Constrained optimization problems are very important as they are encountered in many science and engineering applications.As a novel evolutionary computation technique,cuckoo search(CS) algorithm has attracted much at...Constrained optimization problems are very important as they are encountered in many science and engineering applications.As a novel evolutionary computation technique,cuckoo search(CS) algorithm has attracted much attention and wide applications,owing to its easy implementation and quick convergence.A hybrid cuckoo pattern search algorithm(HCPS) with feasibility-based rule is proposed for solving constrained numerical and engineering design optimization problems.This algorithm can combine the stochastic exploration of the cuckoo search algorithm and the exploitation capability of the pattern search method.Simulation and comparisons based on several well-known benchmark test functions and structural design optimization problems demonstrate the effectiveness,efficiency and robustness of the proposed HCPS algorithm.展开更多
A new method to solve dynamic nonlinear constrained optimization problems （DNCOP） is proposed. First, the time （environment） variable period of DNCOP is divided into several equal subperiods. In each subperiod, th...A new method to solve dynamic nonlinear constrained optimization problems （DNCOP） is proposed. First, the time （environment） variable period of DNCOP is divided into several equal subperiods. In each subperiod, the DNCOP is approximated by a static nonlinear constrained optimization problem （SNCOP）. Second, for each SNCOP, inspired by the idea of multiobjective optimization, it is transformed into a static bi-objective optimization problem. As a result, the original DNCOP is approximately transformed into several static bi-objective optimization problems. Third, a new multiobjective evolutionary algorithm is proposed based on a new selection operator and an improved nonuniformity mutation operator. The simulation results indicate that the proposed algorithm is effective for DNCOP.展开更多
In order to improve the distribution and convergence of constrained optimization algorithms,this paper proposes a constrained optimization algorithm based on double populations. Firstly the feasible solutions and infe...In order to improve the distribution and convergence of constrained optimization algorithms,this paper proposes a constrained optimization algorithm based on double populations. Firstly the feasible solutions and infeasible solutions are stored separately through two populations,which can avoid direct comparison between them. The usage of efficient information carried by the infeasible solutions will enlarge exploitation scope and strength diversity of populations. At the same time,adopting the presented concept of constraints domination to update the infeasible set may keep good variety of population and give consideration to convergence. Also the improved mutation operation is employed to further raise the diversity and convergence.The suggested algorithm is compared with 3 state- of- the- art constrained optimization algorithms on standard test problems g01- g13. Simulation results show that the presented algorithm has certain advantages than other algorithms because it can ensure good convergence accuracy while it has good robustness.展开更多
Evolutionary algorithms(EAs)were shown to be effective for complex constrained optimization problems.However,inflexible exploration in general EAs would lead to losing the global optimum nearby the ill-convergence reg...Evolutionary algorithms(EAs)were shown to be effective for complex constrained optimization problems.However,inflexible exploration in general EAs would lead to losing the global optimum nearby the ill-convergence regions.In this paper,we propose an iterative dynamic diversity evolutionary algorithm(IDDEA)with contractive subregions guiding exploitation through local extrema to the global optimum in suitable steps.In IDDEA,a novel optimum estimation strategy with multi-agents evolving diversely is suggested to e?ciently compute dominance trend and establish a subregion.In addition,a subregion converging iteration is designed to redistrict a smaller subregion in current subregion for next iteration,which is based on a special dominance estimation scheme.Meanwhile,an infimum penalty function is embedded into IDDEA to judge agents and penalize adaptively the unfeasible agents with the lowest fitness of feasible agents.Furthermore,several engineering design optimization problems taken from the specialized literature are successfully solved by the present algorithm with high reliable solutions.展开更多
Differential evolution (DE) algorithm has been shown to be a simple and efficient evolutionary algorithm for global optimization over continuous spaces, and has been widely used in both benchmark test functions and re...Differential evolution (DE) algorithm has been shown to be a simple and efficient evolutionary algorithm for global optimization over continuous spaces, and has been widely used in both benchmark test functions and real-world applications. This paper introduces a novel mutation operator, without using the scaling factor F, a conventional control parameter, and this mutation can generate multiple trial vectors by incorporating different weighted values at each generation, which can make the best of the selected multiple parents to improve the probability of generating a better offspring. In addition, in order to enhance the capacity of adaptation, a new and adaptive control parameter, i.e. the crossover rate CR, is presented and when one variable is beyond its boundary, a repair rule is also applied in this paper. The proposed algorithm ADE is validated on several constrained engineering design optimization problems reported in the specialized literature. Compared with respect to algorithms representative of the state-of-the-art in the area, the experimental results show that ADE can obtain good solutions on a test set of constrained optimization problems in engineering design.展开更多
