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
The two-archive 2 algorithm(Two_Arch2) is a manyobjective evolutionary algorithm for balancing the convergence,diversity,and complexity using diversity archive(DA) and convergence archive(CA).However,the individuals i...The two-archive 2 algorithm(Two_Arch2) is a manyobjective evolutionary algorithm for balancing the convergence,diversity,and complexity using diversity archive(DA) and convergence archive(CA).However,the individuals in DA are selected based on the traditional Pareto dominance which decreases the selection pressure in the high-dimensional problems.The traditional algorithm even cannot converge due to the weak selection pressure.Meanwhile,Two_Arch2 adopts DA as the output of the algorithm which is hard to maintain diversity and coverage of the final solutions synchronously and increase the complexity of the algorithm.To increase the evolutionary pressure of the algorithm and improve distribution and convergence of the final solutions,an ε-domination based Two_Arch2 algorithm(ε-Two_Arch2) for many-objective problems(MaOPs) is proposed in this paper.In ε-Two_Arch2,to decrease the computational complexity and speed up the convergence,a novel evolutionary framework with a fast update strategy is proposed;to increase the selection pressure,ε-domination is assigned to update the individuals in DA;to guarantee the uniform distribution of the solution,a boundary protection strategy based on I_(ε+) indicator is designated as two steps selection strategies to update individuals in CA.To evaluate the performance of the proposed algorithm,a series of benchmark functions with different numbers of objectives is solved.The results demonstrate that the proposed method is competitive with the state-of-the-art multi-objective evolutionary algorithms and the efficiency of the algorithm is significantly improved compared with Two_Arch2.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
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
Due to the security and scalability features of hybrid cloud architecture,it can bettermeet the diverse requirements of users for cloud services.And a reasonable resource allocation solution is the key to adequately u...Due to the security and scalability features of hybrid cloud architecture,it can bettermeet the diverse requirements of users for cloud services.And a reasonable resource allocation solution is the key to adequately utilize the hybrid cloud.However,most previous studies have not comprehensively optimized the performance of hybrid cloud task scheduling,even ignoring the conflicts between its security privacy features and other requirements.Based on the above problems,a many-objective hybrid cloud task scheduling optimization model(HCTSO)is constructed combining risk rate,resource utilization,total cost,and task completion time.Meanwhile,an opposition-based learning knee point-driven many-objective evolutionary algorithm(OBL-KnEA)is proposed to improve the performance of model solving.The algorithm uses opposition-based learning to generate initial populations for faster convergence.Furthermore,a perturbation-based multipoint crossover operator and a dynamic range mutation operator are designed to extend the search range.By comparing the experiments with other excellent algorithms on HCTSO,OBL-KnEA achieves excellent results in terms of evaluation metrics,initial populations,and model optimization effects.展开更多
For many real-world multiobjective optimization problems,the evaluations of the objective functions are computationally expensive.Such problems are usually called expensive multiobjective optimization problems(EMOPs)....For many real-world multiobjective optimization problems,the evaluations of the objective functions are computationally expensive.Such problems are usually called expensive multiobjective optimization problems(EMOPs).One type of feasible approaches for EMOPs is to introduce the computationally efficient surrogates for reducing the number of function evaluations.Inspired from ensemble learning,this paper proposes a multiobjective evolutionary algorithm with an ensemble classifier(MOEA-EC)for EMOPs.More specifically,multiple decision tree models are used as an ensemble classifier for the pre-selection,which is be more helpful for further reducing the function evaluations of the solutions than using single inaccurate model.The extensive experimental studies have been conducted to verify the efficiency of MOEA-EC by comparing it with several advanced multiobjective expensive optimization algorithms.The experimental results show that MOEA-EC outperforms the compared algorithms.展开更多
