In this paper,an adaptive cubic regularisation algorithm based on affine scaling methods(ARCBASM)is proposed for solving nonlinear equality constrained programming with nonnegative constraints on variables.From the op...In this paper,an adaptive cubic regularisation algorithm based on affine scaling methods(ARCBASM)is proposed for solving nonlinear equality constrained programming with nonnegative constraints on variables.From the optimality conditions of the problem,we introduce appropriate affine matrix and construct an affine scaling ARC subproblem with linearized constraints.Composite step methods and reduced Hessian methods are applied to tackle the linearized constraints.As a result,a standard unconstrained ARC subproblem is deduced and its solution can supply sufficient decrease.The fraction to the boundary rule maintains the strict feasibility(for nonnegative constraints on variables)of every iteration point.Reflection techniques are employed to prevent the iterations from approaching zero too early.Under mild assumptions,global convergence of the algorithm is analysed.Preliminary numerical results are reported.展开更多
Constrained multi-objective optimization problems(CMOPs) include the optimization of objective functions and the satisfaction of constraint conditions, which challenge the solvers.To solve CMOPs, constrained multi-obj...Constrained multi-objective optimization problems(CMOPs) include the optimization of objective functions and the satisfaction of constraint conditions, which challenge the solvers.To solve CMOPs, constrained multi-objective evolutionary algorithms(CMOEAs) have been developed. However, most of them tend to converge into local areas due to the loss of diversity. Evolutionary multitasking(EMT) is new model of solving complex optimization problems, through the knowledge transfer between the source task and other related tasks. Inspired by EMT, this paper develops a new EMT-based CMOEA to solve CMOPs, in which the main task, a global auxiliary task, and a local auxiliary task are created and optimized by one specific population respectively. The main task focuses on finding the feasible Pareto front(PF), and global and local auxiliary tasks are used to respectively enhance global and local diversity. Moreover, the global auxiliary task is used to implement the global search by ignoring constraints, so as to help the population of the main task pass through infeasible obstacles. The local auxiliary task is used to provide local diversity around the population of the main task, so as to exploit promising regions. Through the knowledge transfer among the three tasks, the search ability of the population of the main task will be significantly improved. Compared with other state-of-the-art CMOEAs, the experimental results on three benchmark test suites demonstrate the superior or competitive performance of the proposed CMOEA.展开更多
In recent years, a large number of approaches to constrained multi-objective optimization problems(CMOPs) have been proposed, focusing on developing tweaked strategies and techniques for handling constraints. However,...In recent years, a large number of approaches to constrained multi-objective optimization problems(CMOPs) have been proposed, focusing on developing tweaked strategies and techniques for handling constraints. However, an overly finetuned strategy or technique might overfit some problem types,resulting in a lack of versatility. In this article, we propose a generic search strategy that performs an even search in a promising region. The promising region, determined by obtained feasible non-dominated solutions, possesses two general properties.First, the constrained Pareto front(CPF) is included in the promising region. Second, as the number of feasible solutions increases or the convergence performance(i.e., approximation to the CPF) of these solutions improves, the promising region shrinks. Then we develop a new strategy named even search,which utilizes the non-dominated solutions to accelerate convergence and escape from local optima, and the feasible solutions under a constraint relaxation condition to exploit and detect feasible regions. Finally, a diversity measure is adopted to make sure that the individuals in the population evenly cover the valuable areas in the promising region. Experimental results on 45 instances from four benchmark test suites and 14 real-world CMOPs have demonstrated that searching evenly in the promising region can achieve competitive performance and excellent versatility compared to 11 most state-of-the-art methods tailored for CMOPs.展开更多
Constrained multi-objective optimization problems(CMOPs)generally contain multiple constraints,which not only form multiple discrete feasible regions but also reduce the size of optimal feasible regions,thus they prop...Constrained multi-objective optimization problems(CMOPs)generally contain multiple constraints,which not only form multiple discrete feasible regions but also reduce the size of optimal feasible regions,thus they propose serious challenges for solvers.Among all constraints,some constraints are highly correlated with optimal feasible regions;thus they can provide effective help to find feasible Pareto front.However,most of the existing constrained multi-objective evolutionary algorithms tackle constraints by regarding all constraints as a whole or directly ignoring all constraints,and do not consider judging the relations among constraints and do not utilize the information from promising single constraints.Therefore,this paper attempts to identify promising single constraints and utilize them to help solve CMOPs.To be specific,a CMOP is transformed into a multitasking optimization problem,where multiple auxiliary tasks are created to search for the Pareto fronts that only consider a single constraint respectively.Besides,an auxiliary task priority method is designed to identify and retain some high-related auxiliary tasks according to the information of relative positions and dominance relationships.Moreover,an improved tentative method is designed to find and transfer useful knowledge among tasks.Experimental results on three benchmark test suites and 11 realworld problems with different numbers of constraints show better or competitive performance of the proposed method when compared with eight state-of-the-art peer methods.展开更多
Solving constrained multi-objective optimization problems with evolutionary algorithms has attracted considerable attention.Various constrained multi-objective optimization evolutionary algorithms(CMOEAs)have been dev...Solving constrained multi-objective optimization problems with evolutionary algorithms has attracted considerable attention.Various constrained multi-objective optimization evolutionary algorithms(CMOEAs)have been developed with the use of different algorithmic strategies,evolutionary operators,and constraint-handling techniques.The performance of CMOEAs may be heavily dependent on the operators used,however,it is usually difficult to select suitable operators for the problem at hand.Hence,improving operator selection is promising and necessary for CMOEAs.This work proposes an online operator selection framework assisted by Deep Reinforcement Learning.The dynamics of the population,including convergence,diversity,and feasibility,are regarded as the state;the candidate operators are considered as actions;and the improvement of the population state is treated as the reward.By using a Q-network to learn a policy to estimate the Q-values of all actions,the proposed approach can adaptively select an operator that maximizes the improvement of the population according to the current state and thereby improve the algorithmic performance.The framework is embedded into four popular CMOEAs and assessed on 42 benchmark problems.The experimental results reveal that the proposed Deep Reinforcement Learning-assisted operator selection significantly improves the performance of these CMOEAs and the resulting algorithm obtains better versatility compared to nine state-of-the-art CMOEAs.展开更多