In this paper, a primal-dual path-following interior-point algorithm for linearly constrained convex optimization(LCCO) is presented.The algorithm is based on a new technique for finding a class of search directions a...In this paper, a primal-dual path-following interior-point algorithm for linearly constrained convex optimization(LCCO) is presented.The algorithm is based on a new technique for finding a class of search directions and the strategy of the central path.At each iteration, only full-Newton steps are used.Finally, the favorable polynomial complexity bound for the algorithm with the small-update method is deserved, namely, O(√n log n /ε).展开更多
In order to solve the constrained global optimization problem,we use penalty functions not only on constraints but also on objective function. Then within the framework of interval analysis,an interval Branch-and-Boun...In order to solve the constrained global optimization problem,we use penalty functions not only on constraints but also on objective function. Then within the framework of interval analysis,an interval Branch-and-Bound algorithm is given,which does not need to solve a sequence of unconstrained problems. Global convergence is proved. Numerical examples show that this algorithm is efficient.展开更多
The convergence analysis of a nonlinear Lagrange algorithm for solving nonlinear constrained optimization problems with both inequality and equality constraints is explored in detail. The estimates for the derivatives...The convergence analysis of a nonlinear Lagrange algorithm for solving nonlinear constrained optimization problems with both inequality and equality constraints is explored in detail. The estimates for the derivatives of the multiplier mapping and the solution mapping of the proposed algorithm are discussed via the technique of the singular value decomposition of matrix. Based on the estimates, the local convergence results and the rate of convergence of the algorithm are presented when the penalty parameter is less than a threshold under a set of suitable conditions on problem functions. Furthermore, the condition number of the Hessian of the nonlinear Lagrange function with respect to the decision variables is analyzed, which is closely related to efficiency of the algorithm. Finally, the preliminary numericM results for several typical test problems are reported.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
There are three common types of predictability problems in weather and climate, which each involve different constrained nonlinear optimization problems： the lower bound of maximum predictable time, the upper bound o...There are three common types of predictability problems in weather and climate, which each involve different constrained nonlinear optimization problems： the lower bound of maximum predictable time, the upper bound of maximum prediction error, and the lower bound of maximum allowable initial error and parameter error. Highly effcient algorithms have been developed to solve the second optimization problem. And this optimization problem can be used in realistic models for weather and climate to study the upper bound of the maximum prediction error. Although a filtering strategy has been adopted to solve the other two problems, direct solutions are very time-consuming even for a very simple model, which therefore limits the applicability of these two predictability problems in realistic models. In this paper, a new strategy is designed to solve these problems, involving the use of the existing highly effcient algorithms for the second predictability problem in particular. Furthermore, a series of comparisons between the older filtering strategy and the new method are performed. It is demonstrated that the new strategy not only outputs the same results as the old one, but is also more computationally effcient. This would suggest that it is possible to study the predictability problems associated with these two nonlinear optimization problems in realistic forecast models of weather or climate.展开更多
This paper proposes a modified version of the Dwarf Mongoose Optimization Algorithm (IDMO) for constrained engineering design problems. This optimization technique modifies the base algorithm (DMO) in three simple but...This paper proposes a modified version of the Dwarf Mongoose Optimization Algorithm (IDMO) for constrained engineering design problems. This optimization technique modifies the base algorithm (DMO) in three simple but effective ways. First, the alpha selection in IDMO differs from the DMO, where evaluating the probability value of each fitness is just a computational overhead and contributes nothing to the quality of the alpha or other group members. The fittest dwarf mongoose is selected as the alpha, and a new operator ω is introduced, which controls the alpha movement, thereby enhancing the exploration ability and exploitability of the IDMO. Second, the scout group movements are modified by randomization to introduce diversity in the search process and explore unvisited areas. Finally, the babysitter's exchange criterium is modified such that once the criterium is met, the babysitters that are exchanged interact with the dwarf mongoose exchanging them to gain information about food sources and sleeping mounds, which could result in better-fitted mongooses instead of initializing them afresh as done in DMO, then the counter is reset to zero. The proposed IDMO was used to solve the classical and CEC 2020 benchmark functions and 12 continuous/discrete engineering optimization problems. The performance of the IDMO, using different performance metrics and statistical analysis, is compared with the DMO and eight other existing algorithms. In most cases, the results show that solutions achieved by the IDMO are better than those obtained by the existing algorithms.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
