In recent years,decomposition-based evolutionary algorithms have become popular algorithms for solving multi-objective problems in real-life scenarios.In these algorithms,the reference vectors of the Penalty-Based bou...In recent years,decomposition-based evolutionary algorithms have become popular algorithms for solving multi-objective problems in real-life scenarios.In these algorithms,the reference vectors of the Penalty-Based boundary intersection(PBI)are distributed parallelly while those based on the normal boundary intersection(NBI)are distributed radially in a conical shape in the objective space.To improve the problem-solving effectiveness of multi-objective optimization algorithms in engineering applications,this paper addresses the improvement of the Collaborative Decomposition(CoD)method,a multi-objective decomposition technique that integrates PBI and NBI,and combines it with the Elephant Clan Optimization Algorithm,introducing the Collaborative Decomposition Multi-objective Improved Elephant Clan Optimization Algorithm(CoDMOIECO).Specifically,a novel subpopulation construction method with adaptive changes following the number of iterations and a novel individual merit ranking based onNBI and angle are proposed.,enabling the creation of subpopulations closely linked to weight vectors and the identification of diverse individuals within them.Additionally,new update strategies for the clan leader,male elephants,and juvenile elephants are introduced to boost individual exploitation capabilities and further enhance the algorithm’s convergence.Finally,a new CoD-based environmental selection method is proposed,introducing adaptive dynamically adjusted angle coefficients and individual angles on corresponding weight vectors,significantly improving both the convergence and distribution of the algorithm.Experimental comparisons on the ZDT,DTLZ,and WFG function sets with four benchmark multi-objective algorithms—MOEA/D,CAMOEA,VaEA,and MOEA/D-UR—demonstrate that CoDMOIECO achieves superior performance in both convergence and distribution.展开更多
The existing algorithms for solving multi-objective optimization problems fall into three main categories:Decomposition-based,dominance-based,and indicator-based.Traditional multi-objective optimization problemsmainly...The existing algorithms for solving multi-objective optimization problems fall into three main categories:Decomposition-based,dominance-based,and indicator-based.Traditional multi-objective optimization problemsmainly focus on objectives,treating decision variables as a total variable to solve the problem without consideringthe critical role of decision variables in objective optimization.As seen,a variety of decision variable groupingalgorithms have been proposed.However,these algorithms are relatively broad for the changes of most decisionvariables in the evolution process and are time-consuming in the process of finding the Pareto frontier.To solvethese problems,a multi-objective optimization algorithm for grouping decision variables based on extreme pointPareto frontier(MOEA-DV/EPF)is proposed.This algorithm adopts a preprocessing rule to solve the Paretooptimal solution set of extreme points generated by simultaneous evolution in various target directions,obtainsthe basic Pareto front surface to determine the convergence effect,and analyzes the convergence and distributioneffects of decision variables.In the later stages of algorithm optimization,different mutation strategies are adoptedaccording to the nature of the decision variables to speed up the rate of evolution to obtain excellent individuals,thusenhancing the performance of the algorithm.Evaluation validation of the test functions shows that this algorithmcan solve the multi-objective optimization problem more efficiently.展开更多
This paper presents a parallel two-level evolutionary algorithm based on domain decomposition for solving function optimization problem containing multiple solutions. By combining the characteristics of the global sea...This paper presents a parallel two-level evolutionary algorithm based on domain decomposition for solving function optimization problem containing multiple solutions. By combining the characteristics of the global search and local search in each sub-domain, the former enables individual to draw closer to each optima and keeps the diversity of individuals, while the latter selects local optimal solutions known as latent solutions in sub-domain. In the end, by selecting the global optimal solutions from latent solutions in each sub-domain, we can discover all the optimal solutions easily and quickly.展开更多
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
Tourism route planning is widely applied in the smart tourism field.The Pareto-optimal front obtained by the traditional multi-objective evolutionary algorithm exhibits long tails,sharp peaks and disconnected regions ...Tourism route planning is widely applied in the smart tourism field.The Pareto-optimal front obtained by the traditional multi-objective evolutionary algorithm exhibits long tails,sharp peaks and disconnected regions problems,which leads to uneven distribution and weak diversity of optimization solutions of tourism routes.Inspired by these limitations,we propose a multi-objective evolutionary algorithm for tourism route recommendation(MOTRR)with two-stage and Pareto layering based on decomposition.The method decomposes the multiobjective problem into several subproblems,and improves the distribution of solutions through a two-stage method.The crowding degree mechanism between extreme and intermediate populations is used in the two-stage