The intermittency and volatility of wind and photovoltaic power generation exacerbate issues such as wind and solar curtailment,hindering the efficient utilization of renewable energy and the low-carbon development of...The intermittency and volatility of wind and photovoltaic power generation exacerbate issues such as wind and solar curtailment,hindering the efficient utilization of renewable energy and the low-carbon development of energy systems.To enhance the consumption capacity of green power,the green power system consumption optimization scheduling model(GPS-COSM)is proposed,which comprehensively integrates green power system,electric boiler,combined heat and power unit,thermal energy storage,and electrical energy storage.The optimization objectives are to minimize operating cost,minimize carbon emission,and maximize the consumption of wind and solar curtailment.The multi-objective particle swarm optimization algorithm is employed to solve the model,and a fuzzy membership function is introduced to evaluate the satisfaction level of the Pareto optimal solution set,thereby selecting the optimal compromise solution to achieve a dynamic balance among economic efficiency,environmental friendliness,and energy utilization efficiency.Three typical operating modes are designed for comparative analysis.The results demonstrate that the mode involving the coordinated operation of electric boiler,thermal energy storage,and electrical energy storage performs the best in terms of economic efficiency,environmental friendliness,and renewable energy utilization efficiency,achieving the wind and solar curtailment consumption rate of 99.58%.The application of electric boiler significantly enhances the direct accommodation capacity of the green power system.Thermal energy storage optimizes intertemporal regulation,while electrical energy storage strengthens the system’s dynamic regulation capability.The coordinated optimization of multiple devices significantly reduces reliance on fossil fuels.展开更多
The multi-objective optimization of backfill effect based on response surface methodology and desirability function(RSM-DF)was conducted.Firstly,the test results show that the uniaxial compressive strength(UCS)increas...The multi-objective optimization of backfill effect based on response surface methodology and desirability function(RSM-DF)was conducted.Firstly,the test results show that the uniaxial compressive strength(UCS)increases with cement sand ratio(CSR),slurry concentration(SC),and curing age(CA),while flow resistance(FR)increases with SC and backfill flow rate(BFR),and decreases with CSR.Then the regression models of UCS and FR as response values were established through RSM.Multi-factor interaction found that CSR-CA impacted UCS most,while SC-BFR impacted FR most.By introducing the desirability function,the optimal backfill parameters were obtained based on RSM-DF(CSR is 1:6.25,SC is 69%,CA is 11.5 d,and BFR is 90 m^(3)/h),showing close results of Design Expert and high reliability for optimization.For a copper mine in China,RSM-DF optimization will reduce cement consumption by 4758 t per year,increase tailings consumption by about 6700 t,and reduce CO_(2)emission by about 4758 t.Thus,RSM-DF provides a new approach for backfill parameters optimization,which has important theoretical and practical values.展开更多
The spoke as a key component has a significant impact on the performance of the non-pneumatic tire(NPT).The current research has focused on adjusting spoke structures to improve the single performance of NPT.Few studi...The spoke as a key component has a significant impact on the performance of the non-pneumatic tire(NPT).The current research has focused on adjusting spoke structures to improve the single performance of NPT.Few studies have been conducted to synergistically improve multi-performance by optimizing the spoke structure.Inspired by the concept of functionally gradient structures,this paper introduces a functionally gradient honeycomb NPT and its optimization method.Firstly,this paper completes the parameterization of the honeycomb spoke structure and establishes the numerical models of honeycomb NPTs with seven different gradients.Subsequently,the accuracy of the numerical models is verified using experimental methods.Then,the static and dynamic characteristics of these gradient honeycomb NPTs are thoroughly examined by using the finite element method.The findings highlight that the gradient structure of NPT-3 has superior performance.Building upon this,the study investigates the effects of key parameters,such as honeycomb spoke thickness and length,on load-carrying capacity,honeycomb spoke stress and mass.Finally,a multi-objective optimization method is proposed that uses a response surface model(RSM)and the Nondominated Sorting Genetic Algorithm-II(NSGA-II)to further optimize the functional gradient honeycomb NPTs.The optimized NPT-OP shows a 23.48%reduction in radial stiffness,8.95%reduction in maximum spoke stress and 16.86%reduction in spoke mass compared to the initial NPT-1.The damping characteristics of the NPT-OP have also been improved.The results offer a theoretical foundation and technical methodology for the structural design and optimization of gradient honeycomb NPTs.展开更多
Hydrocracking is one of the most important petroleum refining processes that converts heavy oils into gases,naphtha,diesel,and other products through cracking reactions.Multi-objective optimization algorithms can help...Hydrocracking is one of the most important petroleum refining processes that converts heavy oils into gases,naphtha,diesel,and other products through cracking reactions.Multi-objective optimization algorithms can help refining enterprises determine the optimal operating parameters to maximize product quality while ensuring product yield,or to increase product yield while reducing energy consumption.This paper presents a multi-objective optimization scheme for hydrocracking based on an improved SPEA2-PE algorithm,which combines path evolution operator and adaptive step strategy to accelerate the convergence speed and improve the computational accuracy of the algorithm.The reactor model used in this article is simulated based on a twenty-five lumped kinetic model.Through model and test function verification,the proposed optimization scheme exhibits significant advantages in the multiobjective optimization process of hydrocracking.展开更多
A new hang-off system has been proposed to improve the security of risers in hang-off modes during typhoons.However,efficient anti-typhoon evacuation strategies have not been investigated.Optimiza-tion model and metho...A new hang-off system has been proposed to improve the security of risers in hang-off modes during typhoons.However,efficient anti-typhoon evacuation strategies have not been investigated.Optimiza-tion model and method for the anti-typhoon evacuation strategies should be researched.Therefore,multi-objective functions are proposed based on operation time,evacuation speed stability,and steering stability.An evacuation path model and a dynamic model of risers with the new hang-off system are developed for design variables and constraints.A multi-objective optimization model with high-dimensional variables and complex constraints is established.Finally,a three-stage optimization method based on genetic algorithm,least square method,and the penalty function method is proposed to solve the multi-objective optimization model.Optimization results show that the operation time can be reduced through operation parameter optimization,especially evacuation heading optimization.The optimal anti-typhoon strategy is evacuation with all risers suspended along a variable path when the direction angle is large,while evacuation with all risers suspended along a straight path at another di-rection angle.Besides,the influencing factors on anti-typhoon evacuation strategies indicate that the proposed optimization model and method have strong applicability to working conditions and remarkable optimization effects.展开更多
