In recent years,surrogate models derived from genuine data samples have proven to be efficient in addressing optimization challenges that are costly or time⁃intensive.However,the individuals in the population become i...In recent years,surrogate models derived from genuine data samples have proven to be efficient in addressing optimization challenges that are costly or time⁃intensive.However,the individuals in the population become indistinguishable as the curse of dimensionality increases in the objective space and the accumulation of surrogate approximated errors.Therefore,in this paper,each objective function is modeled using a radial basis function approach,and the optimal solution set of the surrogate model is located by the multi⁃objective evolutionary algorithm of strengthened dominance relation.The original objective function values of the true evaluations are converted to two indicator values,and then the surrogate models are set up for the two performance indicators.Finally,an adaptive infill sampling strategy that relies on approximate performance indicators is proposed to assist in selecting individuals for real evaluations from the potential optimal solution set.The algorithm is contrasted against several advanced surrogate⁃assisted evolutionary algorithms on two suites of test cases,and the experimental findings prove that the approach is competitive in solving expensive many⁃objective optimization problems.展开更多
This study presents an autoencoder-embedded optimization(AEO)algorithm which involves a bi-population cooperative strategy for medium-scale expensive problems(MEPs).A huge search space can be compressed to an informat...This study presents an autoencoder-embedded optimization(AEO)algorithm which involves a bi-population cooperative strategy for medium-scale expensive problems(MEPs).A huge search space can be compressed to an informative lowdimensional space by using an autoencoder as a dimension reduction tool.The search operation conducted in this low space facilitates the population with fast convergence towards the optima.To strike the balance between exploration and exploitation during optimization,two phases of a tailored teaching-learning-based optimization(TTLBO)are adopted to coevolve solutions in a distributed fashion,wherein one is assisted by an autoencoder and the other undergoes a regular evolutionary process.Also,a dynamic size adjustment scheme according to problem dimension and evolutionary progress is proposed to promote information exchange between these two phases and accelerate evolutionary convergence speed.The proposed algorithm is validated by testing benchmark functions with dimensions varying from 50 to 200.As indicated in our experiments,TTLBO is suitable for dealing with medium-scale problems and thus incorporated into the AEO framework as a base optimizer.Compared with the state-of-the-art algorithms for MEPs,AEO shows extraordinarily high efficiency for these challenging problems,t hus opening new directions for various evolutionary algorithms under AEO to tackle MEPs and greatly advancing the field of medium-scale computationally expensive optimization.展开更多
In solving many-objective optimization problems(MaO Ps),existing nondominated sorting-based multi-objective evolutionary algorithms suffer from the fast loss of selection pressure.Most candidate solutions become nondo...In solving many-objective optimization problems(MaO Ps),existing nondominated sorting-based multi-objective evolutionary algorithms suffer from the fast loss of selection pressure.Most candidate solutions become nondominated during the evolutionary process,thus leading to the failure of producing offspring toward Pareto-optimal front with diversity.Can we find a more effective way to select nondominated solutions and resolve this issue?To answer this critical question,this work proposes to evolve solutions through line complex rather than solution points in Euclidean space.First,Plücker coordinates are used to project solution points to line complex composed of position vectors and momentum ones.Besides position vectors of the solution points,momentum vectors are used to extend the comparability of nondominated solutions and enhance selection pressure.Then,a new distance function designed for high-dimensional space is proposed to replace Euclidean distance as a more effective distancebased estimator.Based on them,a novel many-objective evolutionary algorithm(MaOEA)is proposed by integrating a line complex-based environmental selection strategy into the NSGAⅢframework.The proposed algorithm is compared with the state of the art on widely used benchmark problems with up to 15 objectives.Experimental results demonstrate its superior competitiveness in solving MaOPs.展开更多
In this work,a hybrid meta-model based design space differentiation（HMDSD）method is proposed for practical problems.In the proposed method,an iteratively reduced promising region is constructed using the expensive p...In this work,a hybrid meta-model based design space differentiation（HMDSD）method is proposed for practical problems.In the proposed method,an iteratively reduced promising region is constructed using the expensive points,with two different search strategies respectively applied inside and outside the promising region.Besides,the hybrid meta-model strategy applied in the search process makes it possible to solve the complex practical problems.Tested upon a serial of benchmark math functions,the HMDSD method shows great efficiency and search accuracy.On top of that,a practical lightweight design demonstrates its superior performance.展开更多