method.The neighborhood is determined according to the weight of the subproblem for crossover mutation.Finally,Pareto layering is used to improve the updating efficiency and population diversity of the solution.The two-stage method is combined with the Pareto layering structure,which not only maintains the distribution and diversity of the algorithm,but also avoids the same solutions.Compared with several classical benchmark algorithms,the experimental results demonstrate competitive advantages on five test functions,hypervolume(HV)and inverted generational distance(IGD)metrics.Using the experimental results of real scenic spot datasets from two famous tourism social networking sites with vast amounts of users and large-scale online comments in Beijing,our proposed algorithm shows better distribution.It proves that the tourism routes recommended by our proposed algorithm have better distribution and diversity,so that the recommended routes can better meet the personalized needs of tourists.展开更多
A multiple-objective evolutionary algorithm (MOEA) with a new Decision Making (DM) scheme for MOD of conceptual missile shapes was presented, which is contrived to determine suitable tradeoffs from Pareto optimal set ...A multiple-objective evolutionary algorithm (MOEA) with a new Decision Making (DM) scheme for MOD of conceptual missile shapes was presented, which is contrived to determine suitable tradeoffs from Pareto optimal set using interactive preference articulation. There are two objective functions, to maximize ratio of lift to drag and to minimize radar cross-section (RCS) value. 3D computational electromagnetic solver was used to evaluate RCS, electromagnetic performance. 3D Navier-Stokes flow solver was adopted to evaluate aerodynamic performance. A flight mechanics solver was used to analyze the stability of the missile. Based on the MOEA, a synergetic optimization of missile shapes for aerodynamic and radar cross-section performance is completed. The results show that the proposed approach can be used in more complex optimization case of flight vehicles.展开更多
The decomposition based approach decomposes a multi-objective problem into a series of single objective subproblems, which are optimized along contours towards the ideal point. But non-dominated solutions cannot sprea...The decomposition based approach decomposes a multi-objective problem into a series of single objective subproblems, which are optimized along contours towards the ideal point. But non-dominated solutions cannot spread uniformly, since the Pareto front shows different features, such as concave and convex. To improve the distribution uniformity of non-dominated solutions, a bidirectional decomposition based approach that constructs two search directions is proposed to provide a uniform distribution no matter what features problems have. Since two populations along two search directions show differently on diversity and convergence, an adaptive neighborhood selection approach is presented to choose suitable parents for the offspring generation. In order to avoid the problem of the shrinking search region caused by the close distance of the ideal and nadir points, a reference point update approach is presented. The performance of the proposed algorithm is validated with four state-of-the-art algorithms. Experimental results demonstrate the superiority of the proposed algorithm on all considered test problems.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 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
The operation variables,including feed rate of ore slurry,caustic solution and live steams in the double-stream alumina digestion process,determine the product quality,process costs and the environment pollution.Previ...The operation variables,including feed rate of ore slurry,caustic solution and live steams in the double-stream alumina digestion process,determine the product quality,process costs and the environment pollution.Previously,they were set by the technical workers according to the offline analysis results and an empirical formula,which leads to unstable process indices and high consumption frequently.So,a multi-objective optimization model is built to maintain the balance between resource consumptions and process indices by taking technical indices and energy efficiency as objectives,where the key technical indices are predicted based on the digestion kinetics of diaspore.A multi-objective state transition algorithm(MOSTA)is improved to solve the problem,in which a self-adaptive strategy is applied to dynamically adjust the operator factors of the MOSTA and dynamic infeasible threshold is used to handle constraints to enhance searching efficiency and ability of the algorithm.Then a rule based strategy is designed to make the final decision from the Pareto frontiers.The method is integrated into an optimal control system for the industrial digestion process and tested in the actual production.Results show that the proposed method can achieve the technical target while reducing the energy consumption.展开更多