This paper presents an improved virtual coupling train set(VCTS)operation control framework to deal with the lack of opti-mization of speed curves in the traditional techniques.The framework takes into account the tem...This paper presents an improved virtual coupling train set(VCTS)operation control framework to deal with the lack of opti-mization of speed curves in the traditional techniques.The framework takes into account the temporary speed limit on the railway line and the communication delay between trains,and it uses a VCTS consisting of three trains as an experimental object.It creates the virtual coupling train tracking and control process by improving the driving strategy of the leader train and using the leader-follower model.The follower train uses the improved speed curve of the leader train as its speed refer-ence curve through knowledge migration,and this completes the multi-objective optimization of the driving strategy for the VCTS.The experimental results confirm that the deep reinforcement learning algorithm effectively achieves the optimization goal of the train driving strategy.They also reveal that the intrinsic curiosity module prioritized experience replay dueling double deep Q-network(ICM-PER-D3QN)algorithm outperforms the deep Q-network(DQN)algorithm in optimizing the driving strategy of the leader train.The ICM-PER-D3QN algorithm enhances the leader train driving strategy by an average of 57%when compared to the DQN algorithm.Furthermore,the particle swarm optimization(PSO)-based model predictive control(MPC)algorithm has also demonstrated tracking accuracy and further improved safety during VCTS operation,with an average increase of 37.7%in tracking accuracy compared to the traditional MPC algorithm.展开更多
In tunnel construction,tunnel boring machine(TBM)tunnelling typically relies on manual experience with sub-optimal control parameters,which can easily lead to inefficiency and high costs.This study proposed an intelli...In tunnel construction,tunnel boring machine(TBM)tunnelling typically relies on manual experience with sub-optimal control parameters,which can easily lead to inefficiency and high costs.This study proposed an intelligent decision-making method for TBM tunnelling control parameters based on multiobjective optimization(MOO).First,the effective TBM operation dataset is obtained through data preprocessing of the Songhua River(YS)tunnel project in China.Next,the proposed method begins with developing machine learning models for predicting TBM tunnelling performance parameters(i.e.total thrust and cutterhead torque),rock mass classification,and hazard risks(i.e.tunnel collapse and shield jamming).Then,considering three optimal objectives,(i.e.,penetration rate,rock-breaking energy consumption,and cutterhead hob wear),the MOO framework and corresponding mathematical expression are established.The Pareto optimal front is solved using DE-NSGA-II algorithm.Finally,the optimal control parameters(i.e.,advance rate and cutterhead rotation speed)are obtained by the satisfactory solution determination criterion,which can balance construction safety and efficiency with satisfaction.Furthermore,the proposed method is validated through 50 cases of TBM tunnelling,showing promising potential of application.展开更多
Accurate determination of rock mass parameters is essential for ensuring the accuracy of numericalsimulations. Displacement back-analysis is the most widely used method;however, the reliability of thecurrent approache...Accurate determination of rock mass parameters is essential for ensuring the accuracy of numericalsimulations. Displacement back-analysis is the most widely used method;however, the reliability of thecurrent approaches remains unsatisfactory. Therefore, in this paper, a multistage rock mass parameterback-analysis method, that considers the construction process and displacement losses is proposed andimplemented through the coupling of numerical simulation, auto-machine learning (AutoML), andmulti-objective optimization algorithms (MOOAs). First, a parametric modeling platform for mechanizedtwin tunnels is developed, generating a dataset through extensive numerical simulations. Next, theAutoML method is utilized to establish a surrogate model linking rock parameters and displacements.The tunnel construction process is divided into multiple stages, transforming the rock mass parameterback-analysis into a multi-objective optimization problem, for which multi-objective optimization algorithmsare introduced to obtain the rock mass parameters. The newly proposed rock mass parameterback-analysis method is validated in a mechanized twin tunnel project, and its accuracy and effectivenessare demonstrated. Compared with traditional single-stage back-analysis methods, the proposedmodel decreases the average absolute percentage error from 12.73% to 4.34%, significantly improving theaccuracy of the back-analysis. Moreover, although the accuracy of back analysis significantly increaseswith the number of construction stages considered, the back analysis time is acceptable. This studyprovides a new method for displacement back analysis that is efficient and accurate, thereby paving theway for precise parameter determination in numerical simulations.展开更多
This paper investigates a class of constrained distributed zeroth-order optimization(ZOO) problems over timevarying unbalanced graphs while ensuring privacy preservation among individual agents. Not taking into accoun...This paper investigates a class of constrained distributed zeroth-order optimization(ZOO) problems over timevarying unbalanced graphs while ensuring privacy preservation among individual agents. Not taking into account recent progress and addressing these concerns separately, there remains a lack of solutions offering theoretical guarantees for both privacy protection and constrained ZOO over time-varying unbalanced graphs.We hereby propose a novel algorithm, termed the differential privacy(DP) distributed push-sum based zeroth-order constrained optimization algorithm(DP-ZOCOA). Operating over time-varying unbalanced graphs, DP-ZOCOA obviates the need for supplemental suboptimization problem computations, thereby reducing overhead in comparison to distributed primary-dual methods. DP-ZOCOA is specifically tailored to tackle constrained ZOO problems over time-varying unbalanced graphs,offering a guarantee of convergence to the optimal solution while robustly preserving privacy. Moreover, we provide rigorous proofs of convergence and privacy for DP-ZOCOA, underscoring its efficacy in attaining optimal convergence without constraints. To enhance its applicability, we incorporate DP-ZOCOA into the federated learning framework and formulate a decentralized zeroth-order constrained federated learning algorithm(ZOCOA-FL) to address challenges stemming from the timevarying imbalance of communication topology. Finally, the performance and effectiveness of the proposed algorithms are thoroughly evaluated through simulations on distributed least squares(DLS) and decentralized federated learning(DFL) tasks.展开更多
This work addresses the cut order planning(COP)problem for multi-color garment production,which is the first step in the clothing industry.First,a multi-objective optimization model of multicolor COP(MCOP)is establish...This work addresses the cut order planning(COP)problem for multi-color garment production,which is the first step in the clothing industry.First,a multi-objective optimization model of multicolor COP(MCOP)is established with production error and production cost as optimization objectives,combined with constraints such as the number of equipment and the number of layers.Second,a decoupled multi-objective optimization algorithm(DMOA)is proposed based on the linear programming decoupling strategy and non-dominated sorting in genetic algorithmsⅡ(NSGAII).The size-combination matrix and the fabric-layer matrix are decoupled to improve the accuracy of the algorithm.Meanwhile,an improved NSGAII algorithm is designed to obtain the optimal Pareto solution to the MCOP problem,thereby constructing a practical intelligent production optimization algorithm.Finally,the effectiveness and superiority of the proposed DMOA are verified through practical cases and comparative experiments,which can effectively optimize the production process for garment enterprises.展开更多
