with a fully fuzzybased approach,this study offers an effective tool to improve decision-making and optimize complex networks under real-world conditions in practical settings.In this paper,we utilize LINGO 18 software to solve the provided numerical example,demonstrating the effectiveness of the proposed method.展开更多
To solve the Laplacian problems,we adopt a meshless method with the multiquadric radial basis function(MQRBF)as a basis whose center is distributed inside a circle with a fictitious radius.A maximal projection techniq...To solve the Laplacian problems,we adopt a meshless method with the multiquadric radial basis function(MQRBF)as a basis whose center is distributed inside a circle with a fictitious radius.A maximal projection technique is developed to identify the optimal shape factor and fictitious radius by minimizing a merit function.A sample function is interpolated by theMQ-RBF to provide a trial coefficient vector to compute the merit function.We can quickly determine the optimal values of the parameters within a preferred rage using the golden section search algorithm.The novel method provides the optimal values of parameters and,hence,an optimal MQ-RBF;the performance of the method is validated in numerical examples.Moreover,nonharmonic problems are transformed to the Poisson equation endowed with a homogeneous boundary condition;this can overcome the problem of these problems being ill-posed.The optimal MQ-RBF is extremely accurate.We further propose a novel optimal polynomial method to solve the nonharmonic problems,which achieves high precision up to an order of 10^(−11).展开更多
Snake Optimizer(SO)is a novel Meta-heuristic Algorithm(MA)inspired by the mating behaviour of snakes,which has achieved success in global numerical optimization problems and practical engineering applications.However,...Snake Optimizer(SO)is a novel Meta-heuristic Algorithm(MA)inspired by the mating behaviour of snakes,which has achieved success in global numerical optimization problems and practical engineering applications.However,it also has certain drawbacks for the exploration stage and the egg hatch process,resulting in slow convergence speed and inferior solution quality.To address the above issues,a novel multi-strategy improved SO(MISO)with the assistance of population crowding analysis is proposed in this article.In the algorithm,a novel multi-strategy operator is designed for the exploration stage,which not only focuses on using the information of better performing individuals to improve the quality of solution,but also focuses on maintaining population diversity.To boost the efficiency of the egg hatch process,the multi-strategy egg hatch process is proposed to regenerate individuals according to the results of the population crowding analysis.In addition,a local search method is employed to further enhance the convergence speed and the local search capability.MISO is first compared with three sets of algorithms in the CEC2020 benchmark functions,including SO with its two recently discussed variants,ten advanced MAs,and six powerful CEC competition algorithms.The performance of MISO is then verified on five practical engineering design problems.The experimental results show that MISO provides a promising performance for the above optimization cases in terms of convergence speed and solution quality.展开更多
A bicubic B-spline finite element method is proposed to solve optimal control problems governed by fourth-order semilinear parabolic partial differential equations.Its key feature is the selection of bicubic B-splines...A bicubic B-spline finite element method is proposed to solve optimal control problems governed by fourth-order semilinear parabolic partial differential equations.Its key feature is the selection of bicubic B-splines as trial functions to approximate the state and costate variables in two space dimensions.A Crank-Nicolson difference scheme is constructed for time discretization.The resulting numerical solutions belong to C2in space,and the order of the coefficient matrix is low.Moreover,the Bogner-Fox-Schmit element is considered for comparison.Two numerical experiments demonstrate the feasibility and effectiveness of the proposed method.展开更多
This work investigates a multi-product parallel disassembly line balancing problem considering multi-skilled workers.A mathematical model for the parallel disassembly line is established to achieve maximized disassemb...This work investigates a multi-product parallel disassembly line balancing problem considering multi-skilled workers.A mathematical model for the parallel disassembly line is established to achieve maximized disassembly profit and minimized workstation cycle time.Based on a product’s AND/OR graph,matrices for task-skill,worker-skill,precedence relationships,and disassembly correlations are developed.A multi-objective discrete chemical reaction optimization algorithm is designed.To enhance solution diversity,improvements are made to four reactions:decomposition,synthesis,intermolecular ineffective collision,and wall invalid collision reaction,completing the evolution of molecular individuals.The established model and improved algorithm are applied to ball pen,flashlight,washing machine,and radio combinations,respectively.Introducing a Collaborative Resource Allocation(CRA)strategy based on a Decomposition-Based Multi-Objective Evolutionary Algorithm,the experimental results are compared with four classical algorithms:MOEA/D,MOEAD-CRA,Non-dominated Sorting Genetic Algorithm Ⅱ(NSGA-Ⅱ),and Non-dominated Sorting Genetic Algorithm Ⅲ(NSGA-Ⅲ).This validates the feasibility and superiority of the proposed algorithm in parallel disassembly production lines.展开更多
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In this paper, both Fritz John and Karush-Kuhn-Tucker necessary optimality conditions are established for a （weakly） LU-efficient solution in the considered nonsmooth multiobjective programming problem with the multiple interval-objective function. Further, the sufficient optimality conditions for a （weakly） LU-efficient solution and several duality results in Mond-Weir sense are proved under assumptions that the functions constituting the considered nondifferentiable multiobjective programming problem with the multiple interval- objective function are convex.