In recent years, a large number of approaches to constrained multi-objective optimization problems(CMOPs) have been proposed, focusing on developing tweaked strategies and techniques for handling constraints. However,...In recent years, a large number of approaches to constrained multi-objective optimization problems(CMOPs) have been proposed, focusing on developing tweaked strategies and techniques for handling constraints. However, an overly finetuned strategy or technique might overfit some problem types,resulting in a lack of versatility. In this article, we propose a generic search strategy that performs an even search in a promising region. The promising region, determined by obtained feasible non-dominated solutions, possesses two general properties.First, the constrained Pareto front(CPF) is included in the promising region. Second, as the number of feasible solutions increases or the convergence performance(i.e., approximation to the CPF) of these solutions improves, the promising region shrinks. Then we develop a new strategy named even search,which utilizes the non-dominated solutions to accelerate convergence and escape from local optima, and the feasible solutions under a constraint relaxation condition to exploit and detect feasible regions. Finally, a diversity measure is adopted to make sure that the individuals in the population evenly cover the valuable areas in the promising region. Experimental results on 45 instances from four benchmark test suites and 14 real-world CMOPs have demonstrated that searching evenly in the promising region can achieve competitive performance and excellent versatility compared to 11 most state-of-the-art methods tailored for CMOPs.展开更多
In this paper, we focus on a class of nonlinear bilevel programming problems where the follower’s objective is a function of the linear expression of all variables, and the follower’s constraint functions are convex...In this paper, we focus on a class of nonlinear bilevel programming problems where the follower’s objective is a function of the linear expression of all variables, and the follower’s constraint functions are convex with respect to the follower’s variables. First, based on the features of the follower’s problem, we give a new decomposition scheme by which the follower’s optimal solution can be obtained easily. Then, to solve efficiently this class of problems by using evolutionary algorithm, novel evolutionary operators are designed by considering the best individuals and the diversity of individuals in the populations. Finally, based on these techniques, a new evolutionary algorithm is proposed. The numerical results on 20 test problems illustrate that the proposed algorithm is efficient and stable.展开更多
Decomposition of a complex multi-objective optimisation problem(MOP)to multiple simple subMOPs,known as M2M for short,is an effective approach to multi-objective optimisation.However,M2M facilitates little communicati...Decomposition of a complex multi-objective optimisation problem(MOP)to multiple simple subMOPs,known as M2M for short,is an effective approach to multi-objective optimisation.However,M2M facilitates little communication/collaboration between subMOPs,which limits its use in complex optimisation scenarios.This paper extends the M2M framework to develop a unified algorithm for both multi-objective and manyobjective optimisation.Through bilevel decomposition,an MOP is divided into multiple subMOPs at upper level,each of which is further divided into a number of single-objective subproblems at lower level.Neighbouring subMOPs are allowed to share some subproblems so that the knowledge gained from solving one subMOP can be transferred to another,and eventually to all the subMOPs.The bilevel decomposition is readily combined with some new mating selection and population update strategies,leading to a high-performance algorithm that competes effectively against a number of state-of-the-arts studied in this paper for both multiand many-objective optimisation.Parameter analysis and component analysis have been also carried out to further justify the proposed algorithm.展开更多
Solving constrained multi-objective optimization problems with evolutionary algorithms has attracted considerable attention.Various constrained multi-objective optimization evolutionary algorithms(CMOEAs)have been dev...Solving constrained multi-objective optimization problems with evolutionary algorithms has attracted considerable attention.Various constrained multi-objective optimization evolutionary algorithms(CMOEAs)have been developed with the use of different algorithmic strategies,evolutionary operators,and constraint-handling techniques.The performance of CMOEAs may be heavily dependent on the operators used,however,it is usually difficult to select suitable operators for the problem at hand.Hence,improving operator selection is promising and necessary for CMOEAs.This work proposes an online operator selection framework assisted by Deep Reinforcement Learning.The dynamics of the population,including convergence,diversity,and feasibility,are regarded as the state;the candidate operators are considered as actions;and the improvement of the population state is treated as the reward.By using a Q-network to learn a policy to estimate the Q-values of all actions,the proposed approach can adaptively select an operator that maximizes the improvement of the population according to the current state and thereby improve the algorithmic performance.The framework is embedded into four popular CMOEAs and assessed on 42 benchmark problems.The experimental results reveal that the proposed Deep Reinforcement Learning-assisted operator selection significantly improves the performance of these CMOEAs and the resulting algorithm obtains better versatility compared to nine state-of-the-art CMOEAs.展开更多