To address the challenges of high-dimensional constrained optimization problems with expensive simulation models,a Surrogate-Assisted Differential Evolution using Manifold Learning-based Sampling(SADE-MLS)is proposed....To address the challenges of high-dimensional constrained optimization problems with expensive simulation models,a Surrogate-Assisted Differential Evolution using Manifold Learning-based Sampling(SADE-MLS)is proposed.In SADE-MLS,differential evolution operators are executed to generate numerous high-dimensional candidate points.To alleviate the curse of dimensionality,a Manifold Learning-based Sampling(MLS)mechanism is developed to explore the high-dimensional design space effectively.In MLS,the intrinsic dimensionality of the candidate points is determined by a maximum likelihood estimator.Then,the candidate points are mapped into a low-dimensional space using the dimensionality reduction technique,which can avoid significant information loss during dimensionality reduction.Thus,Kriging surrogates are constructed in the low-dimensional space to predict the responses of the mapped candidate points.The candidate points with high constrained expected improvement values are selected for global exploration.Moreover,the local search process assisted by radial basis function and differential evolution is performed to exploit the design space efficiently.Several numerical benchmarks are tested to compare SADE-MLS with other algorithms.Finally,SADE-MLS is successfully applied to a solid rocket motor multidisciplinary optimization problem and a re-entry vehicle aerodynamic optimization problem,with the total impulse and lift to drag ratio being increased by 32.7%and 35.5%,respec-tively.The optimization results demonstrate the practicality and effectiveness of the proposed method in real engineering practices.展开更多
Many-objective optimization problems take challenges to multi-objective evolutionary algorithms.A number of nondominated solutions in population cause a difficult selection towards the Pareto front.To tackle this issu...Many-objective optimization problems take challenges to multi-objective evolutionary algorithms.A number of nondominated solutions in population cause a difficult selection towards the Pareto front.To tackle this issue,a series of indicatorbased multi-objective evolutionary algorithms(MOEAs)have been proposed to guide the evolution progress and shown promising performance.This paper proposes an indicator-based manyobjective evolutionary algorithm calledε-indicator-based shuffled frog leaping algorithm(ε-MaOSFLA),which adopts the shuffled frog leaping algorithm as an evolutionary strategy and a simple and effectiveε-indicator as a fitness assignment scheme to press the population towards the Pareto front.Compared with four stateof-the-art MOEAs on several standard test problems with up to 50 objectives,the experimental results show thatε-MaOSFLA outperforms the competitors.展开更多
It is still a huge challenge for traditional Pareto-dominatedmany-objective optimization algorithms to solve manyobjective optimization problems because these algorithms hardly maintain the balance between convergence...It is still a huge challenge for traditional Pareto-dominatedmany-objective optimization algorithms to solve manyobjective optimization problems because these algorithms hardly maintain the balance between convergence and diversity and can only find a group of solutions focused on a small area on the Pareto front,resulting in poor performance of those algorithms.For this reason,we propose a reference vector-assisted algorithmwith an adaptive niche dominance relation,for short MaOEA-AR.The new dominance relation forms a niche based on the angle between candidate solutions.By comparing these solutions,the solutionwith the best convergence is found to be the non-dominated solution to improve the selection pressure.In reproduction,a mutation strategy of k-bit crossover and hybrid mutation is used to generate high-quality offspring.On 23 test problems with up to 15-objective,we compared the proposed algorithm with five state-of-the-art algorithms.The experimental results verified that the proposed algorithm is competitive.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
When dealing with expensive multiobjective optimization problems,majority of existing surrogate-assisted evolutionary algorithms(SAEAs)generate solutions in decision space and screen candidate solutions mostly by usin...When dealing with expensive multiobjective optimization problems,majority of existing surrogate-assisted evolutionary algorithms(SAEAs)generate solutions in decision space and screen candidate solutions mostly by using designed surrogate models.The generated solutions exhibit excessive randomness,which tends to reduce the likelihood of generating good-quality solutions and cause a long evolution to the optima.To improve SAEAs greatly,this work proposes an evolutionary algorithm based on surrogate and inverse surrogate models by 1)Employing a surrogate model in lieu of expensive(true)function evaluations;and 2)Proposing and using an inverse surrogate model to generate new solutions.By using the same training data but with its inputs and outputs being reversed,the latter is simple to train.It is then used to generate new vectors in objective space,which are mapped into decision space to obtain their corresponding solutions.Using a particular example,this work shows its advantages over existing SAEAs.The results of comparing it with state-of-the-art algorithms on expensive optimization problems show that it is highly competitive in both solution performance and efficiency.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
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