In this paper, a variable metric algorithm is proposed with Broyden rank one modifications for the equality constrained optimization. This method is viewed expansion in constrained optimization as the quasi-Newton met...In this paper, a variable metric algorithm is proposed with Broyden rank one modifications for the equality constrained optimization. This method is viewed expansion in constrained optimization as the quasi-Newton method to unconstrained optimization. The theoretical analysis shows that local convergence can be induced under some suitable conditions. In the end, it is established an equivalent condition of superlinear convergence.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
In this paper, a new augmented Lagrangian penalty function for constrained optimization problems is studied. The dual properties of the augmented Lagrangian objective penalty function for constrained optimization prob...In this paper, a new augmented Lagrangian penalty function for constrained optimization problems is studied. The dual properties of the augmented Lagrangian objective penalty function for constrained optimization problems are proved. Under some conditions, the saddle point of the augmented Lagrangian objective penalty function satisfies the first-order Karush-Kuhn-Tucker (KKT) condition. Especially, when the KKT condition holds for convex programming its saddle point exists. Based on the augmented Lagrangian objective penalty function, an algorithm is developed for finding a global solution to an inequality constrained optimization problem and its global convergence is also proved under some conditions.展开更多
The particle swarm optimization(PSO)algorithm is an established nature-inspired population-based meta-heuristic that replicates the synchronizing movements of birds and sh.PSO is essentially an unconstrained algorithm...The particle swarm optimization(PSO)algorithm is an established nature-inspired population-based meta-heuristic that replicates the synchronizing movements of birds and sh.PSO is essentially an unconstrained algorithm and requires constraint handling techniques(CHTs)to solve constrained optimization problems(COPs).For this purpose,we integrate two CHTs,the superiority of feasibility(SF)and the violation constraint-handling(VCH),with a PSO.These CHTs distinguish feasible solutions from infeasible ones.Moreover,in SF,the selection of infeasible solutions is based on their degree of constraint violations,whereas in VCH,the number of constraint violations by an infeasible solution is of more importance.Therefore,a PSO is adapted for constrained optimization,yielding two constrained variants,denoted SF-PSO and VCH-PSO.Both SF-PSO and VCH-PSO are evaluated with respect to ve engineering problems:the Himmelblau’s nonlinear optimization,the welded beam design,the spring design,the pressure vessel design,and the three-bar truss design.The simulation results show that both algorithms are consistent in terms of their solutions to these problems,including their different available versions.Comparison of the SF-PSO and the VCHPSO with other existing algorithms on the tested problems shows that the proposed algorithms have lower computational cost in terms of the number of function evaluations used.We also report our disagreement with some unjust comparisons made by other researchers regarding the tested problems and their different variants.展开更多
Iterative methods for solving discrete optimal control problems are constructed and investigated. These discrete problems arise when approximating by finite difference method or by finite element method the optimal co...Iterative methods for solving discrete optimal control problems are constructed and investigated. These discrete problems arise when approximating by finite difference method or by finite element method the optimal control problems which contain a linear elliptic boundary value problem as a state equation, control in the righthand side of the equation or in the boundary conditions, and point-wise constraints for both state and control functions. The convergence of the constructed iterative methods is proved, the implementation problems are discussed, and the numerical comparison of the methods is executed.展开更多