To solve single-objective constrained optimization problems,a new population-based evolutionary algorithm with elite strategy(PEAES) is proposed with the concept of single and multi-objective optimization.Constrained ...To solve single-objective constrained optimization problems,a new population-based evolutionary algorithm with elite strategy(PEAES) is proposed with the concept of single and multi-objective optimization.Constrained functions are combined to be an objective function.During the evolutionary process,the current optimal solution is found and treated as the reference point to divide the population into three sub-populations:one feasible and two infeasible ones.Different evolutionary operations of single or multi-objective optimization are respectively performed in each sub-population with elite strategy.Thirteen famous benchmark functions are selected to evaluate the performance of PEAES in comparison of other three optimization methods.The results show the proposed method is valid in efficiency,precision and probability for solving single-objective constrained optimization problems.展开更多
The paper evaluates the suitability of examples used in developing averaging techniques of multi-objective optimization (MOO). Most of the examples used for proposing these techniques were not suitable. The results of...The paper evaluates the suitability of examples used in developing averaging techniques of multi-objective optimization (MOO). Most of the examples used for proposing these techniques were not suitable. The results of these examples have also not been interpreted correctly. An appropriate example has also been solved with existing and improved averaging techniques of multi-objective optimization.展开更多
Most of the current evolutionary algorithms for constrained optimization algorithm are low computational efficiency. In order to improve efficiency, an improved differential evolution with shrinking space technique an...Most of the current evolutionary algorithms for constrained optimization algorithm are low computational efficiency. In order to improve efficiency, an improved differential evolution with shrinking space technique and adaptive trade-off model, named ATMDE, is proposed to solve constrained optimization problems. The proposed ATMDE algorithm employs an improved differential evolution as the search optimizer to generate new offspring individuals into evolutionary population. For the con- straints, the adaptive trade-off model as one of the most important constraint-handling techniques is employed to select better individuals to retain into the next population, which could effectively handle multiple constraints. Then the shrinking space technique is designed to shrink the search region according to feedback information in order to improve computational efficiency without losing accuracy. The improved DE algorithm introduces three different mutant strategies to generate different offspring into evo- lutionary population. Moreover, a new mutant strategy called ＂DE/rand/best/l＂ is constructed to generate new individuals according to the feasibility proportion ofcurrent population. Finally, the effectiveness of the pro- posed method is verified by a suite of benchmark functions and practical engineering problems. This research presents a constrained evolutionary algorithm with high efficiency and accuracy for constrained optimization problems.展开更多
During the last three decades,evolutionary algorithms(EAs)have shown superiority in solving complex optimization problems,especially those with multiple objectives and non-differentiable landscapes.However,due to the ...During the last three decades,evolutionary algorithms(EAs)have shown superiority in solving complex optimization problems,especially those with multiple objectives and non-differentiable landscapes.However,due to the stochastic search strategies,the performance of most EAs deteriorates drastically when handling a large number of decision variables.To tackle the curse of dimensionality,this work proposes an efficient EA for solving super-large-scale multi-objective optimization problems with sparse optimal solutions.The proposed algorithm estimates the sparse distribution of optimal solutions by optimizing a binary vector for each solution,and provides a fast clustering method to highly reduce the dimensionality of the search space.More importantly,all the operations related to the decision variables only contain several matrix calculations,which can be directly accelerated by GPUs.While existing EAs are capable of handling fewer than 10000 real variables,the proposed algorithm is verified to be effective in handling 1000000 real variables.Furthermore,since the proposed algorithm handles the large number of variables via accelerated matrix calculations,its runtime can be reduced to less than 10%of the runtime of existing EAs.展开更多
Large-scale multi-objective optimization problems(LSMOPs)pose challenges to existing optimizers since a set of well-converged and diverse solutions should be found in huge search spaces.While evolutionary algorithms a...Large-scale multi-objective optimization problems(LSMOPs)pose challenges to existing optimizers since a set of well-converged and diverse solutions should be found in huge search spaces.While evolutionary algorithms are good at solving small-scale multi-objective optimization problems,they are criticized for low efficiency in converging to the optimums of LSMOPs.By contrast,mathematical programming methods offer fast convergence speed on large-scale single-objective optimization problems,but they have difficulties in finding diverse solutions for LSMOPs.Currently,how to integrate evolutionary algorithms with mathematical programming methods to solve LSMOPs remains unexplored.In this paper,a hybrid algorithm is tailored for LSMOPs by coupling differential evolution and a conjugate gradient method.On the one hand,conjugate gradients and differential evolution are used to update different decision variables of a set of solutions,where the former drives the solutions to quickly converge towards the Pareto front and the latter promotes the diversity of the solutions to cover the whole Pareto front.On the other hand,objective decomposition strategy of evolutionary multi-objective optimization is used to differentiate the conjugate gradients of solutions,and the line search strategy of mathematical programming is used to ensure the higher quality of each offspring than its parent.In comparison with state-of-the-art evolutionary algorithms,mathematical programming methods,and hybrid algorithms,the proposed algorithm exhibits better convergence and diversity performance on a variety of benchmark and real-world LSMOPs.展开更多
基金Supported by the National Natural Science Foundation of China(12071133)Natural Science Foundation of Henan Province(252300421993)Key Scientific Research Project of Higher Education Institutions in Henan Province(25B110005)。
文摘In this paper,an adaptive cubic regularisation algorithm based on affine scaling methods(ARCBASM)is proposed for solving nonlinear equality constrained programming with nonnegative constraints on variables.From the optimality conditions of the problem,we introduce appropriate affine matrix and construct an affine scaling ARC subproblem with linearized constraints.Composite step methods and reduced Hessian methods are applied to tackle the linearized constraints.As a result,a standard unconstrained ARC subproblem is deduced and its solution can supply sufficient decrease.The fraction to the boundary rule maintains the strict feasibility(for nonnegative constraints on variables)of every iteration point.Reflection techniques are employed to prevent the iterations from approaching zero too early.Under mild assumptions,global convergence of the algorithm is analysed.Preliminary numerical results are reported.