From the perspective of the geographical distribution, considering production fare, supply chain information and quality rating of the manufacturing resource(MR), a manufacturing resource allocation(MRA) model conside...From the perspective of the geographical distribution, considering production fare, supply chain information and quality rating of the manufacturing resource(MR), a manufacturing resource allocation(MRA) model considering the geographical distribution in cloud manufacturing(CM) environment is built. The model includes two stages, preliminary selection stage and optimal selection stage. The membership function is used to select MRs from cloud resource pool(CRP) in the first stage, and then the candidate resource pool is built. In the optimal selection stage, a multi-objective optimization algorithm, particle swarm optimization(PSO) based on the method of relative entropy of fuzzy sets(REFS_PSO), is used to select optimal MRs from the candidate resource pool, and an optimal manufacturing resource supply chain is obtained at last. To verify the performance of REFS_PSO, NSGA-Ⅱ and PSO based on random weighting(RW_PSO) are selected as the comparison algorithms. They all are used to select optimal MRs at the second stage. The experimental results show solution obtained by REFS_PSO is the best. The model and the method proposed are appropriate for MRA in CM.展开更多
This paper develops a many-objective optimization model, which contains objectives representing the interests of the electricity and gas networks, as well as the distributed district heating and cooling units, to coor...This paper develops a many-objective optimization model, which contains objectives representing the interests of the electricity and gas networks, as well as the distributed district heating and cooling units, to coordinate the benefits of all parties participated in the integrated energy system(IES). In order to solve the many-objective optimization model efficiently, an improved objective reduction(IOR) approach is proposed, aiming at acquiring the smallest set of objectives. The IOR approach utilizes the Spearman’s rank correlation coefficient to measure the relationship between objectives based on the Pareto-optimal front captured by the multi-objective group search optimizer with adaptive covariance and Lévy flights algorithm, and adopts various strategies to reduce the number of objectives gradually. Simulation studies are conducted on an IES consisting of a modified IEEE 30-bus electricity network and a 15-node gas network. The results show that the many-objective optimization problem is transformed into a bi-objective formulation by the IOR. Furthermore,our approach improves the overall quality of dispatch solutions and alleviates the decision making burden.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
Large-scale cooling energy system has developed well in the past decade.However,its optimization is still a problem to be tackled due to the nonlinearity and large scale of existing systems.Reducing the scale of probl...Large-scale cooling energy system has developed well in the past decade.However,its optimization is still a problem to be tackled due to the nonlinearity and large scale of existing systems.Reducing the scale of problems without oversimplifying the actual system model is a big challenge nowadays.This paper proposes a dimension reduction-based many-objective optimization(DRMO)method to solve an accurate nonlinear model of a practical large-scale cooling energy system.In the first stage,many-objective and many-variable of the large system are pre-processed to reduce the overall scale of the optimization problem.The relationships between many objectives are analyzed to find a few representative objectives.Key control variables are extracted to reduce the dimension of variables and the number of equality constraints.In the second stage,the manyobjective group search optimization(GSO)method is used to solve the low-dimensional nonlinear model,and a Pareto-front is obtained.In the final stage,candidate solutions along the Paretofront are graded on many-objective levels of system operators.The candidate solution with the highest average utility value is selected as the best running mode.Simulations are carried out on a 619-node-614-branch cooling system,and results show the ability of the proposed method in solving large-scale system operation problems.展开更多
In this paper, a new preference multi-objective optimization algorithm called immune clone algorithm based on reference direction method （RD-ICA） is proposed for solving many-objective optimization problems. First, ...In this paper, a new preference multi-objective optimization algorithm called immune clone algorithm based on reference direction method （RD-ICA） is proposed for solving many-objective optimization problems. First, an intelligent recombination operator, which performs well on the functions comprising many parameters, is introduced into an immune clone algorithm so as to explore the potentially excellent gene segments of all individuals in the antibody pop- ulation. Second, a reference direction method, a very strict ranking based on the desire of decision makers （DMs）, is used to guide selection and clone of the active population. Then a light beam search （LBS） is borrowed to pick out a small set of individuals filling the external population. The proposed method has been extensively compared with other recently proposed evolutionary multi-objective optimization （EMO） approaches over DTLZ problems with from 4 to 100 objectives. Experimental results indicate RD-ICA can achieve competitive results.展开更多
