Sparse large-scale multi-objective optimization problems(SLMOPs)are common in science and engineering.However,the large-scale problem represents the high dimensionality of the decision space,requiring algorithms to tr...Sparse large-scale multi-objective optimization problems(SLMOPs)are common in science and engineering.However,the large-scale problem represents the high dimensionality of the decision space,requiring algorithms to traverse vast expanse with limited computational resources.Furthermore,in the context of sparse,most variables in Pareto optimal solutions are zero,making it difficult for algorithms to identify non-zero variables efficiently.This paper is dedicated to addressing the challenges posed by SLMOPs.To start,we introduce innovative objective functions customized to mine maximum and minimum candidate sets.This substantial enhancement dramatically improves the efficacy of frequent pattern mining.In this way,selecting candidate sets is no longer based on the quantity of nonzero variables they contain but on a higher proportion of nonzero variables within specific dimensions.Additionally,we unveil a novel approach to association rule mining,which delves into the intricate relationships between non-zero variables.This novel methodology aids in identifying sparse distributions that can potentially expedite reductions in the objective function value.We extensively tested our algorithm across eight benchmark problems and four real-world SLMOPs.The results demonstrate that our approach achieves competitive solutions across various challenges.展开更多
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
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
Evolutionary algorithms have been shown to be very successful in solving multi-objective optimization problems(MOPs).However,their performance often deteriorates when solving MOPs with irregular Pareto fronts.To remed...Evolutionary algorithms have been shown to be very successful in solving multi-objective optimization problems(MOPs).However,their performance often deteriorates when solving MOPs with irregular Pareto fronts.To remedy this issue,a large body of research has been performed in recent years and many new algorithms have been proposed.This paper provides a comprehensive survey of the research on MOPs with irregular Pareto fronts.We start with a brief introduction to the basic concepts,followed by a summary of the benchmark test problems with irregular problems,an analysis of the causes of the irregularity,and real-world optimization problems with irregular Pareto fronts.Then,a taxonomy of the existing methodologies for handling irregular problems is given and representative algorithms are reviewed with a discussion of their strengths and weaknesses.Finally,open challenges are pointed out and a few promising future directions are suggested.展开更多
To solve single-objective constrained optimization problems,a new population-based evolutionary algorithm with elite strategy(PEAES) is proposed with the concept of single and multi-objective optimization.Constrained ...To solve single-objective constrained optimization problems,a new population-based evolutionary algorithm with elite strategy(PEAES) is proposed with the concept of single and multi-objective optimization.Constrained functions are combined to be an objective function.During the evolutionary process,the current optimal solution is found and treated as the reference point to divide the population into three sub-populations:one feasible and two infeasible ones.Different evolutionary operations of single or multi-objective optimization are respectively performed in each sub-population with elite strategy.Thirteen famous benchmark functions are selected to evaluate the performance of PEAES in comparison of other three optimization methods.The results show the proposed method is valid in efficiency,precision and probability for solving single-objective constrained optimization problems.展开更多
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 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
A new algorithm based on genetic algorithm(GA) is developed for solving function optimization problems with inequality constraints. This algorithm has been used to a series of standard test problems and exhibited good...A new algorithm based on genetic algorithm(GA) is developed for solving function optimization problems with inequality constraints. This algorithm has been used to a series of standard test problems and exhibited good performance. The computation results show that its generality, precision, robustness, simplicity and performance are all satisfactory.展开更多