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funded by Firat University Scientific Research Projects Management Unit for the scientific research project of Feyza AltunbeyÖzbay,numbered MF.23.49.
文摘Artificial rabbits optimization(ARO)is a recently proposed biology-based optimization algorithm inspired by the detour foraging and random hiding behavior of rabbits in nature.However,for solving optimization problems,the ARO algorithm shows slow convergence speed and can fall into local minima.To overcome these drawbacks,this paper proposes chaotic opposition-based learning ARO(COARO),an improved version of the ARO algorithm that incorporates opposition-based learning(OBL)and chaotic local search(CLS)techniques.By adding OBL to ARO,the convergence speed of the algorithm increases and it explores the search space better.Chaotic maps in CLS provide rapid convergence by scanning the search space efficiently,since their ergodicity and non-repetitive properties.The proposed COARO algorithm has been tested using thirty-three distinct benchmark functions.The outcomes have been compared with the most recent optimization algorithms.Additionally,the COARO algorithm’s problem-solving capabilities have been evaluated using six different engineering design problems and compared with various other algorithms.This study also introduces a binary variant of the continuous COARO algorithm,named BCOARO.The performance of BCOARO was evaluated on the breast cancer dataset.The effectiveness of BCOARO has been compared with different feature selection algorithms.The proposed BCOARO outperforms alternative algorithms,according to the findings obtained for real applications in terms of accuracy performance,and fitness value.Extensive experiments show that the COARO and BCOARO algorithms achieve promising results compared to other metaheuristic algorithms.
基金supported by the National Natural Science Foundation of China(Grant No.92365206)the support of the China Postdoctoral Science Foundation(Certificate Number:2023M740272)+1 种基金supported by the National Natural Science Foundation of China(Grant No.12247168)China Postdoctoral Science Foundation(Certificate Number:2022TQ0036)。
文摘We introduce Quafu-Qcover,an open-source cloud-based software package developed for solving combinatorial optimization problems using quantum simulators and hardware backends.Quafu-Qcover provides a standardized and comprehensive workflow that utilizes the quantum approximate optimization algorithm(QAOA).It facilitates the automatic conversion of the original problem into a quadratic unconstrained binary optimization(QUBO)model and its corresponding Ising model,which can be subsequently transformed into a weight graph.The core of Qcover relies on a graph decomposition-based classical algorithm,which efficiently derives the optimal parameters for the shallow QAOA circuit.Quafu-Qcover incorporates a dedicated compiler capable of translating QAOA circuits into physical quantum circuits that can be executed on Quafu cloud quantum computers.Compared to a general-purpose compiler,our compiler demonstrates the ability to generate shorter circuit depths,while also exhibiting superior speed performance.Additionally,the Qcover compiler has the capability to dynamically create a library of qubits coupling substructures in real-time,utilizing the most recent calibration data from the superconducting quantum devices.This ensures that computational tasks can be assigned to connected physical qubits with the highest fidelity.The Quafu-Qcover allows us to retrieve quantum computing sampling results using a task ID at any time,enabling asynchronous processing.Moreover,it incorporates modules for results preprocessing and visualization,facilitating an intuitive display of solutions for combinatorial optimization problems.We hope that Quafu-Qcover can serve as an instructive illustration for how to explore application problems on the Quafu cloud quantum computers.