The deployment of dynamic reactive power sourcecan effectively improve the voltage performance after a disturbance for a power system with increasing wind power penetration level and ubiquitous induction loads.To impr...The deployment of dynamic reactive power sourcecan effectively improve the voltage performance after a disturbance for a power system with increasing wind power penetration level and ubiquitous induction loads.To improve the voltage stability of the power system,this paper proposes an adaptive many-objective robust optimization model to deal with thedeployment issue of dynamic reactive power sources.Firstly,two metrics are adopted to assess the voltage stability of the system at two different stages,and one metric is proposed to assess the tie-line reactive power flow.Then,a robustness index isdeveloped to assess the sensitivity of a solution when subjectedto operational uncertainties,using the estimation of acceptablesensitivity region(ASR)and D-vine Copula.Five objectives areoptimized simultaneously:①total equipment investment;②adaptive short-term voltage stability evaluation;③tie-line power flow evaluation;④prioritized steady-state voltage stabilityevaluation;and⑤robustness evaluation.Finally,an anglebased adaptive many-objective evolutionary algorithm(MaOEA)is developed with two improvements designed for the application in a practical engineering problem:①adaptive mutationrate;and②elimination procedure without a requirement for athreshold value.The proposed model is verified on a modifiedNordic 74-bus system and a real-world power system.Numerical results demonstrate the effectiveness and efficiency of theproposed model.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 by the National Natural Science Foundation of ChinaNatural Science Foundation of Zhejiang Province (52077203,LY19E070003)the Fundamental Research Funds for the Provincial Universities of Zhejiang (2021YW06)。
文摘The two-archive 2 algorithm(Two_Arch2) is a manyobjective evolutionary algorithm for balancing the convergence,diversity,and complexity using diversity archive(DA) and convergence archive(CA).However,the individuals in DA are selected based on the traditional Pareto dominance which decreases the selection pressure in the high-dimensional problems.The traditional algorithm even cannot converge due to the weak selection pressure.Meanwhile,Two_Arch2 adopts DA as the output of the algorithm which is hard to maintain diversity and coverage of the final solutions synchronously and increase the complexity of the algorithm.To increase the evolutionary pressure of the algorithm and improve distribution and convergence of the final solutions,an ε-domination based Two_Arch2 algorithm(ε-Two_Arch2) for many-objective problems(MaOPs) is proposed in this paper.In ε-Two_Arch2,to decrease the computational complexity and speed up the convergence,a novel evolutionary framework with a fast update strategy is proposed;to increase the selection pressure,ε-domination is assigned to update the individuals in DA;to guarantee the uniform distribution of the solution,a boundary protection strategy based on I_(ε+) indicator is designated as two steps selection strategies to update individuals in CA.To evaluate the performance of the proposed algorithm,a series of benchmark functions with different numbers of objectives is solved.The results demonstrate that the proposed method is competitive with the state-of-the-art multi-objective evolutionary algorithms and the efficiency of the algorithm is significantly improved compared with Two_Arch2.
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 by National Natural Science Foundation of China(Grant No.61806138)the Central Government Guides Local Science and Technology Development Funds(Grant No.YDZJSX2021A038)+2 种基金Key RD Program of Shanxi Province(International Cooperation)under Grant No.201903D421048Outstanding Innovation Project for Graduate Students of Taiyuan University of Science and Technology(Project No.XCX211004)China University Industry-University-Research Collaborative Innovation Fund(Future Network Innovation Research and Application Project)(Grant 2021FNA04014).
文摘Due to the security and scalability features of hybrid cloud architecture,it can bettermeet the diverse requirements of users for cloud services.And a reasonable resource allocation solution is the key to adequately utilize the hybrid cloud.However,most previous studies have not comprehensively optimized the performance of hybrid cloud task scheduling,even ignoring the conflicts between its security privacy features and other requirements.Based on the above problems,a many-objective hybrid cloud task scheduling optimization model(HCTSO)is constructed combining risk rate,resource utilization,total cost,and task completion time.Meanwhile,an opposition-based learning knee point-driven many-objective evolutionary algorithm(OBL-KnEA)is proposed to improve the performance of model solving.The algorithm uses opposition-based learning to generate initial populations for faster convergence.Furthermore,a perturbation-based multipoint crossover operator and a dynamic range mutation operator are designed to extend the search range.By comparing the experiments with other excellent algorithms on HCTSO,OBL-KnEA achieves excellent results in terms of evaluation metrics,initial populations,and model optimization effects.