Many image inverse problems are ill-posed for no unique solutions. Most of them have incommensurable or mixed-type objectives. In this study, a multi-objective optimization framework is introduced to model such ill-po...Many image inverse problems are ill-posed for no unique solutions. Most of them have incommensurable or mixed-type objectives. In this study, a multi-objective optimization framework is introduced to model such ill-posed inverse problems. The conflicting objectives are designed according to the properties of ill-posedness and certain techniques. Multi-objective evolutionary algorithms have capability to optimize multiple objectives simultaneously and obtain a set of trade-off solutions. For that reason, we use multi-objective evolutionary algorithms to keep the trade-off between these objectives for image ill-posed problems. Two case studies of sparse reconstruction and change detection are imple- mented. In the case study of sparse reconstruction, the measurement error term and the sparsity term are optimized by multi-objective evolutionary algorithms, which aims at balancing the trade-off between enforcing sparsity and reducing measurement error. In the case study of image change detection, two conflicting objectives are constructed to keep the trade-off between robustness to noise and preserving the image details. Experimental results of the two case studies confirm the multi-objective optimization framework for ill-posed inverse problems in image processing is effective.展开更多
In recent years, a large number of approaches to constrained multi-objective optimization problems(CMOPs) have been proposed, focusing on developing tweaked strategies and techniques for handling constraints. However,...In recent years, a large number of approaches to constrained multi-objective optimization problems(CMOPs) have been proposed, focusing on developing tweaked strategies and techniques for handling constraints. However, an overly finetuned strategy or technique might overfit some problem types,resulting in a lack of versatility. In this article, we propose a generic search strategy that performs an even search in a promising region. The promising region, determined by obtained feasible non-dominated solutions, possesses two general properties.First, the constrained Pareto front(CPF) is included in the promising region. Second, as the number of feasible solutions increases or the convergence performance(i.e., approximation to the CPF) of these solutions improves, the promising region shrinks. Then we develop a new strategy named even search,which utilizes the non-dominated solutions to accelerate convergence and escape from local optima, and the feasible solutions under a constraint relaxation condition to exploit and detect feasible regions. Finally, a diversity measure is adopted to make sure that the individuals in the population evenly cover the valuable areas in the promising region. Experimental results on 45 instances from four benchmark test suites and 14 real-world CMOPs have demonstrated that searching evenly in the promising region can achieve competitive performance and excellent versatility compared to 11 most state-of-the-art methods tailored for CMOPs.展开更多
Traditional large-scale multi-objective optimization algorithms(LSMOEAs)encounter difficulties when dealing with sparse large-scale multi-objective optimization problems(SLM-OPs)where most decision variables are zero....Traditional large-scale multi-objective optimization algorithms(LSMOEAs)encounter difficulties when dealing with sparse large-scale multi-objective optimization problems(SLM-OPs)where most decision variables are zero.As a result,many algorithms use a two-layer encoding approach to optimize binary variable Mask and real variable Dec separately.Nevertheless,existing optimizers often focus on locating non-zero variable posi-tions to optimize the binary variables Mask.However,approxi-mating the sparse distribution of real Pareto optimal solutions does not necessarily mean that the objective function is optimized.In data mining,it is common to mine frequent itemsets appear-ing together in a dataset to reveal the correlation between data.Inspired by this,we propose a novel two-layer encoding learning swarm optimizer based on frequent itemsets(TELSO)to address these SLMOPs.TELSO mined the frequent terms of multiple particles with better target values to find mask combinations that can obtain better objective values for fast convergence.Experi-mental results on five real-world problems and eight benchmark sets demonstrate that TELSO outperforms existing state-of-the-art sparse large-scale multi-objective evolutionary algorithms(SLMOEAs)in terms of performance and convergence speed.展开更多
The material distribution routing problem in the manufacturing system is a complex combinatorial optimization problem and its main task is to deliver materials to the working stations with low cost and high efficiency...The material distribution routing problem in the manufacturing system is a complex combinatorial optimization problem and its main task is to deliver materials to the working stations with low cost and high efficiency. A multi-objective model was presented for the material distribution routing problem in mixed manufacturing systems, and it was solved by a hybrid multi-objective evolutionary algorithm (HMOEA). The characteristics of the HMOEA are as follows: 1) A route pool is employed to preserve the best routes for the population initiation; 2) A specialized best?worst route crossover (BWRC) mode is designed to perform the crossover operators for selecting the best route from Chromosomes 1 to exchange with the worst one in Chromosomes 2, so that the better genes are inherited to the offspring; 3) A route swap mode is used to perform the mutation for improving the convergence speed and preserving the better gene; 4) Local heuristics search methods are applied in this algorithm. Computational study of a practical case shows that the proposed algorithm can decrease the total travel distance by 51.66%, enhance the average vehicle load rate by 37.85%, cut down 15 routes and reduce a deliver vehicle. The convergence speed of HMOEA is faster than that of famous NSGA-II.展开更多