基金supported in part by the National Natural Science Fund for Outstanding Young Scholars of China (61922072)the National Natural Science Foundation of China (62176238, 61806179, 61876169, 61976237)+2 种基金China Postdoctoral Science Foundation (2020M682347)the Training Program of Young Backbone Teachers in Colleges and Universities in Henan Province (2020GGJS006)Henan Provincial Young Talents Lifting Project (2021HYTP007)。
文摘Constrained multi-objective optimization problems(CMOPs) include the optimization of objective functions and the satisfaction of constraint conditions, which challenge the solvers.To solve CMOPs, constrained multi-objective evolutionary algorithms(CMOEAs) have been developed. However, most of them tend to converge into local areas due to the loss of diversity. Evolutionary multitasking(EMT) is new model of solving complex optimization problems, through the knowledge transfer between the source task and other related tasks. Inspired by EMT, this paper develops a new EMT-based CMOEA to solve CMOPs, in which the main task, a global auxiliary task, and a local auxiliary task are created and optimized by one specific population respectively. The main task focuses on finding the feasible Pareto front(PF), and global and local auxiliary tasks are used to respectively enhance global and local diversity. Moreover, the global auxiliary task is used to implement the global search by ignoring constraints, so as to help the population of the main task pass through infeasible obstacles. The local auxiliary task is used to provide local diversity around the population of the main task, so as to exploit promising regions. Through the knowledge transfer among the three tasks, the search ability of the population of the main task will be significantly improved. Compared with other state-of-the-art CMOEAs, the experimental results on three benchmark test suites demonstrate the superior or competitive performance of the proposed CMOEA.
基金partly supported by the National Natural Science Foundation of China(62076225)。
文摘In recent years, a large number of approaches to constrained multi-objective optimization problems(CMOPs) have been proposed, focusing on developing tweaked strategies and techniques for handling constraints. However, an overly finetuned strategy or technique might overfit some problem types,resulting in a lack of versatility. In this article, we propose a generic search strategy that performs an even search in a promising region. The promising region, determined by obtained feasible non-dominated solutions, possesses two general properties.First, the constrained Pareto front(CPF) is included in the promising region. Second, as the number of feasible solutions increases or the convergence performance(i.e., approximation to the CPF) of these solutions improves, the promising region shrinks. Then we develop a new strategy named even search,which utilizes the non-dominated solutions to accelerate convergence and escape from local optima, and the feasible solutions under a constraint relaxation condition to exploit and detect feasible regions. Finally, a diversity measure is adopted to make sure that the individuals in the population evenly cover the valuable areas in the promising region. Experimental results on 45 instances from four benchmark test suites and 14 real-world CMOPs have demonstrated that searching evenly in the promising region can achieve competitive performance and excellent versatility compared to 11 most state-of-the-art methods tailored for CMOPs.
基金supported in part by the National Key Research and Development Program of China(2022YFD2001200)the National Natural Science Foundation of China(62176238,61976237,62206251,62106230)+3 种基金China Postdoctoral Science Foundation(2021T140616,2021M692920)the Natural Science Foundation of Henan Province(222300420088)the Program for Science&Technology Innovation Talents in Universities of Henan Province(23HASTIT023)the Program for Science&Technology Innovation Teams in Universities of Henan Province(23IRTSTHN010).
文摘Constrained multi-objective optimization problems(CMOPs)generally contain multiple constraints,which not only form multiple discrete feasible regions but also reduce the size of optimal feasible regions,thus they propose serious challenges for solvers.Among all constraints,some constraints are highly correlated with optimal feasible regions;thus they can provide effective help to find feasible Pareto front.However,most of the existing constrained multi-objective evolutionary algorithms tackle constraints by regarding all constraints as a whole or directly ignoring all constraints,and do not consider judging the relations among constraints and do not utilize the information from promising single constraints.Therefore,this paper attempts to identify promising single constraints and utilize them to help solve CMOPs.To be specific,a CMOP is transformed into a multitasking optimization problem,where multiple auxiliary tasks are created to search for the Pareto fronts that only consider a single constraint respectively.Besides,an auxiliary task priority method is designed to identify and retain some high-related auxiliary tasks according to the information of relative positions and dominance relationships.Moreover,an improved tentative method is designed to find and transfer useful knowledge among tasks.Experimental results on three benchmark test suites and 11 realworld problems with different numbers of constraints show better or competitive performance of the proposed method when compared with eight state-of-the-art peer methods.
基金the National Natural Science Foundation of China(62076225,62073300)the Natural Science Foundation for Distinguished Young Scholars of Hubei(2019CFA081)。
文摘Solving constrained multi-objective optimization problems with evolutionary algorithms has attracted considerable attention.Various constrained multi-objective optimization evolutionary algorithms(CMOEAs)have been developed with the use of different algorithmic strategies,evolutionary operators,and constraint-handling techniques.The performance of CMOEAs may be heavily dependent on the operators used,however,it is usually difficult to select suitable operators for the problem at hand.Hence,improving operator selection is promising and necessary for CMOEAs.This work proposes an online operator selection framework assisted by Deep Reinforcement Learning.The dynamics of the population,including convergence,diversity,and feasibility,are regarded as the state;the candidate operators are considered as actions;and the improvement of the population state is treated as the reward.By using a Q-network to learn a policy to estimate the Q-values of all actions,the proposed approach can adaptively select an operator that maximizes the improvement of the population according to the current state and thereby improve the algorithmic performance.The framework is embedded into four popular CMOEAs and assessed on 42 benchmark problems.The experimental results reveal that the proposed Deep Reinforcement Learning-assisted operator selection significantly improves the performance of these CMOEAs and the resulting algorithm obtains better versatility compared to nine state-of-the-art CMOEAs.