文摘For many real-world multiobjective optimization problems,the evaluations of the objective functions are computationally expensive.Such problems are usually called expensive multiobjective optimization problems(EMOPs).One type of feasible approaches for EMOPs is to introduce the computationally efficient surrogates for reducing the number of function evaluations.Inspired from ensemble learning,this paper proposes a multiobjective evolutionary algorithm with an ensemble classifier(MOEA-EC)for EMOPs.More specifically,multiple decision tree models are used as an ensemble classifier for the pre-selection,which is be more helpful for further reducing the function evaluations of the solutions than using single inaccurate model.The extensive experimental studies have been conducted to verify the efficiency of MOEA-EC by comparing it with several advanced multiobjective expensive optimization algorithms.The experimental results show that MOEA-EC outperforms the compared algorithms.
基金co-supported by the National Natural Science Foundation of China(Nos.52272360,52232014,52005288,52201327)Beijing Natural Science Foundation,China(No.3222019)+1 种基金Beijing Institute of Technology Research Fund Program for Young Scholars,China(No.XSQD-202101006)BIT Research and Innovation Promoting Project(No.2022YCXZ017).
文摘To address the challenges of high-dimensional constrained optimization problems with expensive simulation models,a Surrogate-Assisted Differential Evolution using Manifold Learning-based Sampling(SADE-MLS)is proposed.In SADE-MLS,differential evolution operators are executed to generate numerous high-dimensional candidate points.To alleviate the curse of dimensionality,a Manifold Learning-based Sampling(MLS)mechanism is developed to explore the high-dimensional design space effectively.In MLS,the intrinsic dimensionality of the candidate points is determined by a maximum likelihood estimator.Then,the candidate points are mapped into a low-dimensional space using the dimensionality reduction technique,which can avoid significant information loss during dimensionality reduction.Thus,Kriging surrogates are constructed in the low-dimensional space to predict the responses of the mapped candidate points.The candidate points with high constrained expected improvement values are selected for global exploration.Moreover,the local search process assisted by radial basis function and differential evolution is performed to exploit the design space efficiently.Several numerical benchmarks are tested to compare SADE-MLS with other algorithms.Finally,SADE-MLS is successfully applied to a solid rocket motor multidisciplinary optimization problem and a re-entry vehicle aerodynamic optimization problem,with the total impulse and lift to drag ratio being increased by 32.7%and 35.5%,respec-tively.The optimization results demonstrate the practicality and effectiveness of the proposed method in real engineering practices.
基金supported by the Shenzhen Innovation Technology Program(JCYJ20160422112909302)
文摘Many-objective optimization problems take challenges to multi-objective evolutionary algorithms.A number of nondominated solutions in population cause a difficult selection towards the Pareto front.To tackle this issue,a series of indicatorbased multi-objective evolutionary algorithms(MOEAs)have been proposed to guide the evolution progress and shown promising performance.This paper proposes an indicator-based manyobjective evolutionary algorithm calledε-indicator-based shuffled frog leaping algorithm(ε-MaOSFLA),which adopts the shuffled frog leaping algorithm as an evolutionary strategy and a simple and effectiveε-indicator as a fitness assignment scheme to press the population towards the Pareto front.Compared with four stateof-the-art MOEAs on several standard test problems with up to 50 objectives,the experimental results show thatε-MaOSFLA outperforms the competitors.
基金supported by the National Natural Science Foundation of China(Grant No.61976101)the University Natural Science Research Project of Anhui Province(Grant No.2023AH040056)+4 种基金the Natural Science Research Project of Anhui Province(Graduate Research Project,Grant No.YJS20210463)the Funding Plan for Scientic Research Activities of Academic and Technical Leaders and Reserve Candidates in Anhui Province(Grant No.2021H264)the Top Talent Project of Disciplines(Majors)in Colleges and Universities in Anhui Province(Grant No.gxbjZD2022021)the University Synergy Innovation Program of Anhui Province,China(GXXT-2022-033)supported by the Innovation Fund for Postgraduates of Huaibei Normal University(Grant Nos.cx2022041,yx2021023,CX2023043).