For the carbon-neutral,a multi-carrier renewable energy system(MRES),driven by the wind,solar and geothermal,was considered as an effective solution to mitigate CO2emissions and reduce energy usage in the building sec...For the carbon-neutral,a multi-carrier renewable energy system(MRES),driven by the wind,solar and geothermal,was considered as an effective solution to mitigate CO2emissions and reduce energy usage in the building sector.A proper sizing method was essential for achieving the desired 100%renewable energy system of resources.This paper presented a bi-objective optimization formulation for sizing the MRES using a constrained genetic algorithm(GA)coupled with the loss of power supply probability(LPSP)method to achieve the minimal cost of the system and the reliability of the system to the load real time requirement.An optimization App has been developed in MATLAB environment to offer a user-friendly interface and output the optimized design parameters when given the load demand.A case study of a swimming pool building was used to demonstrate the process of the proposed design method.Compared to the conventional distributed energy system,the MRES is feasible with a lower annual total cost(ATC).Additionally,the ATC decreases as the power supply reliability of the renewable system decreases.There is a decrease of 24%of the annual total cost when the power supply probability is equal to 8%compared to the baseline case with 0%power supply probability.展开更多
Till now,several novel metaheuristic algorithms are proposed for global search.But only specific algorithms have become popular or attracted researchers,who are efficient in solving global optimization problems as wel...Till now,several novel metaheuristic algorithms are proposed for global search.But only specific algorithms have become popular or attracted researchers,who are efficient in solving global optimization problems as well as real-world application problems.The Social Group Optimization(SGO)algorithm is a new metaheuristic bioinspired algorithm inspired by human social behavior that attracted researchers due to its simplicity and problem-solving capability.In this study,to deal with the problems of low accuracy and local convergence in SGO,the chaos theory is introduced into the evolutionary process of SGO.Since chaotic mapping has certainty,ergodicity,and stochastic property,by replacing the constant value of the self-introspection parameter with chaotic maps,the proposed chaotic social group optimization algorithm increases its convergence rate and resulting precision.The proposal chaotic SGO is validated through 13 benchmark functions and after that 9 structural engineering design problems have been solved.The simulated results have been noticed as competent with that of state-of-art algorithms regarding convergence quality and accuracy,which certifies that improved SGO with chaos is valid and feasible.展开更多
To study the uncertain optimization problems on implementation schedule, time-cost trade-off and quality in enterprise resource planning （ERP） implementation, combined with program evaluation and review technique （...To study the uncertain optimization problems on implementation schedule, time-cost trade-off and quality in enterprise resource planning （ERP） implementation, combined with program evaluation and review technique （PERT）, some optimization models are proposed, which include the implementation schedule model, the timecost trade-off model, the quality model, and the implementation time-cost-quality synthetic optimization model. A PERT-embedded genetic algorithm （GA） based on stochastic simulation technique is introduced to the optimization models solution. Finally, an example is presented to show that the models and algorithm are reasonable and effective, which can offer a reliable quantitative decision method for ERP implementation.展开更多
基金Projects([2013]2082,[2009]2061)supported by the Science Technology Foundation of Guizhou Province,ChinaProject([2013]140)supported by the Excellent Science Technology Innovation Talents in Universities of Guizhou Province,ChinaProject(2008040)supported by the Natural Science Research in Education Department of Guizhou Province,China
文摘Constrained optimization problems are very important as they are encountered in many science and engineering applications.As a novel evolutionary computation technique,cuckoo search(CS) algorithm has attracted much attention and wide applications,owing to its easy implementation and quick convergence.A hybrid cuckoo pattern search algorithm(HCPS) with feasibility-based rule is proposed for solving constrained numerical and engineering design optimization problems.This algorithm can combine the stochastic exploration of the cuckoo search algorithm and the exploitation capability of the pattern search method.Simulation and comparisons based on several well-known benchmark test functions and structural design optimization problems demonstrate the effectiveness,efficiency and robustness of the proposed HCPS algorithm.
基金supported by the National Natural Science Foundation of China (60374063)the Natural Science Basic Research Plan Project in Shaanxi Province (2006A12)+1 种基金the Science and Technology Research Project of the Educational Department in Shaanxi Province (07JK180)the Emphasis Research Plan Project of Baoji University of Arts and Science (ZK0840)
文摘A new method to solve dynamic nonlinear constrained optimization problems （DNCOP） is proposed. First, the time （environment） variable period of DNCOP is divided into several equal subperiods. In each subperiod, the DNCOP is approximated by a static nonlinear constrained optimization problem （SNCOP）. Second, for each SNCOP, inspired by the idea of multiobjective optimization, it is transformed into a static bi-objective optimization problem. As a result, the original DNCOP is approximately transformed into several static bi-objective optimization problems. Third, a new multiobjective evolutionary algorithm is proposed based on a new selection operator and an improved nonuniformity mutation operator. The simulation results indicate that the proposed algorithm is effective for DNCOP.