文摘Real-world engineering design problems with complex objective functions under some constraints are relatively difficult problems to solve.Such design problems are widely experienced in many engineering fields,such as industry,automotive,construction,machinery,and interdisciplinary research.However,there are established optimization techniques that have shown effectiveness in addressing these types of issues.This research paper gives a comparative study of the implementation of seventeen new metaheuristic methods in order to optimize twelve distinct engineering design issues.The algorithms used in the study are listed as:transient search optimization(TSO),equilibrium optimizer(EO),grey wolf optimizer(GWO),moth-flame optimization(MFO),whale optimization algorithm(WOA),slimemould algorithm(SMA),harris hawks optimization(HHO),chimp optimization algorithm(COA),coot optimization algorithm(COOT),multi-verse optimization(MVO),arithmetic optimization algorithm(AOA),aquila optimizer(AO),sine cosine algorithm(SCA),smell agent optimization(SAO),and seagull optimization algorithm(SOA),pelican optimization algorithm(POA),and coati optimization algorithm(CA).As far as we know,there is no comparative analysis of recent and popular methods against the concrete conditions of real-world engineering problems.Hence,a remarkable research guideline is presented in the study for researchersworking in the fields of engineering and artificial intelligence,especiallywhen applying the optimization methods that have emerged recently.Future research can rely on this work for a literature search on comparisons of metaheuristic optimization methods in real-world problems under similar conditions.
基金supported in part by the Science and Technology Project of Yunnan Tobacco Industrial Company under Grant JB2022YL02in part by the Natural Science Foundation of Henan Province of China under Grant 242300421413in part by the Henan Province Science and Technology Research Projects under Grants 242102110334 and 242102110375.
文摘In practical engineering,multi-objective optimization often encounters situations where multiple Pareto sets(PS)in the decision space correspond to the same Pareto front(PF)in the objective space,known as Multi-Modal Multi-Objective Optimization Problems(MMOP).Locating multiple equivalent global PSs poses a significant challenge in real-world applications,especially considering the existence of local PSs.Effectively identifying and locating both global and local PSs is a major challenge.To tackle this issue,we introduce an immune-inspired reproduction strategy designed to produce more offspring in less crowded,promising regions and regulate the number of offspring in areas that have been thoroughly explored.This approach achieves a balanced trade-off between exploration and exploitation.Furthermore,we present an interval allocation strategy that adaptively assigns fitness levels to each antibody.This strategy ensures a broader survival margin for solutions in their initial stages and progressively amplifies the differences in individual fitness values as the population matures,thus fostering better population convergence.Additionally,we incorporate a multi-population mechanism that precisely manages each subpopulation through the interval allocation strategy,ensuring the preservation of both global and local PSs.Experimental results on 21 test problems,encompassing both global and local PSs,are compared with eight state-of-the-art multimodal multi-objective optimization algorithms.The results demonstrate the effectiveness of our proposed algorithm in simultaneously identifying global Pareto sets and locally high-quality PSs.
基金support by the Open Project of Xiangjiang Laboratory(22XJ02003)the University Fundamental Research Fund(23-ZZCX-JDZ-28,ZK21-07)+5 种基金the National Science Fund for Outstanding Young Scholars(62122093)the National Natural Science Foundation of China(72071205)the Hunan Graduate Research Innovation Project(CX20230074)the Hunan Natural Science Foundation Regional Joint Project(2023JJ50490)the Science and Technology Project for Young and Middle-aged Talents of Hunan(2023TJZ03)the Science and Technology Innovation Program of Humnan Province(2023RC1002).