Multi-objective optimal evolutionary algorithms (MOEAs) are a kind of new effective algorithms to solve Multi-objective optimal problem (MOP). Because ranking, a method which is used by most MOEAs to solve MOP, has so...Multi-objective optimal evolutionary algorithms (MOEAs) are a kind of new effective algorithms to solve Multi-objective optimal problem (MOP). Because ranking, a method which is used by most MOEAs to solve MOP, has some shortcoming s, in this paper, we proposed a new method using tree structure to express the relationship of solutions. Experiments prove that the method can reach the Pare-to front, retain the diversity of the population, and use less time.展开更多
Evolutionary algorithm is an effective strategy for solving many-objective optimization problems.At present,most evolutionary many-objective algorithms are designed for solving many-objective optimization problems whe...Evolutionary algorithm is an effective strategy for solving many-objective optimization problems.At present,most evolutionary many-objective algorithms are designed for solving many-objective optimization problems where the objectives conflict with each other.In some cases,however,the objectives are not always in conflict.It consists of multiple independent objective subsets and the relationship between objectives is unknown in advance.The classical evolutionary many-objective algorithms may not be able to effectively solve such problems.Accordingly,we propose an objective set decomposition strategy based on the partial set covering model.It decomposes the objectives into a collection of objective subsets to preserve the nondominance relationship as much as possible.An optimization subproblem is defined on each objective subset.A coevolutionary algorithm is presented to optimize all subproblems simultaneously,in which a nondominance ranking is presented to interact information among these sub-populations.The proposed algorithm is compared with five popular many-objective evolutionary algorithms and four objective set decomposition based evolutionary algorithms on a series of test problems.Numerical experiments demonstrate that the proposed algorithm can achieve promising results for the many-objective optimization problems with independent and harmonious objectives.展开更多
The allocation of heterogeneous battlefield resources is crucial in Command and Control(C2).Balancing multiple competing objectives under complex constraints so as to provide decisionmakers with diverse feasible candi...The allocation of heterogeneous battlefield resources is crucial in Command and Control(C2).Balancing multiple competing objectives under complex constraints so as to provide decisionmakers with diverse feasible candidate decision schemes remains an urgent challenge.Based on these requirements,a constrained multi-objective multi-stage weapon-target assignment(CMOMWTA)model is established in this paper.To solve this problem,three constraint-feature-guided multi-objective evolutionary algorithms(CFG-MOEAs)are proposed under three typical multi-objective evolutionary frameworks(i.e.,NSGA-Ⅱ,NSGA-Ⅲ,and MOEA/D)to obtain various high-quality candidate decision schemes.Firstly,a constraint-feature-guided reproduction strategy incorporating crossover,mutation,and repair is developed to handle complex constraints.It extracts common row and column features from different linear constraints to generate the feasible offspring population.Then,a variable-length integer encoding method is adopted to concisely denote the decision schemes.Moreover,a hybrid initialization method incorporating both heuristic methods and random sampling is designed to better guide the population.Systemic experiments are conducted on three CFG-MOEAs to verify their effectiveness.The superior algorithm CFG-NSGA-Ⅱamong three CFG-MOEAs is compared with two state-of-the-art CMOMWTA algorithms,and extensive experimental results demonstrate the effectiveness and superiority of CFG-NSGA-Ⅱ.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
In the previous papers,Quantum-inspired multi-objective evolutionary algorithm(QMEA) was proved to be better than conventional genetic algorithms for multi-objective optimization problem.To improve the quality of the ...In the previous papers,Quantum-inspired multi-objective evolutionary algorithm(QMEA) was proved to be better than conventional genetic algorithms for multi-objective optimization problem.To improve the quality of the non-dominated set as well as the diversity of population in multi-objective problems,in this paper,a Novel Cloud -based quantum -inspired multi-objective evolutionary Algorithm(CQMEA) is proposed.CQMEA is proposed by employing the concept and principles of Cloud theory.The algorithm utilizes the random orientation and stability of the cloud model,uses a self-adaptive mechanism with cloud model of Quantum gates updating strategy to implement global search efficient.By using the self-adaptive mechanism and the better solution which is determined by the membership function uncertainly,Compared with several well-known algorithms such as NSGA-Ⅱ,QMEA.Experimental results show that(CQMEA) is more effective than QMEA and NSGA -Ⅱ.展开更多