In recent years,the development of new types of nuclear reactors,such as transportable,marine,and space reactors,has presented new challenges for the optimization of reactor radiation-shielding design.Shielding struct...In recent years,the development of new types of nuclear reactors,such as transportable,marine,and space reactors,has presented new challenges for the optimization of reactor radiation-shielding design.Shielding structures typically need to be lightweight,miniaturized,and radiation-protected,which is a multi-parameter and multi-objective optimization problem.The conventional multi-objective(two or three objectives)optimization method for radiation-shielding design exhibits limitations for a number of optimization objectives and variable parameters,as well as a deficiency in achieving a global optimal solution,thereby failing to meet the requirements of shielding optimization for newly developed reactors.In this study,genetic and artificial bee-colony algorithms are combined with a reference-point-selection strategy and applied to the many-objective(having four or more objectives)optimal design of reactor radiation shielding.To validate the reliability of the methods,an optimization simulation is conducted on three-dimensional shielding structures and another complicated shielding-optimization problem.The numerical results demonstrate that the proposed algorithms outperform conventional shielding-design methods in terms of optimization performance,and they exhibit their reliability in practical engineering problems.The many-objective optimization algorithms developed in this study are proven to efficiently and consistently search for Pareto-front shielding schemes.Therefore,the algorithms proposed in this study offer novel insights into improving the shielding-design performance and shielding quality of new reactor types.展开更多
Modern engineering design optimization often relies on computer simulations to evaluate candidate designs, a setup which results in expensive black-box optimization problems. Such problems introduce unique challenges,...Modern engineering design optimization often relies on computer simulations to evaluate candidate designs, a setup which results in expensive black-box optimization problems. Such problems introduce unique challenges, which has motivated the application of metamodel-assisted computational intelligence algorithms to solve them. Such algorithms combine a computational intelligence optimizer which employs a population of candidate solutions, with a metamodel which is a computationally cheaper approximation of the expensive computer simulation. However, although a variety of metamodels and optimizers have been proposed, the optimal types to employ are problem dependant. Therefore, a priori prescribing the type of metamodel and optimizer to be used may degrade its effectiveness. Leveraging on this issue, this study proposes a new computational intelligence algorithm which autonomously adapts the type of the metamodel and optimizer during the search by selecting the most suitable types out of a family of candidates at each stage. Performance analysis using a set of test functions demonstrates the effectiveness of the proposed algorithm, and highlights the merit of the proposed adaptation approach.展开更多
With the increase of problem dimensions,most solutions of existing many-objective optimization algorithms are non-dominant.Therefore,the selection of individuals and the retention of elite individuals are important.Ex...With the increase of problem dimensions,most solutions of existing many-objective optimization algorithms are non-dominant.Therefore,the selection of individuals and the retention of elite individuals are important.Existing algorithms cannot provide sufficient solution precision and guarantee the diversity and convergence of solution sets when solving practical many-objective industrial problems.Thus,this work proposes an improved many-objective pigeon-inspired optimization(ImMAPIO)algorithm with multiple selection strategies to solve many-objective optimization problems.Multiple selection strategies integrating hypervolume,knee point,and vector angles are utilized to increase selection pressure to the true Pareto Front.Thus,the accuracy,convergence,and diversity of solutions are improved.ImMAPIO is applied to the DTLZ and WFG test functions with four to fifteen objectives and compared against NSGA-III,GrEA,MOEA/D,RVEA,and many-objective Pigeon-inspired optimization algorithm.Experimental results indicate the superiority of ImMAPIO on these test functions.展开更多
Expensive optimization problem(EOP) widely exists in various significant real-world applications. However, EOP requires expensive or even unaffordable costs for evaluating candidate solutions, which is expensive for t...Expensive optimization problem(EOP) widely exists in various significant real-world applications. However, EOP requires expensive or even unaffordable costs for evaluating candidate solutions, which is expensive for the algorithm to find a satisfactory solution. Moreover, due to the fast-growing application demands in the economy and society, such as the emergence of the smart cities, the internet of things, and the big data era, solving EOP more efficiently has become increasingly essential in various fields, which poses great challenges on the problem-solving ability of optimization approach for EOP. Among various optimization approaches, evolutionary computation(EC) is a promising global optimization tool widely used for solving EOP efficiently in the past decades. Given the fruitful advancements of EC for EOP, it is essential to review these advancements in order to synthesize