文摘In order to improve the distribution and convergence of constrained optimization algorithms,this paper proposes a constrained optimization algorithm based on double populations. Firstly the feasible solutions and infeasible solutions are stored separately through two populations,which can avoid direct comparison between them. The usage of efficient information carried by the infeasible solutions will enlarge exploitation scope and strength diversity of populations. At the same time,adopting the presented concept of constraints domination to update the infeasible set may keep good variety of population and give consideration to convergence. Also the improved mutation operation is employed to further raise the diversity and convergence.The suggested algorithm is compared with 3 state- of- the- art constrained optimization algorithms on standard test problems g01- g13. Simulation results show that the presented algorithm has certain advantages than other algorithms because it can ensure good convergence accuracy while it has good robustness.
基金Supported by National Natural Science Foundation of China(61074020)
文摘Evolutionary algorithms(EAs)were shown to be effective for complex constrained optimization problems.However,inflexible exploration in general EAs would lead to losing the global optimum nearby the ill-convergence regions.In this paper,we propose an iterative dynamic diversity evolutionary algorithm(IDDEA)with contractive subregions guiding exploitation through local extrema to the global optimum in suitable steps.In IDDEA,a novel optimum estimation strategy with multi-agents evolving diversely is suggested to e?ciently compute dominance trend and establish a subregion.In addition,a subregion converging iteration is designed to redistrict a smaller subregion in current subregion for next iteration,which is based on a special dominance estimation scheme.Meanwhile,an infimum penalty function is embedded into IDDEA to judge agents and penalize adaptively the unfeasible agents with the lowest fitness of feasible agents.Furthermore,several engineering design optimization problems taken from the specialized literature are successfully solved by the present algorithm with high reliable solutions.
文摘Differential evolution (DE) algorithm has been shown to be a simple and efficient evolutionary algorithm for global optimization over continuous spaces, and has been widely used in both benchmark test functions and real-world applications. This paper introduces a novel mutation operator, without using the scaling factor F, a conventional control parameter, and this mutation can generate multiple trial vectors by incorporating different weighted values at each generation, which can make the best of the selected multiple parents to improve the probability of generating a better offspring. In addition, in order to enhance the capacity of adaptation, a new and adaptive control parameter, i.e. the crossover rate CR, is presented and when one variable is beyond its boundary, a repair rule is also applied in this paper. The proposed algorithm ADE is validated on several constrained engineering design optimization problems reported in the specialized literature. Compared with respect to algorithms representative of the state-of-the-art in the area, the experimental results show that ADE can obtain good solutions on a test set of constrained optimization problems in engineering design.
基金supported by the Shanghai Pujiang Program (Grant No.06PJ14039)the Science Foundation of Shanghai Municipal Commission of Education (Grant No.06NS031)
文摘In this paper, a primal-dual path-following interior-point algorithm for linearly constrained convex optimization(LCCO) is presented.The algorithm is based on a new technique for finding a class of search directions and the strategy of the central path.At each iteration, only full-Newton steps are used.Finally, the favorable polynomial complexity bound for the algorithm with the small-update method is deserved, namely, O(√n log n /ε).
基金This research is supported by the National Science Foundation of China.
文摘In order to solve the constrained global optimization problem,we use penalty functions not only on constraints but also on objective function. Then within the framework of interval analysis,an interval Branch-and-Bound algorithm is given,which does not need to solve a sequence of unconstrained problems. Global convergence is proved. Numerical examples show that this algorithm is efficient.