文摘Sparse large-scale multi-objective optimization problems(SLMOPs)are common in science and engineering.However,the large-scale problem represents the high dimensionality of the decision space,requiring algorithms to traverse vast expanse with limited computational resources.Furthermore,in the context of sparse,most variables in Pareto optimal solutions are zero,making it difficult for algorithms to identify non-zero variables efficiently.This paper is dedicated to addressing the challenges posed by SLMOPs.To start,we introduce innovative objective functions customized to mine maximum and minimum candidate sets.This substantial enhancement dramatically improves the efficacy of frequent pattern mining.In this way,selecting candidate sets is no longer based on the quantity of nonzero variables they contain but on a higher proportion of nonzero variables within specific dimensions.Additionally,we unveil a novel approach to association rule mining,which delves into the intricate relationships between non-zero variables.This novel methodology aids in identifying sparse distributions that can potentially expedite reductions in the objective function value.We extensively tested our algorithm across eight benchmark problems and four real-world SLMOPs.The results demonstrate that our approach achieves competitive solutions across various challenges.
基金supported by the NationalNatural Science Foundation of China(No.61866023).
文摘Drone logistics is a novel method of distribution that will become prevalent.The advantageous location of the logistics hub enables quicker customer deliveries and lower fuel consumption,resulting in cost savings for the company’s transportation operations.Logistics firms must discern the ideal location for establishing a logistics hub,which is challenging due to the simplicity of existing models and the intricate delivery factors.To simulate the drone logistics environment,this study presents a new mathematical model.The model not only retains the aspects of the current models,but also considers the degree of transportation difficulty from the logistics hub to the village,the capacity of drones for transportation,and the distribution of logistics hub locations.Moreover,this paper proposes an improved particle swarm optimization(PSO)algorithm which is a diversity-based hybrid PSO(DHPSO)algorithm to solve this model.In DHPSO,the Gaussian random walk can enhance global search in the model space,while the bubble-net attacking strategy can speed convergence.Besides,Archimedes spiral strategy is employed to overcome the local optima trap in the model and improve the exploitation of the algorithm.DHPSO maintains a balance between exploration and exploitation while better defining the distribution of logistics hub locations Numerical experiments show that the newly proposed model always achieves better locations than the current model.Comparing DHPSO with other state-of-the-art intelligent algorithms,the efficiency of the scheme can be improved by 42.58%.This means that logistics companies can reduce distribution costs and consumers can enjoy a more enjoyable shopping experience by using DHPSO’s location selection.All the results show the location of the drone logistics hub is solved by DHPSO effectively.
基金supported by the Fundamental Research Funds for the Central Universities(No.2024JBZX029)Shijiazhuang High Level Science and Technology Innovation and Entrepreneurship Talent Project(No.08202307)the National Natural Science Foundation of China(NSFC)(No.22173004).
文摘The optimization of polymer structures aims to determine an optimal sequence or topology that achieves a given target property or structural performance.This inverse design problem involves searching within a vast combinatorial phase space defined by components,se-quences,and topologies,and is often computationally intractable due to its NP-hard nature.At the core of this challenge lies the need to evalu-ate complex correlations among structural variables,a classical problem in both statistical physics and combinatorial optimization.To address this,we adopt a mean-field approach that decouples direct variable-variable interactions into effective interactions between each variable and an auxiliary field.The simulated bifurcation(SB)algorithm is employed as a mean-field-based optimization framework.It constructs a Hamiltonian dynamical system by introducing generalized momentum fields,enabling efficient decoupling and dynamic evolution of strongly coupled struc-tural variables.Using the sequence optimization of a linear copolymer adsorbing on a solid surface as a case study,we demonstrate the applica-bility of the SB algorithm to high-dimensional,non-differentiable combinatorial optimization problems.Our results show that SB can efficiently discover polymer sequences with excellent adsorption performance within a reasonable computational time.Furthermore,it exhibits robust con-vergence and high parallel scalability across large design spaces.The approach developed in this work offers a new computational pathway for polymer structure optimization.It also lays a theoretical foundation for future extensions to topological design problems,such as optimizing the number and placement of side chains,as well as the co-optimization of sequence and topology.
基金supported by the Fundamental Research Funds for the Central Universities of China(No.300102122105)the Natural Science Basic Research Plan in Shaanxi Province of China(2023-JC-YB-023).