and give previous research experiences and references to aid the development of relevant research fields and real-world applications. Motivated by this, this paper aims to provide a comprehensive survey to show why and how EC can solve EOP efficiently. For this aim, this paper firstly analyzes the total optimization cost of EC in solving EOP. Then, based on the analysis, three promising research directions are pointed out for solving EOP, which are problem approximation and substitution, algorithm design and enhancement, and parallel and distributed computation. Note that, to the best of our knowledge, this paper is the first that outlines the possible directions for efficiently solving EOP by analyzing the total expensive cost. Based on this, existing works are reviewed comprehensively via a taxonomy with four parts, including the above three research directions and the real-world application part. Moreover, some future research directions are also discussed in this paper. It is believed that such a survey can attract attention, encourage discussions, and stimulate new EC research ideas for solving EOP and related real-world applications more efficiently.展开更多
The multi-objective optimization problem has been encountered in numerous fields such as high-speed train head shape design,overlapping community detection,power dispatch,and unmanned aerial vehicle formation.To addre...The multi-objective optimization problem has been encountered in numerous fields such as high-speed train head shape design,overlapping community detection,power dispatch,and unmanned aerial vehicle formation.To address such issues,current approaches focus mainly on problems with regular Pareto front rather than solving the irregular Pareto front.Considering this situation,we propose a many-objective evolutionary algorithm based on decomposition with dynamic resource allocation(Ma OEA/D-DRA)for irregular optimization.The proposed algorithm can dynamically allocate computing resources to different search areas according to different shapes of the problem’s Pareto front.An evolutionary population and an external archive are used in the search process,and information extracted from the external archive is used to guide the evolutionary population to different search regions.The evolutionary population evolves with the Tchebycheff approach to decompose a problem into several subproblems,and all the subproblems are optimized in a collaborative manner.The external archive is updated with the method of rithms using a variety of test problems with irregular Pareto front.Experimental results show that the proposed algorithèm out-p￡performs these five algorithms with respect to convergence speed and diversity of population members.By comparison with the weighted-sum approach and penalty-based boundary intersection approach,there is an improvement in performance after integration of the Tchebycheff approach into the proposed algorithm.展开更多
Some optimization problems in scientific research,such as the robustness optimization for the Internet of Things and the neural architecture search,are large-scale in decision space and expensive for objective evaluat...Some optimization problems in scientific research,such as the robustness optimization for the Internet of Things and the neural architecture search,are large-scale in decision space and expensive for objective evaluation.In order to get a good solution in a limited budget for the large-scale expensive optimization,a random grouping strategy is adopted to divide the problem into some low-dimensional sub-problems.A surrogate model is then trained for each sub-problem using different strategies to select training data adaptively.After that,a dynamic infill criterion is proposed corresponding to the models currently used in the surrogate-assisted sub-problem optimization.Furthermore,an escape mechanism is proposed to keep the diversity of the population.The performance of the method is evaluated on CEC’2013 benchmark functions.Experimental results show that the algorithm has better performance in solving expensive large-scale optimization problems.展开更多
基金Sponsored by Scientific and Technological Innovation Programs of Higher Education Institutions in Shanxi(Grant No.2022L294)Taiyuan University of Science and Technology Scientific Research Initial Funding(Grant Nos.W2022018,W20242012)Foundamental Research Program of Shanxi Province(Grant No.202403021212170).
文摘In recent years,surrogate models derived from genuine data samples have proven to be efficient in addressing optimization challenges that are costly or time⁃intensive.However,the individuals in the population become indistinguishable as the curse of dimensionality increases in the objective space and the accumulation of surrogate approximated errors.Therefore,in this paper,each objective function is modeled using a radial basis function approach,and the optimal solution set of the surrogate model is located by the multi⁃objective evolutionary algorithm of strengthened dominance relation.The original objective function values of the true evaluations are converted to two indicator values,and then the surrogate models are set up for the two performance indicators.Finally,an adaptive infill sampling strategy that relies on approximate performance indicators is proposed to assist in selecting individuals for real evaluations from the potential optimal solution set.The algorithm is contrasted against several advanced surrogate⁃assisted evolutionary algorithms on two suites of test cases,and the experimental findings prove that the approach is competitive in solving expensive many⁃objective optimization problems.