Hybrid metaheuristic algorithms play a prominent role in improving algorithms'searchability by combining each algorithm's advantages and minimizing any substantial shortcomings.The Quantum-based Avian Navigati...Hybrid metaheuristic algorithms play a prominent role in improving algorithms'searchability by combining each algorithm's advantages and minimizing any substantial shortcomings.The Quantum-based Avian Navigation Optimizer Algorithm(QANA)is a recent metaheuristic algorithm inspired by the navigation behavior of migratory birds.Different experimental results show that QANA is a competitive and applicable algorithm in different optimization fields.However,it suffers from shortcomings such as low solution quality and premature convergence when tackling some complex problems.Therefore,instead of proposing a new algorithm to solve these weaknesses,we use the advantages of the bonobo optimizer to improve global search capability and mitigate premature convergence of the original QANA.The effectiveness of the proposed Hybrid Quantum-based Avian Navigation Optimizer Algorithm(HQANA)is assessed on 29 test functions of the CEC 2018 benchmark test suite with different dimensions,30,50,and 100.The results are then statistically investigated by the Friedman test and compared with the results of eight well-known optimization algorithms,including PSO,KH,GWO,WOA,CSA,HOA,BO,and QANA.Ultimately,five constrained engineering optimization problems from the latest test suite,CEC 2020 are used to assess the applicability of HQANA to solve complex real-world engineering optimization problems.The experimental and statistical findings prove that the proposed HQANA algorithm is superior to the comparative algorithms.展开更多
基金support by the Open Project of Xiangjiang Laboratory(22XJ02003)the University Fundamental Research Fund(23-ZZCX-JDZ-28,ZK21-07)+5 种基金the National Science Fund for Outstanding Young Scholars(62122093)the National Natural Science Foundation of China(72071205)the Hunan Graduate Research Innovation Project(CX20230074)the Hunan Natural Science Foundation Regional Joint Project(2023JJ50490)the Science and Technology Project for Young and Middle-aged Talents of Hunan(2023TJZ03)the Science and Technology Innovation Program of Humnan Province(2023RC1002).
文摘Sparse large-scale multi-objective optimization problems(SLMOPs)are common in science and engineering.However,the large-scale problem represents the high dimensionality of the decision space,requiring algorithms to traverse vast expanse with limited computational resources.Furthermore,in the context of sparse,most variables in Pareto optimal solutions are zero,making it difficult for algorithms to identify non-zero variables efficiently.This paper is dedicated to addressing the challenges posed by SLMOPs.To start,we introduce innovative objective functions customized to mine maximum and minimum candidate sets.This substantial enhancement dramatically improves the efficacy of frequent pattern mining.In this way,selecting candidate sets is no longer based on the quantity of nonzero variables they contain but on a higher proportion of nonzero variables within specific dimensions.Additionally,we unveil a novel approach to association rule mining,which delves into the intricate relationships between non-zero variables.This novel methodology aids in identifying sparse distributions that can potentially expedite reductions in the objective function value.We extensively tested our algorithm across eight benchmark problems and four real-world SLMOPs.The results demonstrate that our approach achieves competitive solutions across various challenges.
基金supported by the 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 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 in part by the National Natural Science Foundation of China(61806051,61903078)Natural Science Foundation of Shanghai(20ZR1400400)+2 种基金Agricultural Project of the Shanghai Committee of Science and Technology(16391902800)the Fundamental Research Funds for the Central Universities(2232020D-48)the Project of the Humanities and Social Sciences on Young Fund of the Ministry of Education in China(Research on swarm intelligence collaborative robust optimization scheduling for high-dimensional dynamic decisionmaking system(20YJCZH052))。
文摘Evolutionary algorithms have been shown to be very successful in solving multi-objective optimization problems(MOPs).However,their performance often deteriorates when solving MOPs with irregular Pareto fronts.To remedy this issue,a large body of research has been performed in recent years and many new algorithms have been proposed.This paper provides a comprehensive survey of the research on MOPs with irregular Pareto fronts.We start with a brief introduction to the basic concepts,followed by a summary of the benchmark test problems with irregular problems,an analysis of the causes of the irregularity,and real-world optimization problems with irregular Pareto fronts.Then,a taxonomy of the existing methodologies for handling irregular problems is given and representative algorithms are reviewed with a discussion of their strengths and weaknesses.Finally,open challenges are pointed out and a few promising future directions are suggested.