文摘Feature selection(FS)is essential in machine learning(ML)and data mapping by its ability to preprocess high-dimensional data.By selecting a subset of relevant features,feature selection cuts down on the dimension of the data.It excludes irrelevant or surplus features,thus boosting the performance and efficiency of the model.Particle Swarm Optimization(PSO)boasts a streamlined algorithmic framework and exhibits rapid convergence traits.Compared with other algorithms,it incurs reduced computational expenses when tackling high-dimensional datasets.However,PSO faces challenges like inadequate convergence precision.Therefore,regarding FS problems,this paper presents a binary version enhanced PSO based on the Support Vector Machines(SVM)classifier.First,the Sand Cat Swarm Optimization(SCSO)is added to enhance the global search capability of PSO and improve the accuracy of the solution.Secondly,the Latin hypercube sampling strategy initializes populations more uniformly and helps to increase population diversity.The last is the roundup search strategy introducing the grey wolf hierarchy idea to help improve convergence speed.To verify the capability of Self-adaptive Cooperative Particle Swarm Optimization(SCPSO),the CEC2020 test suite and CEC2022 test suite are selected for experiments and applied to three engineering problems.Compared with the standard PSO algorithm,SCPSO converges faster,and the convergence accuracy is significantly improved.Moreover,SCPSO’s comprehensive performance far exceeds that of other algorithms.Six datasets from the University of California,Irvine(UCI)database were selected to evaluate SCPSO’s effectiveness in solving feature selection problems.The results indicate that SCPSO has significant potential for addressing these problems.
文摘Hybrid renewable energy systems(HRES)offer cost-effectiveness,low-emission power solutions,and reduced dependence on fossil fuels.However,the renewable energy allocation problem remains challenging due to complex system interactions and multiple operational constraints.This study develops a novel Multi-Neighborhood Enhanced Harris Hawks Optimization(MNEHHO)algorithm to address the allocation of HRES components.The proposed approach integrates key technical parameters,including charge-discharge efficiency,storage device configurations,and renewable energy fraction.We formulate a comprehensive mathematical model that simultaneously minimizes levelized energy costs and pollutant emissions while maintaining system reliability.The MNEHHO algorithm employs multiple neighborhood structures to enhance solution diversity and exploration capabilities.The model’s effectiveness is validated through case studies across four distinct institutional energy demand profiles.Results demonstrate that our approach successfully generates practically feasible HRES configurations while achieving significant reductions in costs and emissions compared to conventional methods.The enhanced search mechanisms of MNEHHO show superior performance in avoiding local optima and achieving consistent solutions.Experimental results demonstrate concrete improvements in solution quality(up to 46% improvement in objective value)and computational efficiency(average coefficient of variance of 24%-27%)across diverse institutional settings.This confirms the robustness and scalability of our method under various operational scenarios,providing a reliable framework for solving renewable energy allocation problems.
基金Sponsored by Scientific and Technological Innovation Programs of Higher Education Institutions in Shanxi(Grant No.2022L294)Taiyuan University of Science and Technology Scientific Research Initial Funding(Grant Nos.W2022018,W20242012)Foundamental Research Program of Shanxi Province(Grant No.202403021212170).
文摘In recent years,surrogate models derived from genuine data samples have proven to be efficient in addressing optimization challenges that are costly or time⁃intensive.However,the individuals in the population become indistinguishable as the curse of dimensionality increases in the objective space and the accumulation of surrogate approximated errors.Therefore,in this paper,each objective function is modeled using a radial basis function approach,and the optimal solution set of the surrogate model is located by the multi⁃objective evolutionary algorithm of strengthened dominance relation.The original objective function values of the true evaluations are converted to two indicator values,and then the surrogate models are set up for the two performance indicators.Finally,an adaptive infill sampling strategy that relies on approximate performance indicators is proposed to assist in selecting individuals for real evaluations from the potential optimal solution set.The algorithm is contrasted against several advanced surrogate⁃assisted evolutionary algorithms on two suites of test cases,and the experimental findings prove that the approach is competitive in solving expensive many⁃objective optimization problems.
基金supported by the National Nature Science Foundation of China(Nos.62063019)Natural Science Foundation of Gansu Province(22JR5RA241,2023CXZX-465).