基金supported in part by the National Natural Science Foundation of China(72171172,62088101)in part by the Shanghai Science and Technology Major Special Project of Shanghai Development and Reform Commission(2021SHZDZX0100)+2 种基金in part by the Shanghai Commission of Science and Technology(19511132100,19511132101)in part by the China Scholarship Councilin part by the Deanship of Scientific Research(DSR)at King Abdulaziz University(KAU),Jeddah,Saudi Arabia(FP-146-43)。
文摘This study presents an autoencoder-embedded optimization(AEO)algorithm which involves a bi-population cooperative strategy for medium-scale expensive problems(MEPs).A huge search space can be compressed to an informative lowdimensional space by using an autoencoder as a dimension reduction tool.The search operation conducted in this low space facilitates the population with fast convergence towards the optima.To strike the balance between exploration and exploitation during optimization,two phases of a tailored teaching-learning-based optimization(TTLBO)are adopted to coevolve solutions in a distributed fashion,wherein one is assisted by an autoencoder and the other undergoes a regular evolutionary process.Also,a dynamic size adjustment scheme according to problem dimension and evolutionary progress is proposed to promote information exchange between these two phases and accelerate evolutionary convergence speed.The proposed algorithm is validated by testing benchmark functions with dimensions varying from 50 to 200.As indicated in our experiments,TTLBO is suitable for dealing with medium-scale problems and thus incorporated into the AEO framework as a base optimizer.Compared with the state-of-the-art algorithms for MEPs,AEO shows extraordinarily high efficiency for these challenging problems,t hus opening new directions for various evolutionary algorithms under AEO to tackle MEPs and greatly advancing the field of medium-scale computationally expensive optimization.
基金supported in part by the National Natural Science Foundation of China(51775385)the Natural Science Foundation of Shanghai(23ZR1466000)+3 种基金the Shanghai Industrial Collaborative Science and Technology Innovation Project(2021-cyxt2-kj10)the Innovation Program of Shanghai Municipal Education Commission(202101070007E00098)the Innovation Project of Engineering Research Center of Integration and Application of Digital Learning Technology of MOE(1221046)the Program to Cultivate Middle-Aged and Young Cadre Teacher of Jiangsu Province。
文摘In solving many-objective optimization problems(MaO Ps),existing nondominated sorting-based multi-objective evolutionary algorithms suffer from the fast loss of selection pressure.Most candidate solutions become nondominated during the evolutionary process,thus leading to the failure of producing offspring toward Pareto-optimal front with diversity.Can we find a more effective way to select nondominated solutions and resolve this issue?To answer this critical question,this work proposes to evolve solutions through line complex rather than solution points in Euclidean space.First,Plücker coordinates are used to project solution points to line complex composed of position vectors and momentum ones.Besides position vectors of the solution points,momentum vectors are used to extend the comparability of nondominated solutions and enhance selection pressure.Then,a new distance function designed for high-dimensional space is proposed to replace Euclidean distance as a more effective distancebased estimator.Based on them,a novel many-objective evolutionary algorithm(MaOEA)is proposed by integrating a line complex-based environmental selection strategy into the NSGAⅢframework.The proposed algorithm is compared with the state of the art on widely used benchmark problems with up to 15 objectives.Experimental results demonstrate its superior competitiveness in solving MaOPs.
基金Project supported by the Plan for the growth of young teachers,the National Natural Science Foundation of China(No.51505138)the National 973 Program of China(No.2010CB328005)+1 种基金Outstanding Youth Foundation of NSFC(No.50625519)Program for Changjiang Scholars
文摘In this work,a hybrid meta-model based design space differentiation（HMDSD）method is proposed for practical problems.In the proposed method,an iteratively reduced promising region is constructed using the expensive points,with two different search strategies respectively applied inside and outside the promising region.Besides,the hybrid meta-model strategy applied in the search process makes it possible to solve the complex practical problems.Tested upon a serial of benchmark math functions,the HMDSD method shows great efficiency and search accuracy.On top of that,a practical lightweight design demonstrates its superior performance.