文摘To solve single-objective constrained optimization problems,a new population-based evolutionary algorithm with elite strategy(PEAES) is proposed with the concept of single and multi-objective optimization.Constrained functions are combined to be an objective function.During the evolutionary process,the current optimal solution is found and treated as the reference point to divide the population into three sub-populations:one feasible and two infeasible ones.Different evolutionary operations of single or multi-objective optimization are respectively performed in each sub-population with elite strategy.Thirteen famous benchmark functions are selected to evaluate the performance of PEAES in comparison of other three optimization methods.The results show the proposed method is valid in efficiency,precision and probability for solving single-objective constrained optimization problems.
基金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.
文摘A new algorithm based on genetic algorithm(GA) is developed for solving function optimization problems with inequality constraints. This algorithm has been used to a series of standard test problems and exhibited good performance. The computation results show that its generality, precision, robustness, simplicity and performance are all satisfactory.
基金This work was supported by the National Natural Science Foundation of China （Grant no. 61273317 and 61422209）, the National Top Youth Talents Program of China, the Specialized Research Fund for the Doctoral Program of Higher Education （Grant no. 20130203110011） and the Fundamental Research Fund for the Central Universities （Grant no. K5051202053）.
文摘Many image inverse problems are ill-posed for no unique solutions. Most of them have incommensurable or mixed-type objectives. In this study, a multi-objective optimization framework is introduced to model such ill-posed inverse problems. The conflicting objectives are designed according to the properties of ill-posedness and certain techniques. Multi-objective evolutionary algorithms have capability to optimize multiple objectives simultaneously and obtain a set of trade-off solutions. For that reason, we use multi-objective evolutionary algorithms to keep the trade-off between these objectives for image ill-posed problems. Two case studies of sparse reconstruction and change detection are imple- mented. In the case study of sparse reconstruction, the measurement error term and the sparsity term are optimized by multi-objective evolutionary algorithms, which aims at balancing the trade-off between enforcing sparsity and reducing measurement error. In the case study of image change detection, two conflicting objectives are constructed to keep the trade-off between robustness to noise and preserving the image details. Experimental results of the two case studies confirm the multi-objective optimization framework for ill-posed inverse problems in image processing is effective.
基金partly supported by the National Natural Science Foundation of China(62076225)。
文摘In recent years, a large number of approaches to constrained multi-objective optimization problems(CMOPs) have been proposed, focusing on developing tweaked strategies and techniques for handling constraints. However, an overly finetuned strategy or technique might overfit some problem types,resulting in a lack of versatility. In this article, we propose a generic search strategy that performs an even search in a promising region. The promising region, determined by obtained feasible non-dominated solutions, possesses two general properties.First, the constrained Pareto front(CPF) is included in the promising region. Second, as the number of feasible solutions increases or the convergence performance(i.e., approximation to the CPF) of these solutions improves, the promising region shrinks. Then we develop a new strategy named even search,which utilizes the non-dominated solutions to accelerate convergence and escape from local optima, and the feasible solutions under a constraint relaxation condition to exploit and detect feasible regions. Finally, a diversity measure is adopted to make sure that the individuals in the population evenly cover the valuable areas in the promising region. Experimental results on 45 instances from four benchmark test suites and 14 real-world CMOPs have demonstrated that searching evenly in the promising region can achieve competitive performance and excellent versatility compared to 11 most state-of-the-art methods tailored for CMOPs.