文摘In this study,we construct a bi-level optimization model based on the Stackelberg game and propose a robust optimization algorithm for solving the bi-level model,assuming an actual situation with several participants in energy trading.Firstly,the energy trading process is analyzed between each subject based on the establishment of the operation framework of multi-agent participation in energy trading.Secondly,the optimal operation model of each energy trading agent is established to develop a bi-level game model including each energy participant.Finally,a combination algorithm of improved robust optimization over time(ROOT)and CPLEX is proposed to solve the established game model.The experimental results indicate that under different fitness thresholds,the robust optimization results of the proposed algorithm are increased by 56.91%and 68.54%,respectively.The established bi-level game model effectively balances the benefits of different energy trading entities.The proposed algorithm proposed can increase the income of each participant in the game by an average of 8.59%.
基金funded by Hanoi University of Industry,Hanoi,Vietnam,under contract number 25−2024−RD/HD−DHCN.
文摘Efficient warehouse management is critical for modern supply chain systems,particularly in the era of e-commerce and automation.The Multi-Picker Robot Routing Problem(MPRRP)presents a complex challenge involving the optimization of routes for multiple robots assigned to retrieve items from distinct locations within a warehouse.This study introduces optimized metaheuristic strategies to address MPRRP,with the aim of minimizing travel distances,energy consumption,and order fulfillment time while ensuring operational efficiency.Advanced algorithms,including an enhanced Particle Swarm Optimization(PSO-MPRRP)and a tailored Genetic Algorithm(GA-MPRRP),are specifically designed with customized evolutionary operators to effectively solve the MPRRP.Comparative experiments are conducted to evaluate the proposed strategies against benchmark approaches,demonstrating significant improvements in solution quality and computational efficiency.The findings contribute to the development of intelligent,scalable,and environmentally friendly warehouse systems,paving the way for future advances in robotics and automated logistics management.
基金the financial support of the European Union under the REFRESH-Research Excellence for Region Sustainability and High-tech Industries project number CZ.10.03.01/00/22_003/0000048 via the Operational Programme Just Transition and has been done in connection with project Students Grant Competition SP2025/062"specific research on progressive and sustainable production technologies"and SP2025/063"specific research on innovative and progressive manufacturing technologies"financed by the Ministry of Education,Youth and Sports and Faculty of Mechanical Engineering VSB-TUOThe authors would like to extend their sincere appreciation to Researchers Supporting Project number(RSP2025R472)King Saud University,Riyadh,Saudi Arabia.
文摘In a world where supply chains are increasingly complex and unpredictable,finding the optimal way to move goods through transshipment networks is more important and challenging than ever.In addition to addressing the complexity of transportation costs and demand,this study presents a novel method that offers flexible routing alternatives to manage these complexities.When real-world variables such as fluctuating costs,variable capacity,and unpredictable demand are considered,traditional transshipment models often prove inadequate.To overcome these challenges,we propose an innovative fully fuzzy-based framework using LR flat fuzzy numbers.This framework allows for more adaptable and flexible decision-making in multi-objective transshipment situations by effectively capturing uncertain parameters.To overcome these challenges,we develop an innovative,fully fuzzy-based framework using LR flat fuzzy numbers to effectively capture uncertainty in key parameters,offering more flexible and adaptive decision-making in multi-objective transshipment problems.The proposed model also presents alternative route options,giving decisionmakers a range of choices to satisfy multiple requirements,including reducing costs,improving service quality,and expediting delivery.Through extensive numerical experiments,we demonstrate that the model can achieve greater adaptability,efficiency,and flexibility than standard approaches.This multi-path structure provides additional flexibility to adapt to dynamic network conditions.Using ranking strategies,we compared our multi-objective transshipment model with existing methods.The results indicate that,while traditional methods such as goal and fuzzy programming generate results close to the anti-ideal value,thus reducing their efficiency,our model produces solutions close to the ideal value,thereby facilitating better decision making.By combining dynamic routing alternatives with a fully fuzzybased approach,this study offers an effective tool to improve decision-making and optimize complex networks under real-world conditions in practical settings.In this paper,we utilize LINGO 18 software to solve the provided numerical example,demonstrating the effectiveness of the proposed method.
基金supported by the the National Science and Technology Council(Grant Number:NSTC 112-2221-E239-022).