Large-scale multi-objective optimization problems(MOPs)that involve a large number of decision variables,have emerged from many real-world applications.While evolutionary algorithms(EAs)have been widely acknowledged a...Large-scale multi-objective optimization problems(MOPs)that involve a large number of decision variables,have emerged from many real-world applications.While evolutionary algorithms(EAs)have been widely acknowledged as a mainstream method for MOPs,most research progress and successful applications of EAs have been restricted to MOPs with small-scale decision variables.More recently,it has been reported that traditional multi-objective EAs(MOEAs)suffer severe deterioration with the increase of decision variables.As a result,and motivated by the emergence of real-world large-scale MOPs,investigation of MOEAs in this aspect has attracted much more attention in the past decade.This paper reviews the progress of evolutionary computation for large-scale multi-objective optimization from two angles.From the key difficulties of the large-scale MOPs,the scalability analysis is discussed by focusing on the performance of existing MOEAs and the challenges induced by the increase of the number of decision variables.From the perspective of methodology,the large-scale MOEAs are categorized into three classes and introduced respectively:divide and conquer based,dimensionality reduction based and enhanced search-based approaches.Several future research directions are also discussed.展开更多
In order to solve the flexible job shop scheduling problem with variable batches,we propose an improved multiobjective optimization algorithm,which combines the idea of inverse scheduling.First,a flexible job shop pro...In order to solve the flexible job shop scheduling problem with variable batches,we propose an improved multiobjective optimization algorithm,which combines the idea of inverse scheduling.First,a flexible job shop problem with the variable batches scheduling model is formulated.Second,we propose a batch optimization algorithm with inverse scheduling in which the batch size is adjusted by the dynamic feedback batch adjusting method.Moreover,in order to increase the diversity of the population,two methods are developed.One is the threshold to control the neighborhood updating,and the other is the dynamic clustering algorithm to update the population.Finally,a group of experiments are carried out.The results show that the improved multi-objective optimization algorithm can ensure the diversity of Pareto solutions effectively,and has effective performance in solving the flexible job shop scheduling problem with variable batches.展开更多
The recently proposed Cuckoo search algorithm is an evolutionary algorithm based on probability. It surpasses other algorithms in solving the multi-modal discontinuous and nonlinear problems. Searches made by it are v...The recently proposed Cuckoo search algorithm is an evolutionary algorithm based on probability. It surpasses other algorithms in solving the multi-modal discontinuous and nonlinear problems. Searches made by it are very efficient because it adopts Levy flight to carry out random walks. This paper proposes an improved version of cuckoo search for multi-objective problems（IMOCS）. Combined with nondominated sorting, crowding distance and Levy flights, elitism strategy is applied to improve the algorithm. Then numerical studies are conducted to compare the algorithm with DEMO and NSGA-II against some benchmark test functions. Result shows that our improved cuckoo search algorithm convergences rapidly and performs efficienly.展开更多
This work proposes a novel approach for multi-type optimal placement of flexible AC transmission system(FACTS) devices so as to optimize multi-objective voltage stability problem. The current study discusses a way for...This work proposes a novel approach for multi-type optimal placement of flexible AC transmission system(FACTS) devices so as to optimize multi-objective voltage stability problem. The current study discusses a way for locating and setting of thyristor controlled series capacitor(TCSC) and static var compensator(SVC) using the multi-objective optimization approach named strength pareto multi-objective evolutionary algorithm(SPMOEA). Maximization of the static voltage stability margin(SVSM) and minimizations of real power losses(RPL) and load voltage deviation(LVD) are taken as the goals or three objective functions, when optimally locating multi-type FACTS devices. The performance and effectiveness of the proposed approach has been validated by the simulation results of the IEEE 30-bus and IEEE 118-bus test systems. The proposed approach is compared with non-dominated sorting particle swarm optimization(NSPSO) algorithm. This comparison confirms the usefulness of the multi-objective proposed technique that makes it promising for determination of combinatorial problems of FACTS devices location and setting in large scale power systems.展开更多
To accelerate the multi-objective optimization for expensive engineering cases, a Knowledge-Extraction-based Variable-Fidelity Surrogate-assisted Covariance Matrix Adaptation Evolution Strategy(KE-VFS-CMA-ES) is prese...To accelerate the multi-objective optimization for expensive engineering cases, a Knowledge-Extraction-based Variable-Fidelity Surrogate-assisted Covariance Matrix Adaptation Evolution Strategy(KE-VFS-CMA-ES) is presented. In the first part, the KE-VFS model is established. Firstly, the optimization is performed using the low-fidelity surrogate model to obtain the Low-Fidelity Non-Dominated Solutions(LF-NDS). Secondly, aiming to obtain the High-Fidelity(HF) sample points located in promising areas, the K-means clustering algorithm and the space-filling strategy are used to extract knowledge from the LF-NDS to the HF space. Finally,the KE-VFS model is established by means of the obtained HF and LF sample points. In the second part, a novel model management based on the Modified Hypervolume Improvement(MHVI) criterion and pre-screening strategy is proposed. In each generation of KE-VFS-CMA-ES, excessive candidate points are firstly generated and then calculated by the MHVI criterion to find out a few potential points, which will be evaluated by the HF model. Through the above two parts,the promising areas can be detected and the potential points can be screened out, which contributes to speeding up the optimization process twofold. Three classic benchmark functions and a time-consuming engineering case of the aerospace integrally stiffened shell are studied, and results illustrate the excellent efficiency, robustness and applicability of KE-VFS-CMA-ES compared with other four known multi-objective optimization algorithms.展开更多