基金Supported by the National Natural Science Foundation of China(11201357,81271513 and 91324201)the Fundamental Research Funds for the Central Universities under project(2014-Ia-001)
文摘The convergence analysis of a nonlinear Lagrange algorithm for solving nonlinear constrained optimization problems with both inequality and equality constraints is explored in detail. The estimates for the derivatives of the multiplier mapping and the solution mapping of the proposed algorithm are discussed via the technique of the singular value decomposition of matrix. Based on the estimates, the local convergence results and the rate of convergence of the algorithm are presented when the penalty parameter is less than a threshold under a set of suitable conditions on problem functions. Furthermore, the condition number of the Hessian of the nonlinear Lagrange function with respect to the decision variables is analyzed, which is closely related to efficiency of the algorithm. Finally, the preliminary numericM results for several typical test problems are reported.
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.
基金sponsored by the Key Knowledge Innovation Program of the Chinese Academy of Sciences (Grant. No. KZCX2-YW-QN203)the National Basic Research Program of China(2007CB411800),the GYHY200906009 of China Meteorological Administration
文摘There are three common types of predictability problems in weather and climate, which each involve different constrained nonlinear optimization problems： the lower bound of maximum predictable time, the upper bound of maximum prediction error, and the lower bound of maximum allowable initial error and parameter error. Highly effcient algorithms have been developed to solve the second optimization problem. And this optimization problem can be used in realistic models for weather and climate to study the upper bound of the maximum prediction error. Although a filtering strategy has been adopted to solve the other two problems, direct solutions are very time-consuming even for a very simple model, which therefore limits the applicability of these two predictability problems in realistic models. In this paper, a new strategy is designed to solve these problems, involving the use of the existing highly effcient algorithms for the second predictability problem in particular. Furthermore, a series of comparisons between the older filtering strategy and the new method are performed. It is demonstrated that the new strategy not only outputs the same results as the old one, but is also more computationally effcient. This would suggest that it is possible to study the predictability problems associated with these two nonlinear optimization problems in realistic forecast models of weather or climate.
文摘This paper proposes a modified version of the Dwarf Mongoose Optimization Algorithm (IDMO) for constrained engineering design problems. This optimization technique modifies the base algorithm (DMO) in three simple but effective ways. First, the alpha selection in IDMO differs from the DMO, where evaluating the probability value of each fitness is just a computational overhead and contributes nothing to the quality of the alpha or other group members. The fittest dwarf mongoose is selected as the alpha, and a new operator ω is introduced, which controls the alpha movement, thereby enhancing the exploration ability and exploitability of the IDMO. Second, the scout group movements are modified by randomization to introduce diversity in the search process and explore unvisited areas. Finally, the babysitter's exchange criterium is modified such that once the criterium is met, the babysitters that are exchanged interact with the dwarf mongoose exchanging them to gain information about food sources and sleeping mounds, which could result in better-fitted mongooses instead of initializing them afresh as done in DMO, then the counter is reset to zero. The proposed IDMO was used to solve the classical and CEC 2020 benchmark functions and 12 continuous/discrete engineering optimization problems. The performance of the IDMO, using different performance metrics and statistical analysis, is compared with the DMO and eight other existing algorithms. In most cases, the results show that solutions achieved by the IDMO are better than those obtained by the existing algorithms.
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.
文摘In this paper, a variable metric algorithm is proposed with Broyden rank one modifications for the equality constrained optimization. This method is viewed expansion in constrained optimization as the quasi-Newton method to unconstrained optimization. The theoretical analysis shows that local convergence can be induced under some suitable conditions. In the end, it is established an equivalent condition of superlinear convergence.
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.
文摘In this paper, a new augmented Lagrangian penalty function for constrained optimization problems is studied. The dual properties of the augmented Lagrangian objective penalty function for constrained optimization problems are proved. Under some conditions, the saddle point of the augmented Lagrangian objective penalty function satisfies the first-order Karush-Kuhn-Tucker (KKT) condition. Especially, when the KKT condition holds for convex programming its saddle point exists. Based on the augmented Lagrangian objective penalty function, an algorithm is developed for finding a global solution to an inequality constrained optimization problem and its global convergence is also proved under some conditions.