文摘To solve the Laplacian problems,we adopt a meshless method with the multiquadric radial basis function(MQRBF)as a basis whose center is distributed inside a circle with a fictitious radius.A maximal projection technique is developed to identify the optimal shape factor and fictitious radius by minimizing a merit function.A sample function is interpolated by theMQ-RBF to provide a trial coefficient vector to compute the merit function.We can quickly determine the optimal values of the parameters within a preferred rage using the golden section search algorithm.The novel method provides the optimal values of parameters and,hence,an optimal MQ-RBF;the performance of the method is validated in numerical examples.Moreover,nonharmonic problems are transformed to the Poisson equation endowed with a homogeneous boundary condition;this can overcome the problem of these problems being ill-posed.The optimal MQ-RBF is extremely accurate.We further propose a novel optimal polynomial method to solve the nonharmonic problems,which achieves high precision up to an order of 10^(−11).
基金supported by Grant(42271391 and 62006214)from National Natural Science Foundation of Chinaby Grant(8091B022148)from Joint Funds of Equipment Pre-Research and Ministry of Education of China+1 种基金by Grant(2023BIB015)from Special Project of Hubei Key Research and Development Programby Grant(KLIGIP-2021B03)from Open Research Project of the Hubei Key Laboratory of Intelligent Geo-Information Processing.
文摘Snake Optimizer(SO)is a novel Meta-heuristic Algorithm(MA)inspired by the mating behaviour of snakes,which has achieved success in global numerical optimization problems and practical engineering applications.However,it also has certain drawbacks for the exploration stage and the egg hatch process,resulting in slow convergence speed and inferior solution quality.To address the above issues,a novel multi-strategy improved SO(MISO)with the assistance of population crowding analysis is proposed in this article.In the algorithm,a novel multi-strategy operator is designed for the exploration stage,which not only focuses on using the information of better performing individuals to improve the quality of solution,but also focuses on maintaining population diversity.To boost the efficiency of the egg hatch process,the multi-strategy egg hatch process is proposed to regenerate individuals according to the results of the population crowding analysis.In addition,a local search method is employed to further enhance the convergence speed and the local search capability.MISO is first compared with three sets of algorithms in the CEC2020 benchmark functions,including SO with its two recently discussed variants,ten advanced MAs,and six powerful CEC competition algorithms.The performance of MISO is then verified on five practical engineering design problems.The experimental results show that MISO provides a promising performance for the above optimization cases in terms of convergence speed and solution quality.
基金supported by the National Natural Science Foundation of China(11871312,12131014)the Natural Science Foundation of Shandong Province,China(ZR2023MA086)。
文摘A bicubic B-spline finite element method is proposed to solve optimal control problems governed by fourth-order semilinear parabolic partial differential equations.Its key feature is the selection of bicubic B-splines as trial functions to approximate the state and costate variables in two space dimensions.A Crank-Nicolson difference scheme is constructed for time discretization.The resulting numerical solutions belong to C2in space,and the order of the coefficient matrix is low.Moreover,the Bogner-Fox-Schmit element is considered for comparison.Two numerical experiments demonstrate the feasibility and effectiveness of the proposed method.
文摘This work investigates a multi-product parallel disassembly line balancing problem considering multi-skilled workers.A mathematical model for the parallel disassembly line is established to achieve maximized disassembly profit and minimized workstation cycle time.Based on a product’s AND/OR graph,matrices for task-skill,worker-skill,precedence relationships,and disassembly correlations are developed.A multi-objective discrete chemical reaction optimization algorithm is designed.To enhance solution diversity,improvements are made to four reactions:decomposition,synthesis,intermolecular ineffective collision,and wall invalid collision reaction,completing the evolution of molecular individuals.The established model and improved algorithm are applied to ball pen,flashlight,washing machine,and radio combinations,respectively.Introducing a Collaborative Resource Allocation(CRA)strategy based on a Decomposition-Based Multi-Objective Evolutionary Algorithm,the experimental results are compared with four classical algorithms:MOEA/D,MOEAD-CRA,Non-dominated Sorting Genetic Algorithm Ⅱ(NSGA-Ⅱ),and Non-dominated Sorting Genetic Algorithm Ⅲ(NSGA-Ⅲ).This validates the feasibility and superiority of the proposed algorithm in parallel disassembly production lines.