文摘It is still a huge challenge for traditional Pareto-dominatedmany-objective optimization algorithms to solve manyobjective optimization problems because these algorithms hardly maintain the balance between convergence and diversity and can only find a group of solutions focused on a small area on the Pareto front,resulting in poor performance of those algorithms.For this reason,we propose a reference vector-assisted algorithmwith an adaptive niche dominance relation,for short MaOEA-AR.The new dominance relation forms a niche based on the angle between candidate solutions.By comparing these solutions,the solutionwith the best convergence is found to be the non-dominated solution to improve the selection pressure.In reproduction,a mutation strategy of k-bit crossover and hybrid mutation is used to generate high-quality offspring.On 23 test problems with up to 15-objective,we compared the proposed algorithm with five state-of-the-art algorithms.The experimental results verified that the proposed algorithm is competitive.
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.
基金supported in part by the National Natural Science Foundation of China(51775385)the Natural Science Foundation of Shanghai(23ZR1466000)+2 种基金the Shanghai Industrial Collaborative Science and Technology Innovation Project(2021-cyxt2-kj10)the Innovation Program of Shanghai Municipal Education Commission(202101070007E00098)Fundo para o Desenvolvimento das Ciencias e da Tecnologia(FDCT)(0147/2024/AFJ).
文摘When dealing with expensive multiobjective optimization problems,majority of existing surrogate-assisted evolutionary algorithms(SAEAs)generate solutions in decision space and screen candidate solutions mostly by using designed surrogate models.The generated solutions exhibit excessive randomness,which tends to reduce the likelihood of generating good-quality solutions and cause a long evolution to the optima.To improve SAEAs greatly,this work proposes an evolutionary algorithm based on surrogate and inverse surrogate models by 1)Employing a surrogate model in lieu of expensive(true)function evaluations;and 2)Proposing and using an inverse surrogate model to generate new solutions.By using the same training data but with its inputs and outputs being reversed,the latter is simple to train.It is then used to generate new vectors in objective space,which are mapped into decision space to obtain their corresponding solutions.Using a particular example,this work shows its advantages over existing SAEAs.The results of comparing it with state-of-the-art algorithms on expensive optimization problems show that it is highly competitive in both solution performance and efficiency.
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Sponsored by the Program of Department of Science and Technology of Fujian Province(Grant No.2016H0015)the Collaborative Innovation Center of High-End Equipment Manufacturing in Fujian(Grant No.2015A003)
文摘From the perspective of the geographical distribution, considering production fare, supply chain information and quality rating of the manufacturing resource(MR), a manufacturing resource allocation(MRA) model considering the geographical distribution in cloud manufacturing(CM) environment is built. The model includes two stages, preliminary selection stage and optimal selection stage. The membership function is used to select MRs from cloud resource pool(CRP) in the first stage, and then the candidate resource pool is built. In the optimal selection stage, a multi-objective optimization algorithm, particle swarm optimization(PSO) based on the method of relative entropy of fuzzy sets(REFS_PSO), is used to select optimal MRs from the candidate resource pool, and an optimal manufacturing resource supply chain is obtained at last. To verify the performance of REFS_PSO, NSGA-Ⅱ and PSO based on random weighting(RW_PSO) are selected as the comparison algorithms. They all are used to select optimal MRs at the second stage. The experimental results show solution obtained by REFS_PSO is the best. The model and the method proposed are appropriate for MRA in CM.
基金supported by the State Key Program of National Natural Science Foundation of China(No.51437006)Guangdong Innovative Research Team Program(No.201001N0104744201)
文摘This paper develops a many-objective optimization model, which contains objectives representing the interests of the electricity and gas networks, as well as the distributed district heating and cooling units, to coordinate the benefits of all parties participated in the integrated energy system(IES). In order to solve the many-objective optimization model efficiently, an improved objective reduction(IOR) approach is proposed, aiming at acquiring the smallest set of objectives. The IOR approach utilizes the Spearman’s rank correlation coefficient to measure the relationship between objectives based on the Pareto-optimal front captured by the multi-objective group search optimizer with adaptive covariance and Lévy flights algorithm, and adopts various strategies to reduce the number of objectives gradually. Simulation studies are conducted on an IES consisting of a modified IEEE 30-bus electricity network and a 15-node gas network. The results show that the many-objective optimization problem is transformed into a bi-objective formulation by the IOR. Furthermore,our approach improves the overall quality of dispatch solutions and alleviates the decision making burden.