基金funded by the National Key Research and Development Program of China(2024YFE0106800)Natural Science Foundation of Shandong Province(ZR2021ME199).
文摘The intermittency and volatility of wind and photovoltaic power generation exacerbate issues such as wind and solar curtailment,hindering the efficient utilization of renewable energy and the low-carbon development of energy systems.To enhance the consumption capacity of green power,the green power system consumption optimization scheduling model(GPS-COSM)is proposed,which comprehensively integrates green power system,electric boiler,combined heat and power unit,thermal energy storage,and electrical energy storage.The optimization objectives are to minimize operating cost,minimize carbon emission,and maximize the consumption of wind and solar curtailment.The multi-objective particle swarm optimization algorithm is employed to solve the model,and a fuzzy membership function is introduced to evaluate the satisfaction level of the Pareto optimal solution set,thereby selecting the optimal compromise solution to achieve a dynamic balance among economic efficiency,environmental friendliness,and energy utilization efficiency.Three typical operating modes are designed for comparative analysis.The results demonstrate that the mode involving the coordinated operation of electric boiler,thermal energy storage,and electrical energy storage performs the best in terms of economic efficiency,environmental friendliness,and renewable energy utilization efficiency,achieving the wind and solar curtailment consumption rate of 99.58%.The application of electric boiler significantly enhances the direct accommodation capacity of the green power system.Thermal energy storage optimizes intertemporal regulation,while electrical energy storage strengthens the system’s dynamic regulation capability.The coordinated optimization of multiple devices significantly reduces reliance on fossil fuels.
基金Funded by the Deep Underground National Science&Technology Major Project gram of China(No.2024ZD1003704)the National Natural Science Foundation of China(Nos.51834001 and 52374111)。
文摘The multi-objective optimization of backfill effect based on response surface methodology and desirability function(RSM-DF)was conducted.Firstly,the test results show that the uniaxial compressive strength(UCS)increases with cement sand ratio(CSR),slurry concentration(SC),and curing age(CA),while flow resistance(FR)increases with SC and backfill flow rate(BFR),and decreases with CSR.Then the regression models of UCS and FR as response values were established through RSM.Multi-factor interaction found that CSR-CA impacted UCS most,while SC-BFR impacted FR most.By introducing the desirability function,the optimal backfill parameters were obtained based on RSM-DF(CSR is 1:6.25,SC is 69%,CA is 11.5 d,and BFR is 90 m^(3)/h),showing close results of Design Expert and high reliability for optimization.For a copper mine in China,RSM-DF optimization will reduce cement consumption by 4758 t per year,increase tailings consumption by about 6700 t,and reduce CO_(2)emission by about 4758 t.Thus,RSM-DF provides a new approach for backfill parameters optimization,which has important theoretical and practical values.
基金Supported by National Natural Science Foundation of China(Grant Nos.52072156,52272366)Postdoctoral Foundation of China(Grant No.2020M682269).
文摘The spoke as a key component has a significant impact on the performance of the non-pneumatic tire(NPT).The current research has focused on adjusting spoke structures to improve the single performance of NPT.Few studies have been conducted to synergistically improve multi-performance by optimizing the spoke structure.Inspired by the concept of functionally gradient structures,this paper introduces a functionally gradient honeycomb NPT and its optimization method.Firstly,this paper completes the parameterization of the honeycomb spoke structure and establishes the numerical models of honeycomb NPTs with seven different gradients.Subsequently,the accuracy of the numerical models is verified using experimental methods.Then,the static and dynamic characteristics of these gradient honeycomb NPTs are thoroughly examined by using the finite element method.The findings highlight that the gradient structure of NPT-3 has superior performance.Building upon this,the study investigates the effects of key parameters,such as honeycomb spoke thickness and length,on load-carrying capacity,honeycomb spoke stress and mass.Finally,a multi-objective optimization method is proposed that uses a response surface model(RSM)and the Nondominated Sorting Genetic Algorithm-II(NSGA-II)to further optimize the functional gradient honeycomb NPTs.The optimized NPT-OP shows a 23.48%reduction in radial stiffness,8.95%reduction in maximum spoke stress and 16.86%reduction in spoke mass compared to the initial NPT-1.The damping characteristics of the NPT-OP have also been improved.The results offer a theoretical foundation and technical methodology for the structural design and optimization of gradient honeycomb NPTs.
基金supported by National Key Research and Development Program of China (2023YFB3307800)National Natural Science Foundation of China (Key Program: 62136003, 62373155)+1 种基金Major Science and Technology Project of Xinjiang (No. 2022A01006-4)the Fundamental Research Funds for the Central Universities。
文摘Hydrocracking is one of the most important petroleum refining processes that converts heavy oils into gases,naphtha,diesel,and other products through cracking reactions.Multi-objective optimization algorithms can help refining enterprises determine the optimal operating parameters to maximize product quality while ensuring product yield,or to increase product yield while reducing energy consumption.This paper presents a multi-objective optimization scheme for hydrocracking based on an improved SPEA2-PE algorithm,which combines path evolution operator and adaptive step strategy to accelerate the convergence speed and improve the computational accuracy of the algorithm.The reactor model used in this article is simulated based on a twenty-five lumped kinetic model.Through model and test function verification,the proposed optimization scheme exhibits significant advantages in the multiobjective optimization process of hydrocracking.
基金supported by the National Natural Science Foundation of China(Grant No:52271300,52071337)National Key Research and Development Program of China(2022YFC2806501)+1 种基金High-tech Ship Research Projects Sponsored by MIIT(CBG2N21-4-25)Program for Changjiang Scholars and Innovative Research Team in University(Grant No.IRT14R58).