基金supported by the National Natural Science Foundation of China(Nos.12475174 and 12175101)Yue Lu Shan Center Industrial Innovation(No.2024YCII0108)。
文摘In recent years,the development of new types of nuclear reactors,such as transportable,marine,and space reactors,has presented new challenges for the optimization of reactor radiation-shielding design.Shielding structures typically need to be lightweight,miniaturized,and radiation-protected,which is a multi-parameter and multi-objective optimization problem.The conventional multi-objective(two or three objectives)optimization method for radiation-shielding design exhibits limitations for a number of optimization objectives and variable parameters,as well as a deficiency in achieving a global optimal solution,thereby failing to meet the requirements of shielding optimization for newly developed reactors.In this study,genetic and artificial bee-colony algorithms are combined with a reference-point-selection strategy and applied to the many-objective(having four or more objectives)optimal design of reactor radiation shielding.To validate the reliability of the methods,an optimization simulation is conducted on three-dimensional shielding structures and another complicated shielding-optimization problem.The numerical results demonstrate that the proposed algorithms outperform conventional shielding-design methods in terms of optimization performance,and they exhibit their reliability in practical engineering problems.The many-objective optimization algorithms developed in this study are proven to efficiently and consistently search for Pareto-front shielding schemes.Therefore,the algorithms proposed in this study offer novel insights into improving the shielding-design performance and shielding quality of new reactor types.
文摘Modern engineering design optimization often relies on computer simulations to evaluate candidate designs, a setup which results in expensive black-box optimization problems. Such problems introduce unique challenges, which has motivated the application of metamodel-assisted computational intelligence algorithms to solve them. Such algorithms combine a computational intelligence optimizer which employs a population of candidate solutions, with a metamodel which is a computationally cheaper approximation of the expensive computer simulation. However, although a variety of metamodels and optimizers have been proposed, the optimal types to employ are problem dependant. Therefore, a priori prescribing the type of metamodel and optimizer to be used may degrade its effectiveness. Leveraging on this issue, this study proposes a new computational intelligence algorithm which autonomously adapts the type of the metamodel and optimizer during the search by selecting the most suitable types out of a family of candidates at each stage. Performance analysis using a set of test functions demonstrates the effectiveness of the proposed algorithm, and highlights the merit of the proposed adaptation approach.
基金This work was supported by the National Key Research and Development Program of China(No.2018YFC1604000)the National Natural Science Foundation of China(Nos.61806138,61772478,U1636220,61961160707,and 61976212)+2 种基金the Key R&D Program of Shanxi Province(High Technology)(No.201903D121119)the Key R&D Program of Shanxi Province(International Cooperation)(No.201903D421048)the Key R&D Program(International Science and Technology Cooperation Project)of Shanxi Province,China(No.201903D421003).
文摘With the increase of problem dimensions,most solutions of existing many-objective optimization algorithms are non-dominant.Therefore,the selection of individuals and the retention of elite individuals are important.Existing algorithms cannot provide sufficient solution precision and guarantee the diversity and convergence of solution sets when solving practical many-objective industrial problems.Thus,this work proposes an improved many-objective pigeon-inspired optimization(ImMAPIO)algorithm with multiple selection strategies to solve many-objective optimization problems.Multiple selection strategies integrating hypervolume,knee point,and vector angles are utilized to increase selection pressure to the true Pareto Front.Thus,the accuracy,convergence,and diversity of solutions are improved.ImMAPIO is applied to the DTLZ and WFG test functions with four to fifteen objectives and compared against NSGA-III,GrEA,MOEA/D,RVEA,and many-objective Pigeon-inspired optimization algorithm.Experimental results indicate the superiority of ImMAPIO on these test functions.