基金The authors thank the Higher Education Commission,Pakistan,for supporting this research under the project NRPU-8925(M.A.J.and H.U.K.),https://www.hec.gowpk/。
文摘The particle swarm optimization(PSO)algorithm is an established nature-inspired population-based meta-heuristic that replicates the synchronizing movements of birds and sh.PSO is essentially an unconstrained algorithm and requires constraint handling techniques(CHTs)to solve constrained optimization problems(COPs).For this purpose,we integrate two CHTs,the superiority of feasibility(SF)and the violation constraint-handling(VCH),with a PSO.These CHTs distinguish feasible solutions from infeasible ones.Moreover,in SF,the selection of infeasible solutions is based on their degree of constraint violations,whereas in VCH,the number of constraint violations by an infeasible solution is of more importance.Therefore,a PSO is adapted for constrained optimization,yielding two constrained variants,denoted SF-PSO and VCH-PSO.Both SF-PSO and VCH-PSO are evaluated with respect to ve engineering problems:the Himmelblau’s nonlinear optimization,the welded beam design,the spring design,the pressure vessel design,and the three-bar truss design.The simulation results show that both algorithms are consistent in terms of their solutions to these problems,including their different available versions.Comparison of the SF-PSO and the VCHPSO with other existing algorithms on the tested problems shows that the proposed algorithms have lower computational cost in terms of the number of function evaluations used.We also report our disagreement with some unjust comparisons made by other researchers regarding the tested problems and their different variants.
文摘Iterative methods for solving discrete optimal control problems are constructed and investigated. These discrete problems arise when approximating by finite difference method or by finite element method the optimal control problems which contain a linear elliptic boundary value problem as a state equation, control in the righthand side of the equation or in the boundary conditions, and point-wise constraints for both state and control functions. The convergence of the constructed iterative methods is proved, the implementation problems are discussed, and the numerical comparison of the methods is executed.
基金Project(52108101)supported by the National Natural Science Foundation of ChinaProjects(2020GK4057,2021JJ40759)supported by the Hunan Provincial Science and Technology Department,China。
文摘For the carbon-neutral,a multi-carrier renewable energy system(MRES),driven by the wind,solar and geothermal,was considered as an effective solution to mitigate CO2emissions and reduce energy usage in the building sector.A proper sizing method was essential for achieving the desired 100%renewable energy system of resources.This paper presented a bi-objective optimization formulation for sizing the MRES using a constrained genetic algorithm(GA)coupled with the loss of power supply probability(LPSP)method to achieve the minimal cost of the system and the reliability of the system to the load real time requirement.An optimization App has been developed in MATLAB environment to offer a user-friendly interface and output the optimized design parameters when given the load demand.A case study of a swimming pool building was used to demonstrate the process of the proposed design method.Compared to the conventional distributed energy system,the MRES is feasible with a lower annual total cost(ATC).Additionally,the ATC decreases as the power supply reliability of the renewable system decreases.There is a decrease of 24%of the annual total cost when the power supply probability is equal to 8%compared to the baseline case with 0%power supply probability.
文摘Till now,several novel metaheuristic algorithms are proposed for global search.But only specific algorithms have become popular or attracted researchers,who are efficient in solving global optimization problems as well as real-world application problems.The Social Group Optimization(SGO)algorithm is a new metaheuristic bioinspired algorithm inspired by human social behavior that attracted researchers due to its simplicity and problem-solving capability.In this study,to deal with the problems of low accuracy and local convergence in SGO,the chaos theory is introduced into the evolutionary process of SGO.Since chaotic mapping has certainty,ergodicity,and stochastic property,by replacing the constant value of the self-introspection parameter with chaotic maps,the proposed chaotic social group optimization algorithm increases its convergence rate and resulting precision.The proposal chaotic SGO is validated through 13 benchmark functions and after that 9 structural engineering design problems have been solved.The simulated results have been noticed as competent with that of state-of-art algorithms regarding convergence quality and accuracy,which certifies that improved SGO with chaos is valid and feasible.
基金the National High-Tech. R & D Program for CIMS, China (2003AA413210).
文摘To study the uncertain optimization problems on implementation schedule, time-cost trade-off and quality in enterprise resource planning （ERP） implementation, combined with program evaluation and review technique （PERT）, some optimization models are proposed, which include the implementation schedule model, the timecost trade-off model, the quality model, and the implementation time-cost-quality synthetic optimization model. A PERT-embedded genetic algorithm （GA） based on stochastic simulation technique is introduced to the optimization models solution. Finally, an example is presented to show that the models and algorithm are reasonable and effective, which can offer a reliable quantitative decision method for ERP implementation.