文摘A new hang-off system has been proposed to improve the security of risers in hang-off modes during typhoons.However,efficient anti-typhoon evacuation strategies have not been investigated.Optimiza-tion model and method for the anti-typhoon evacuation strategies should be researched.Therefore,multi-objective functions are proposed based on operation time,evacuation speed stability,and steering stability.An evacuation path model and a dynamic model of risers with the new hang-off system are developed for design variables and constraints.A multi-objective optimization model with high-dimensional variables and complex constraints is established.Finally,a three-stage optimization method based on genetic algorithm,least square method,and the penalty function method is proposed to solve the multi-objective optimization model.Optimization results show that the operation time can be reduced through operation parameter optimization,especially evacuation heading optimization.The optimal anti-typhoon strategy is evacuation with all risers suspended along a variable path when the direction angle is large,while evacuation with all risers suspended along a straight path at another di-rection angle.Besides,the influencing factors on anti-typhoon evacuation strategies indicate that the proposed optimization model and method have strong applicability to working conditions and remarkable optimization effects.
基金supported by the National Natural Science Foundation of China under Grant 52162050.
文摘This paper presents an improved virtual coupling train set(VCTS)operation control framework to deal with the lack of opti-mization of speed curves in the traditional techniques.The framework takes into account the temporary speed limit on the railway line and the communication delay between trains,and it uses a VCTS consisting of three trains as an experimental object.It creates the virtual coupling train tracking and control process by improving the driving strategy of the leader train and using the leader-follower model.The follower train uses the improved speed curve of the leader train as its speed refer-ence curve through knowledge migration,and this completes the multi-objective optimization of the driving strategy for the VCTS.The experimental results confirm that the deep reinforcement learning algorithm effectively achieves the optimization goal of the train driving strategy.They also reveal that the intrinsic curiosity module prioritized experience replay dueling double deep Q-network(ICM-PER-D3QN)algorithm outperforms the deep Q-network(DQN)algorithm in optimizing the driving strategy of the leader train.The ICM-PER-D3QN algorithm enhances the leader train driving strategy by an average of 57%when compared to the DQN algorithm.Furthermore,the particle swarm optimization(PSO)-based model predictive control(MPC)algorithm has also demonstrated tracking accuracy and further improved safety during VCTS operation,with an average increase of 37.7%in tracking accuracy compared to the traditional MPC algorithm.
基金supported by the National Natural Science Foundation of China(Grant No.52179105)China Postdoctoral Science Foundation(Grant No.2024M762193)。
文摘In tunnel construction,tunnel boring machine(TBM)tunnelling typically relies on manual experience with sub-optimal control parameters,which can easily lead to inefficiency and high costs.This study proposed an intelligent decision-making method for TBM tunnelling control parameters based on multiobjective optimization(MOO).First,the effective TBM operation dataset is obtained through data preprocessing of the Songhua River(YS)tunnel project in China.Next,the proposed method begins with developing machine learning models for predicting TBM tunnelling performance parameters(i.e.total thrust and cutterhead torque),rock mass classification,and hazard risks(i.e.tunnel collapse and shield jamming).Then,considering three optimal objectives,(i.e.,penetration rate,rock-breaking energy consumption,and cutterhead hob wear),the MOO framework and corresponding mathematical expression are established.The Pareto optimal front is solved using DE-NSGA-II algorithm.Finally,the optimal control parameters(i.e.,advance rate and cutterhead rotation speed)are obtained by the satisfactory solution determination criterion,which can balance construction safety and efficiency with satisfaction.Furthermore,the proposed method is validated through 50 cases of TBM tunnelling,showing promising potential of application.
基金supported by the National Natural Science Foundation of China(Grant Nos.52090081,52079068)the State Key Laboratory of Hydroscience and Hydraulic Engineering(Grant No.2021-KY-04).
文摘Accurate determination of rock mass parameters is essential for ensuring the accuracy of numericalsimulations. Displacement back-analysis is the most widely used method;however, the reliability of thecurrent approaches remains unsatisfactory. Therefore, in this paper, a multistage rock mass parameterback-analysis method, that considers the construction process and displacement losses is proposed andimplemented through the coupling of numerical simulation, auto-machine learning (AutoML), andmulti-objective optimization algorithms (MOOAs). First, a parametric modeling platform for mechanizedtwin tunnels is developed, generating a dataset through extensive numerical simulations. Next, theAutoML method is utilized to establish a surrogate model linking rock parameters and displacements.The tunnel construction process is divided into multiple stages, transforming the rock mass parameterback-analysis into a multi-objective optimization problem, for which multi-objective optimization algorithmsare introduced to obtain the rock mass parameters. The newly proposed rock mass parameterback-analysis method is validated in a mechanized twin tunnel project, and its accuracy and effectivenessare demonstrated. Compared with traditional single-stage back-analysis methods, the proposedmodel decreases the average absolute percentage error from 12.73% to 4.34%, significantly improving theaccuracy of the back-analysis. Moreover, although the accuracy of back analysis significantly increaseswith the number of construction stages considered, the back analysis time is acceptable. This studyprovides a new method for displacement back analysis that is efficient and accurate, thereby paving theway for precise parameter determination in numerical simulations.
基金supported in part by the National Key Research and Development Program of China(2022ZD0120001)the National Natural Science Foundation of China(62233004,62273090,62073076)the Jiangsu Provincial Scientific Research Center of Applied Mathematics(BK20233002)
文摘This paper investigates a class of constrained distributed zeroth-order optimization(ZOO) problems over timevarying unbalanced graphs while ensuring privacy preservation among individual agents. Not taking into account recent progress and addressing these concerns separately, there remains a lack of solutions offering theoretical guarantees for both privacy protection and constrained ZOO over time-varying unbalanced graphs.We hereby propose a novel algorithm, termed the differential privacy(DP) distributed push-sum based zeroth-order constrained optimization algorithm(DP-ZOCOA). Operating over time-varying unbalanced graphs, DP-ZOCOA obviates the need for supplemental suboptimization problem computations, thereby reducing overhead in comparison to distributed primary-dual methods. DP-ZOCOA is specifically tailored to tackle constrained ZOO problems over time-varying unbalanced graphs,offering a guarantee of convergence to the optimal solution while robustly preserving privacy. Moreover, we provide rigorous proofs of convergence and privacy for DP-ZOCOA, underscoring its efficacy in attaining optimal convergence without constraints. To enhance its applicability, we incorporate DP-ZOCOA into the federated learning framework and formulate a decentralized zeroth-order constrained federated learning algorithm(ZOCOA-FL) to address challenges stemming from the timevarying imbalance of communication topology. Finally, the performance and effectiveness of the proposed algorithms are thoroughly evaluated through simulations on distributed least squares(DLS) and decentralized federated learning(DFL) tasks.