The traveling salesman problem has long been regarded as a challenging application for existing optimization methods as well as a benchmark application for the development of new optimization methods. As with many exi...The traveling salesman problem has long been regarded as a challenging application for existing optimization methods as well as a benchmark application for the development of new optimization methods. As with many existing algorithms, a traditional genetic algorithm will have limited success with this problem class, particularly as the problem size increases. A rule based genetic algorithm is proposed and demonstrated on sets of traveling salesman problems of increasing size. The solution character as well as the solution efficiency is compared against a simulated annealing technique as well as a standard genetic algorithm. The rule based genetic algorithm is shown to provide superior performance for all problem sizes considered. Furthermore, a post optimal analysis provides insight into which rules were successfully applied during the solution process which allows for rule modification to further enhance performance.展开更多
文摘In recent years,decomposition-based evolutionary algorithms have become popular algorithms for solving multi-objective problems in real-life scenarios.In these algorithms,the reference vectors of the Penalty-Based boundary intersection(PBI)are distributed parallelly while those based on the normal boundary intersection(NBI)are distributed radially in a conical shape in the objective space.To improve the problem-solving effectiveness of multi-objective optimization algorithms in engineering applications,this paper addresses the improvement of the Collaborative Decomposition(CoD)method,a multi-objective decomposition technique that integrates PBI and NBI,and combines it with the Elephant Clan Optimization Algorithm,introducing the Collaborative Decomposition Multi-objective Improved Elephant Clan Optimization Algorithm(CoDMOIECO).Specifically,a novel subpopulation construction method with adaptive changes following the number of iterations and a novel individual merit ranking based onNBI and angle are proposed.,enabling the creation of subpopulations closely linked to weight vectors and the identification of diverse individuals within them.Additionally,new update strategies for the clan leader,male elephants,and juvenile elephants are introduced to boost individual exploitation capabilities and further enhance the algorithm’s convergence.Finally,a new CoD-based environmental selection method is proposed,introducing adaptive dynamically adjusted angle coefficients and individual angles on corresponding weight vectors,significantly improving both the convergence and distribution of the algorithm.Experimental comparisons on the ZDT,DTLZ,and WFG function sets with four benchmark multi-objective algorithms—MOEA/D,CAMOEA,VaEA,and MOEA/D-UR—demonstrate that CoDMOIECO achieves superior performance in both convergence and distribution.
基金the Liaoning Province Nature Fundation Project(2022-MS-291)the National Programme for Foreign Expert Projects(G2022006008L)+2 种基金the Basic Research Projects of Liaoning Provincial Department of Education(LJKMZ20220781,LJKMZ20220783,LJKQZ20222457)King Saud University funded this study through theResearcher Support Program Number(RSPD2023R704)King Saud University,Riyadh,Saudi Arabia.
文摘The existing algorithms for solving multi-objective optimization problems fall into three main categories:Decomposition-based,dominance-based,and indicator-based.Traditional multi-objective optimization problemsmainly focus on objectives,treating decision variables as a total variable to solve the problem without consideringthe critical role of decision variables in objective optimization.As seen,a variety of decision variable groupingalgorithms have been proposed.However,these algorithms are relatively broad for the changes of most decisionvariables in the evolution process and are time-consuming in the process of finding the Pareto frontier.To solvethese problems,a multi-objective optimization algorithm for grouping decision variables based on extreme pointPareto frontier(MOEA-DV/EPF)is proposed.This algorithm adopts a preprocessing rule to solve the Paretooptimal solution set of extreme points generated by simultaneous evolution in various target directions,obtainsthe basic Pareto front surface to determine the convergence effect,and analyzes the convergence and distributioneffects of decision variables.In the later stages of algorithm optimization,different mutation strategies are adoptedaccording to the nature of the decision variables to speed up the rate of evolution to obtain excellent individuals,thusenhancing the performance of the algorithm.Evaluation validation of the test functions shows that this algorithmcan solve the multi-objective optimization problem more efficiently.