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supported by the Key-Area Research and Development Program of Guangdong Province(2020B010166004)Natural Science Foundation of China(52007066).
文摘Large-scale cooling energy system has developed well in the past decade.However,its optimization is still a problem to be tackled due to the nonlinearity and large scale of existing systems.Reducing the scale of problems without oversimplifying the actual system model is a big challenge nowadays.This paper proposes a dimension reduction-based many-objective optimization(DRMO)method to solve an accurate nonlinear model of a practical large-scale cooling energy system.In the first stage,many-objective and many-variable of the large system are pre-processed to reduce the overall scale of the optimization problem.The relationships between many objectives are analyzed to find a few representative objectives.Key control variables are extracted to reduce the dimension of variables and the number of equality constraints.In the second stage,the manyobjective group search optimization(GSO)method is used to solve the low-dimensional nonlinear model,and a Pareto-front is obtained.In the final stage,candidate solutions along the Paretofront are graded on many-objective levels of system operators.The candidate solution with the highest average utility value is selected as the best running mode.Simulations are carried out on a 619-node-614-branch cooling system,and results show the ability of the proposed method in solving large-scale system operation problems.
基金The authors would like to thank the editor and the reviewers for helpful comments that greatly improved the paper. This work was supported by the National Natural Science Foundation of China （Grant Nos. 613731 l 1, 61272279, 61003199 and 61203303） the Fundamental Re- search Funds for the Central Universities （K50511020014, K5051302084, K50510020011, K5051302049 and K5051302023）+1 种基金 the Fund for Foreign Scholars in University Research and Teaching Programs （the 111 Project） （B07048） and the Program for New Century Excellent Talents in University （NCET- 12-0920）.
文摘In this paper, a new preference multi-objective optimization algorithm called immune clone algorithm based on reference direction method （RD-ICA） is proposed for solving many-objective optimization problems. First, an intelligent recombination operator, which performs well on the functions comprising many parameters, is introduced into an immune clone algorithm so as to explore the potentially excellent gene segments of all individuals in the antibody pop- ulation. Second, a reference direction method, a very strict ranking based on the desire of decision makers （DMs）, is used to guide selection and clone of the active population. Then a light beam search （LBS） is borrowed to pick out a small set of individuals filling the external population. The proposed method has been extensively compared with other recently proposed evolutionary multi-objective optimization （EMO） approaches over DTLZ problems with from 4 to 100 objectives. Experimental results indicate RD-ICA can achieve competitive results.
基金supported by the International Postdoctoral Exchange Fellowship Program (Talent-Introduction Program)(No.YJ20210337)the Fundamental Research Funds for the Central Universities (No.2022CDJXY-007)。
文摘The deployment of dynamic reactive power sourcecan effectively improve the voltage performance after a disturbance for a power system with increasing wind power penetration level and ubiquitous induction loads.To improve the voltage stability of the power system,this paper proposes an adaptive many-objective robust optimization model to deal with thedeployment issue of dynamic reactive power sources.Firstly,two metrics are adopted to assess the voltage stability of the system at two different stages,and one metric is proposed to assess the tie-line reactive power flow.Then,a robustness index isdeveloped to assess the sensitivity of a solution when subjectedto operational uncertainties,using the estimation of acceptablesensitivity region(ASR)and D-vine Copula.Five objectives areoptimized simultaneously:①total equipment investment;②adaptive short-term voltage stability evaluation;③tie-line power flow evaluation;④prioritized steady-state voltage stabilityevaluation;and⑤robustness evaluation.Finally,an anglebased adaptive many-objective evolutionary algorithm(MaOEA)is developed with two improvements designed for the application in a practical engineering problem:①adaptive mutationrate;and②elimination procedure without a requirement for athreshold value.The proposed model is verified on a modifiedNordic 74-bus system and a real-world power system.Numerical results demonstrate the effectiveness and efficiency of theproposed model.