基金supported by National Key Research and Development Program of China (No. 2019YFB2102102)the Outstanding Youth Science Foundation (No. 61822602)+3 种基金National Natural Science Foundations of China (Nos. 62176094, 61772207 and 61873097)the Key-Area Research and Development of Guangdong Province (No. 2020B010166002)Guangdong Natural Science Foundation Research Team (No. 2018B030312003)National Research Foundation of Korea (No. NRF-2021H1D3A2A01082705)。
文摘Expensive optimization problem(EOP) widely exists in various significant real-world applications. However, EOP requires expensive or even unaffordable costs for evaluating candidate solutions, which is expensive for the algorithm to find a satisfactory solution. Moreover, due to the fast-growing application demands in the economy and society, such as the emergence of the smart cities, the internet of things, and the big data era, solving EOP more efficiently has become increasingly essential in various fields, which poses great challenges on the problem-solving ability of optimization approach for EOP. Among various optimization approaches, evolutionary computation(EC) is a promising global optimization tool widely used for solving EOP efficiently in the past decades. Given the fruitful advancements of EC for EOP, it is essential to review these advancements in order to synthesize and give previous research experiences and references to aid the development of relevant research fields and real-world applications. Motivated by this, this paper aims to provide a comprehensive survey to show why and how EC can solve EOP efficiently. For this aim, this paper firstly analyzes the total optimization cost of EC in solving EOP. Then, based on the analysis, three promising research directions are pointed out for solving EOP, which are problem approximation and substitution, algorithm design and enhancement, and parallel and distributed computation. Note that, to the best of our knowledge, this paper is the first that outlines the possible directions for efficiently solving EOP by analyzing the total expensive cost. Based on this, existing works are reviewed comprehensively via a taxonomy with four parts, including the above three research directions and the real-world application part. Moreover, some future research directions are also discussed in this paper. It is believed that such a survey can attract attention, encourage discussions, and stimulate new EC research ideas for solving EOP and related real-world applications more efficiently.
基金the National Natural Science Foundation of China(Nos.6156301261802085+5 种基金and 61203109)the Guangxi Natural Science Foundation of China(Nos.2014GhXN6SF AA1183712015GXNSFBA139260and 2020GXNSFAA159038)the Guangxi Key Laboratory of Embedded Technology and Intelligent System Foundation(No.2018A-04)the Guangxi Key Laboratory of Trusted Software Foundation(Nos.kx202011 and khx2601926)。
文摘The multi-objective optimization problem has been encountered in numerous fields such as high-speed train head shape design,overlapping community detection,power dispatch,and unmanned aerial vehicle formation.To address such issues,current approaches focus mainly on problems with regular Pareto front rather than solving the irregular Pareto front.Considering this situation,we propose a many-objective evolutionary algorithm based on decomposition with dynamic resource allocation(Ma OEA/D-DRA)for irregular optimization.The proposed algorithm can dynamically allocate computing resources to different search areas according to different shapes of the problem’s Pareto front.An evolutionary population and an external archive are used in the search process,and information extracted from the external archive is used to guide the evolutionary population to different search regions.The evolutionary population evolves with the Tchebycheff approach to decompose a problem into several subproblems,and all the subproblems are optimized in a collaborative manner.The external archive is updated with the method of rithms using a variety of test problems with irregular Pareto front.Experimental results show that the proposed algorithèm out-p￡performs these five algorithms with respect to convergence speed and diversity of population members.By comparison with the weighted-sum approach and penalty-based boundary intersection approach,there is an improvement in performance after integration of the Tchebycheff approach into the proposed algorithm.
基金This work was supported in part by the National Natural Science Foundation of China(No.61876123)Shanxi Key Research and Development Program(No.202102020101002)Natural Science Foundation of Shanxi Province(Nos.201901D111264 and 201901D111262).
文摘Some optimization problems in scientific research,such as the robustness optimization for the Internet of Things and the neural architecture search,are large-scale in decision space and expensive for objective evaluation.In order to get a good solution in a limited budget for the large-scale expensive optimization,a random grouping strategy is adopted to divide the problem into some low-dimensional sub-problems.A surrogate model is then trained for each sub-problem using different strategies to select training data adaptively.After that,a dynamic infill criterion is proposed corresponding to the models currently used in the surrogate-assisted sub-problem optimization.Furthermore,an escape mechanism is proposed to keep the diversity of the population.The performance of the method is evaluated on CEC’2013 benchmark functions.Experimental results show that the algorithm has better performance in solving expensive large-scale optimization problems.