基金Supported by the National Natural Science Foundation of China(60133010,60073043,70071042)
文摘This paper presents a parallel two-level evolutionary algorithm based on domain decomposition for solving function optimization problem containing multiple solutions. By combining the characteristics of the global search and local search in each sub-domain, the former enables individual to draw closer to each optima and keeps the diversity of individuals, while the latter selects local optimal solutions known as latent solutions in sub-domain. In the end, by selecting the global optimal solutions from latent solutions in each sub-domain, we can discover all the optimal solutions easily and quickly.
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partially supported by the National Natural Science Foundation of China(41930644,61972439)the Collaborative Innovation Project of Anhui Province(GXXT-2022-093)the Key Program in the Youth Elite Support Plan in Universities of Anhui Province(gxyqZD2019010)。
文摘Tourism route planning is widely applied in the smart tourism field.The Pareto-optimal front obtained by the traditional multi-objective evolutionary algorithm exhibits long tails,sharp peaks and disconnected regions problems,which leads to uneven distribution and weak diversity of optimization solutions of tourism routes.Inspired by these limitations,we propose a multi-objective evolutionary algorithm for tourism route recommendation(MOTRR)with two-stage and Pareto layering based on decomposition.The method decomposes the multiobjective problem into several subproblems,and improves the distribution of solutions through a two-stage method.The crowding degree mechanism between extreme and intermediate populations is used in the two-stage method.The neighborhood is determined according to the weight of the subproblem for crossover mutation.Finally,Pareto layering is used to improve the updating efficiency and population diversity of the solution.The two-stage method is combined with the Pareto layering structure,which not only maintains the distribution and diversity of the algorithm,but also avoids the same solutions.Compared with several classical benchmark algorithms,the experimental results demonstrate competitive advantages on five test functions,hypervolume(HV)and inverted generational distance(IGD)metrics.Using the experimental results of real scenic spot datasets from two famous tourism social networking sites with vast amounts of users and large-scale online comments in Beijing,our proposed algorithm shows better distribution.It proves that the tourism routes recommended by our proposed algorithm have better distribution and diversity,so that the recommended routes can better meet the personalized needs of tourists.
基金National Natural Science Foundation ofChina( No.90 2 0 5 0 0 6) and Shanghai Rising Star Program( No.0 2 QG14 0 3 1)
文摘A multiple-objective evolutionary algorithm (MOEA) with a new Decision Making (DM) scheme for MOD of conceptual missile shapes was presented, which is contrived to determine suitable tradeoffs from Pareto optimal set using interactive preference articulation. There are two objective functions, to maximize ratio of lift to drag and to minimize radar cross-section (RCS) value. 3D computational electromagnetic solver was used to evaluate RCS, electromagnetic performance. 3D Navier-Stokes flow solver was adopted to evaluate aerodynamic performance. A flight mechanics solver was used to analyze the stability of the missile. Based on the MOEA, a synergetic optimization of missile shapes for aerodynamic and radar cross-section performance is completed. The results show that the proposed approach can be used in more complex optimization case of flight vehicles.
文摘The decomposition based approach decomposes a multi-objective problem into a series of single objective subproblems, which are optimized along contours towards the ideal point. But non-dominated solutions cannot spread uniformly, since the Pareto front shows different features, such as concave and convex. To improve the distribution uniformity of non-dominated solutions, a bidirectional decomposition based approach that constructs two search directions is proposed to provide a uniform distribution no matter what features problems have. Since two populations along two search directions show differently on diversity and convergence, an adaptive neighborhood selection approach is presented to choose suitable parents for the offspring generation. In order to avoid the problem of the shrinking search region caused by the close distance of the ideal and nadir points, a reference point update approach is presented. The performance of the proposed algorithm is validated with four state-of-the-art algorithms. Experimental results demonstrate the superiority of the proposed algorithm on all considered test problems.
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(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.