基金supported by the Scientific Research Project of Xiang Jiang Lab(22XJ02003)the University Fundamental Research Fund(23-ZZCX-JDZ-28)+5 种基金the National Science Fund for Outstanding Young Scholars(62122093)the National Natural Science Foundation of China(72071205)the Hunan Graduate Research Innovation Project(ZC23112101-10)the Hunan Natural Science Foundation Regional Joint Project(2023JJ50490)the Science and Technology Project for Young and Middle-aged Talents of Hunan(2023TJ-Z03)the Science and Technology Innovation Program of Humnan Province(2023RC1002)。
文摘Traditional large-scale multi-objective optimization algorithms(LSMOEAs)encounter difficulties when dealing with sparse large-scale multi-objective optimization problems(SLM-OPs)where most decision variables are zero.As a result,many algorithms use a two-layer encoding approach to optimize binary variable Mask and real variable Dec separately.Nevertheless,existing optimizers often focus on locating non-zero variable posi-tions to optimize the binary variables Mask.However,approxi-mating the sparse distribution of real Pareto optimal solutions does not necessarily mean that the objective function is optimized.In data mining,it is common to mine frequent itemsets appear-ing together in a dataset to reveal the correlation between data.Inspired by this,we propose a novel two-layer encoding learning swarm optimizer based on frequent itemsets(TELSO)to address these SLMOPs.TELSO mined the frequent terms of multiple particles with better target values to find mask combinations that can obtain better objective values for fast convergence.Experi-mental results on five real-world problems and eight benchmark sets demonstrate that TELSO outperforms existing state-of-the-art sparse large-scale multi-objective evolutionary algorithms(SLMOEAs)in terms of performance and convergence speed.
基金Project(50775089)supported by the National Natural Science Foundation of ChinaProject(2007AA04Z190,2009AA043301)supported by the National High Technology Research and Development Program of ChinaProject(2005CB724100)supported by the National Basic Research Program of China
文摘The material distribution routing problem in the manufacturing system is a complex combinatorial optimization problem and its main task is to deliver materials to the working stations with low cost and high efficiency. A multi-objective model was presented for the material distribution routing problem in mixed manufacturing systems, and it was solved by a hybrid multi-objective evolutionary algorithm (HMOEA). The characteristics of the HMOEA are as follows: 1) A route pool is employed to preserve the best routes for the population initiation; 2) A specialized best?worst route crossover (BWRC) mode is designed to perform the crossover operators for selecting the best route from Chromosomes 1 to exchange with the worst one in Chromosomes 2, so that the better genes are inherited to the offspring; 3) A route swap mode is used to perform the mutation for improving the convergence speed and preserving the better gene; 4) Local heuristics search methods are applied in this algorithm. Computational study of a practical case shows that the proposed algorithm can decrease the total travel distance by 51.66%, enhance the average vehicle load rate by 37.85%, cut down 15 routes and reduce a deliver vehicle. The convergence speed of HMOEA is faster than that of famous NSGA-II.
基金Supported by the National Natural Science Foundation of China(60073043,70071042,60133010)
文摘Multi-objective optimal evolutionary algorithms (MOEAs) are a kind of new effective algorithms to solve Multi-objective optimal problem (MOP). Because ranking, a method which is used by most MOEAs to solve MOP, has some shortcoming s, in this paper, we proposed a new method using tree structure to express the relationship of solutions. Experiments prove that the method can reach the Pare-to front, retain the diversity of the population, and use less time.
基金supported in part by the National Natural Science Foundation of China(No.62172110)the Natural Science Foundation of Guangdong Province(Nos.2021A1515011839 and 2022A1515010130)the Programme of Science and Technology of Guangdong Province(No.2021A0505110004).
文摘Evolutionary algorithm is an effective strategy for solving many-objective optimization problems.At present,most evolutionary many-objective algorithms are designed for solving many-objective optimization problems where the objectives conflict with each other.In some cases,however,the objectives are not always in conflict.It consists of multiple independent objective subsets and the relationship between objectives is unknown in advance.The classical evolutionary many-objective algorithms may not be able to effectively solve such problems.Accordingly,we propose an objective set decomposition strategy based on the partial set covering model.It decomposes the objectives into a collection of objective subsets to preserve the nondominance relationship as much as possible.An optimization subproblem is defined on each objective subset.A coevolutionary algorithm is presented to optimize all subproblems simultaneously,in which a nondominance ranking is presented to interact information among these sub-populations.The proposed algorithm is compared with five popular many-objective evolutionary algorithms and four objective set decomposition based evolutionary algorithms on a series of test problems.Numerical experiments demonstrate that the proposed algorithm can achieve promising results for the many-objective optimization problems with independent and harmonious objectives.