基金Supported by the Natural Science Foundation of Zhejiang Province(No.LQ22F030015).
文摘This work addresses the cut order planning(COP)problem for multi-color garment production,which is the first step in the clothing industry.First,a multi-objective optimization model of multicolor COP(MCOP)is established with production error and production cost as optimization objectives,combined with constraints such as the number of equipment and the number of layers.Second,a decoupled multi-objective optimization algorithm(DMOA)is proposed based on the linear programming decoupling strategy and non-dominated sorting in genetic algorithmsⅡ(NSGAII).The size-combination matrix and the fabric-layer matrix are decoupled to improve the accuracy of the algorithm.Meanwhile,an improved NSGAII algorithm is designed to obtain the optimal Pareto solution to the MCOP problem,thereby constructing a practical intelligent production optimization algorithm.Finally,the effectiveness and superiority of the proposed DMOA are verified through practical cases and comparative experiments,which can effectively optimize the production process for garment enterprises.
文摘To solve single-objective constrained optimization problems,a new population-based evolutionary algorithm with elite strategy(PEAES) is proposed with the concept of single and multi-objective optimization.Constrained functions are combined to be an objective function.During the evolutionary process,the current optimal solution is found and treated as the reference point to divide the population into three sub-populations:one feasible and two infeasible ones.Different evolutionary operations of single or multi-objective optimization are respectively performed in each sub-population with elite strategy.Thirteen famous benchmark functions are selected to evaluate the performance of PEAES in comparison of other three optimization methods.The results show the proposed method is valid in efficiency,precision and probability for solving single-objective constrained optimization problems.
文摘The paper evaluates the suitability of examples used in developing averaging techniques of multi-objective optimization (MOO). Most of the examples used for proposing these techniques were not suitable. The results of these examples have also not been interpreted correctly. An appropriate example has also been solved with existing and improved averaging techniques of multi-objective optimization.
基金Supported by National Science Foundation for Excellent Young Scholars,China(Grant No.51222502)Funds for Distinguished Young Scientists of Hunan Province,China(Grant No.14JJ1016)Major Program of National Natural Science Foundation of China(Grant No.51490662)
文摘Most of the current evolutionary algorithms for constrained optimization algorithm are low computational efficiency. In order to improve efficiency, an improved differential evolution with shrinking space technique and adaptive trade-off model, named ATMDE, is proposed to solve constrained optimization problems. The proposed ATMDE algorithm employs an improved differential evolution as the search optimizer to generate new offspring individuals into evolutionary population. For the con- straints, the adaptive trade-off model as one of the most important constraint-handling techniques is employed to select better individuals to retain into the next population, which could effectively handle multiple constraints. Then the shrinking space technique is designed to shrink the search region according to feedback information in order to improve computational efficiency without losing accuracy. The improved DE algorithm introduces three different mutant strategies to generate different offspring into evo- lutionary population. Moreover, a new mutant strategy called ＂DE/rand/best/l＂ is constructed to generate new individuals according to the feasibility proportion ofcurrent population. Finally, the effectiveness of the pro- posed method is verified by a suite of benchmark functions and practical engineering problems. This research presents a constrained evolutionary algorithm with high efficiency and accuracy for constrained optimization problems.
基金This work was supported in part by the National Key Research and Development Program of China(2018AAA0100100)the National Natural Science Foundation of China(61822301,61876123,61906001)+2 种基金the Collaborative Innovation Program of Universities in Anhui Province(GXXT-2020-051)the Hong Kong Scholars Program(XJ2019035)Anhui Provincial Natural Science Foundation(1908085QF271).
文摘During the last three decades,evolutionary algorithms(EAs)have shown superiority in solving complex optimization problems,especially those with multiple objectives and non-differentiable landscapes.However,due to the stochastic search strategies,the performance of most EAs deteriorates drastically when handling a large number of decision variables.To tackle the curse of dimensionality,this work proposes an efficient EA for solving super-large-scale multi-objective optimization problems with sparse optimal solutions.The proposed algorithm estimates the sparse distribution of optimal solutions by optimizing a binary vector for each solution,and provides a fast clustering method to highly reduce the dimensionality of the search space.More importantly,all the operations related to the decision variables only contain several matrix calculations,which can be directly accelerated by GPUs.While existing EAs are capable of handling fewer than 10000 real variables,the proposed algorithm is verified to be effective in handling 1000000 real variables.Furthermore,since the proposed algorithm handles the large number of variables via accelerated matrix calculations,its runtime can be reduced to less than 10%of the runtime of existing EAs.
基金supported in part by the National Key Research and Development Program of China(2018AAA0100100)the National Natural Science Foundation of China(61906001,62136008,U21A20512)+1 种基金the Key Program of Natural Science Project of Educational Commission of Anhui Province(KJ2020A0036)Alexander von Humboldt Professorship for Artificial Intelligence Funded by the Federal Ministry of Education and Research,Germany。
文摘Large-scale multi-objective optimization problems(LSMOPs)pose challenges to existing optimizers since a set of well-converged and diverse solutions should be found in huge search spaces.While evolutionary algorithms are good at solving small-scale multi-objective optimization problems,they are criticized for low efficiency in converging to the optimums of LSMOPs.By contrast,mathematical programming methods offer fast convergence speed on large-scale single-objective optimization problems,but they have difficulties in finding diverse solutions for LSMOPs.Currently,how to integrate evolutionary algorithms with mathematical programming methods to solve LSMOPs remains unexplored.In this paper,a hybrid algorithm is tailored for LSMOPs by coupling differential evolution and a conjugate gradient method.On the one hand,conjugate gradients and differential evolution are used to update different decision variables of a set of solutions,where the former drives the solutions to quickly converge towards the Pareto front and the latter promotes the diversity of the solutions to cover the whole Pareto front.On the other hand,objective decomposition strategy of evolutionary multi-objective optimization is used to differentiate the conjugate gradients of solutions,and the line search strategy of mathematical programming is used to ensure the higher quality of each offspring than its parent.In comparison with state-of-the-art evolutionary algorithms,mathematical programming methods,and hybrid algorithms,the proposed algorithm exhibits better convergence and diversity performance on a variety of benchmark and real-world LSMOPs.