基金Project(62073342)supported by the National Natural Science Foundation of ChinaProject(2014 AA 041803)supported by the Hi-tech Research and Development Program of China。
文摘The operation variables,including feed rate of ore slurry,caustic solution and live steams in the double-stream alumina digestion process,determine the product quality,process costs and the environment pollution.Previously,they were set by the technical workers according to the offline analysis results and an empirical formula,which leads to unstable process indices and high consumption frequently.So,a multi-objective optimization model is built to maintain the balance between resource consumptions and process indices by taking technical indices and energy efficiency as objectives,where the key technical indices are predicted based on the digestion kinetics of diaspore.A multi-objective state transition algorithm(MOSTA)is improved to solve the problem,in which a self-adaptive strategy is applied to dynamically adjust the operator factors of the MOSTA and dynamic infeasible threshold is used to handle constraints to enhance searching efficiency and ability of the algorithm.Then a rule based strategy is designed to make the final decision from the Pareto frontiers.The method is integrated into an optimal control system for the industrial digestion process and tested in the actual production.Results show that the proposed method can achieve the technical target while reducing the energy consumption.
基金partly supported by the National Natural Science Foundation of China(62076225)。
文摘In recent years, a large number of approaches to constrained multi-objective optimization problems(CMOPs) have been proposed, focusing on developing tweaked strategies and techniques for handling constraints. However, an overly finetuned strategy or technique might overfit some problem types,resulting in a lack of versatility. In this article, we propose a generic search strategy that performs an even search in a promising region. The promising region, determined by obtained feasible non-dominated solutions, possesses two general properties.First, the constrained Pareto front(CPF) is included in the promising region. Second, as the number of feasible solutions increases or the convergence performance(i.e., approximation to the CPF) of these solutions improves, the promising region shrinks. Then we develop a new strategy named even search,which utilizes the non-dominated solutions to accelerate convergence and escape from local optima, and the feasible solutions under a constraint relaxation condition to exploit and detect feasible regions. Finally, a diversity measure is adopted to make sure that the individuals in the population evenly cover the valuable areas in the promising region. Experimental results on 45 instances from four benchmark test suites and 14 real-world CMOPs have demonstrated that searching evenly in the promising region can achieve competitive performance and excellent versatility compared to 11 most state-of-the-art methods tailored for CMOPs.
文摘In this paper, we focus on a class of nonlinear bilevel programming problems where the follower’s objective is a function of the linear expression of all variables, and the follower’s constraint functions are convex with respect to the follower’s variables. First, based on the features of the follower’s problem, we give a new decomposition scheme by which the follower’s optimal solution can be obtained easily. Then, to solve efficiently this class of problems by using evolutionary algorithm, novel evolutionary operators are designed by considering the best individuals and the diversity of individuals in the populations. Finally, based on these techniques, a new evolutionary algorithm is proposed. The numerical results on 20 test problems illustrate that the proposed algorithm is efficient and stable.
基金supported in part by the National Natural Science Foundation of China (62376288,U23A20347)the Engineering and Physical Sciences Research Council of UK (EP/X041239/1)the Royal Society International Exchanges Scheme of UK (IEC/NSFC/211404)。
文摘Decomposition of a complex multi-objective optimisation problem(MOP)to multiple simple subMOPs,known as M2M for short,is an effective approach to multi-objective optimisation.However,M2M facilitates little communication/collaboration between subMOPs,which limits its use in complex optimisation scenarios.This paper extends the M2M framework to develop a unified algorithm for both multi-objective and manyobjective optimisation.Through bilevel decomposition,an MOP is divided into multiple subMOPs at upper level,each of which is further divided into a number of single-objective subproblems at lower level.Neighbouring subMOPs are allowed to share some subproblems so that the knowledge gained from solving one subMOP can be transferred to another,and eventually to all the subMOPs.The bilevel decomposition is readily combined with some new mating selection and population update strategies,leading to a high-performance algorithm that competes effectively against a number of state-of-the-arts studied in this paper for both multiand many-objective optimisation.Parameter analysis and component analysis have been also carried out to further justify the proposed algorithm.