基金supported by the National Science Fund of China under Grant Nos.62425304 and 62025301the Basic Science Center Programs of NSFC under Grant No.62088101+1 种基金Shanghai Municipal Science and Technology Major Project under Grant No.2021SHZDZX0100Shanghai Municipal Commission of Science and Technology Project under Grant No.19511132101。
文摘The allocation of heterogeneous battlefield resources is crucial in Command and Control(C2).Balancing multiple competing objectives under complex constraints so as to provide decisionmakers with diverse feasible candidate decision schemes remains an urgent challenge.Based on these requirements,a constrained multi-objective multi-stage weapon-target assignment(CMOMWTA)model is established in this paper.To solve this problem,three constraint-feature-guided multi-objective evolutionary algorithms(CFG-MOEAs)are proposed under three typical multi-objective evolutionary frameworks(i.e.,NSGA-Ⅱ,NSGA-Ⅲ,and MOEA/D)to obtain various high-quality candidate decision schemes.Firstly,a constraint-feature-guided reproduction strategy incorporating crossover,mutation,and repair is developed to handle complex constraints.It extracts common row and column features from different linear constraints to generate the feasible offspring population.Then,a variable-length integer encoding method is adopted to concisely denote the decision schemes.Moreover,a hybrid initialization method incorporating both heuristic methods and random sampling is designed to better guide the population.Systemic experiments are conducted on three CFG-MOEAs to verify their effectiveness.The superior algorithm CFG-NSGA-Ⅱamong three CFG-MOEAs is compared with two state-of-the-art CMOMWTA algorithms,and extensive experimental results demonstrate the effectiveness and superiority of CFG-NSGA-Ⅱ.
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 the National Natural Science Foundation of China under Grant No.60903168the Scientific Research Fund of Hunan Provincial Education Department of China under Grant No.10B062Guangdong University of Petrochemical Technology Youth innovative personnel training project(NO 2010YC09)
文摘In the previous papers,Quantum-inspired multi-objective evolutionary algorithm(QMEA) was proved to be better than conventional genetic algorithms for multi-objective optimization problem.To improve the quality of the non-dominated set as well as the diversity of population in multi-objective problems,in this paper,a Novel Cloud -based quantum -inspired multi-objective evolutionary Algorithm(CQMEA) is proposed.CQMEA is proposed by employing the concept and principles of Cloud theory.The algorithm utilizes the random orientation and stability of the cloud model,uses a self-adaptive mechanism with cloud model of Quantum gates updating strategy to implement global search efficient.By using the self-adaptive mechanism and the better solution which is determined by the membership function uncertainly,Compared with several well-known algorithms such as NSGA-Ⅱ,QMEA.Experimental results show that(CQMEA) is more effective than QMEA and NSGA -Ⅱ.
文摘Hybrid metaheuristic algorithms play a prominent role in improving algorithms'searchability by combining each algorithm's advantages and minimizing any substantial shortcomings.The Quantum-based Avian Navigation Optimizer Algorithm(QANA)is a recent metaheuristic algorithm inspired by the navigation behavior of migratory birds.Different experimental results show that QANA is a competitive and applicable algorithm in different optimization fields.However,it suffers from shortcomings such as low solution quality and premature convergence when tackling some complex problems.Therefore,instead of proposing a new algorithm to solve these weaknesses,we use the advantages of the bonobo optimizer to improve global search capability and mitigate premature convergence of the original QANA.The effectiveness of the proposed Hybrid Quantum-based Avian Navigation Optimizer Algorithm(HQANA)is assessed on 29 test functions of the CEC 2018 benchmark test suite with different dimensions,30,50,and 100.The results are then statistically investigated by the Friedman test and compared with the results of eight well-known optimization algorithms,including PSO,KH,GWO,WOA,CSA,HOA,BO,and QANA.Ultimately,five constrained engineering optimization problems from the latest test suite,CEC 2020 are used to assess the applicability of HQANA to solve complex real-world engineering optimization problems.The experimental and statistical findings prove that the proposed HQANA algorithm is superior to the comparative algorithms.