基金the National Natural Science Foundation of China(62076225,62073300)the Natural Science Foundation for Distinguished Young Scholars of Hubei(2019CFA081)。
文摘Solving constrained multi-objective optimization problems with evolutionary algorithms has attracted considerable attention.Various constrained multi-objective optimization evolutionary algorithms(CMOEAs)have been developed with the use of different algorithmic strategies,evolutionary operators,and constraint-handling techniques.The performance of CMOEAs may be heavily dependent on the operators used,however,it is usually difficult to select suitable operators for the problem at hand.Hence,improving operator selection is promising and necessary for CMOEAs.This work proposes an online operator selection framework assisted by Deep Reinforcement Learning.The dynamics of the population,including convergence,diversity,and feasibility,are regarded as the state;the candidate operators are considered as actions;and the improvement of the population state is treated as the reward.By using a Q-network to learn a policy to estimate the Q-values of all actions,the proposed approach can adaptively select an operator that maximizes the improvement of the population according to the current state and thereby improve the algorithmic performance.The framework is embedded into four popular CMOEAs and assessed on 42 benchmark problems.The experimental results reveal that the proposed Deep Reinforcement Learning-assisted operator selection significantly improves the performance of these CMOEAs and the resulting algorithm obtains better versatility compared to nine state-of-the-art CMOEAs.
基金This work was supported by the Natural Science Foundation of China(Nos.61672478 and 61806090)the National Key Research and Development Program of China(No.2017YFB1003102)+4 种基金the Guangdong Provincial Key Laboratory(No.2020B121201001)the Shenzhen Peacock Plan(No.KQTD2016112514355531)the Guangdong-Hong Kong-Macao Greater Bay Area Center for Brain Science and Brain-inspired Intelligence Fund(No.2019028)the Fellowship of China Postdoctoral Science Foundation(No.2020M671900)the National Leading Youth Talent Support Program of China.
文摘Large-scale multi-objective optimization problems(MOPs)that involve a large number of decision variables,have emerged from many real-world applications.While evolutionary algorithms(EAs)have been widely acknowledged as a mainstream method for MOPs,most research progress and successful applications of EAs have been restricted to MOPs with small-scale decision variables.More recently,it has been reported that traditional multi-objective EAs(MOEAs)suffer severe deterioration with the increase of decision variables.As a result,and motivated by the emergence of real-world large-scale MOPs,investigation of MOEAs in this aspect has attracted much more attention in the past decade.This paper reviews the progress of evolutionary computation for large-scale multi-objective optimization from two angles.From the key difficulties of the large-scale MOPs,the scalability analysis is discussed by focusing on the performance of existing MOEAs and the challenges induced by the increase of the number of decision variables.From the perspective of methodology,the large-scale MOEAs are categorized into three classes and introduced respectively:divide and conquer based,dimensionality reduction based and enhanced search-based approaches.Several future research directions are also discussed.
基金supported by the National Key R&D Plan(2020YFB1712902)the National Natural Science Foundation of China(52075036).
文摘In order to solve the flexible job shop scheduling problem with variable batches,we propose an improved multiobjective optimization algorithm,which combines the idea of inverse scheduling.First,a flexible job shop problem with the variable batches scheduling model is formulated.Second,we propose a batch optimization algorithm with inverse scheduling in which the batch size is adjusted by the dynamic feedback batch adjusting method.Moreover,in order to increase the diversity of the population,two methods are developed.One is the threshold to control the neighborhood updating,and the other is the dynamic clustering algorithm to update the population.Finally,a group of experiments are carried out.The results show that the improved multi-objective optimization algorithm can ensure the diversity of Pareto solutions effectively,and has effective performance in solving the flexible job shop scheduling problem with variable batches.
基金Supported by the National Natural Science Foundation of China(71471140)
文摘The recently proposed Cuckoo search algorithm is an evolutionary algorithm based on probability. It surpasses other algorithms in solving the multi-modal discontinuous and nonlinear problems. Searches made by it are very efficient because it adopts Levy flight to carry out random walks. This paper proposes an improved version of cuckoo search for multi-objective problems（IMOCS）. Combined with nondominated sorting, crowding distance and Levy flights, elitism strategy is applied to improve the algorithm. Then numerical studies are conducted to compare the algorithm with DEMO and NSGA-II against some benchmark test functions. Result shows that our improved cuckoo search algorithm convergences rapidly and performs efficienly.
文摘This work proposes a novel approach for multi-type optimal placement of flexible AC transmission system(FACTS) devices so as to optimize multi-objective voltage stability problem. The current study discusses a way for locating and setting of thyristor controlled series capacitor(TCSC) and static var compensator(SVC) using the multi-objective optimization approach named strength pareto multi-objective evolutionary algorithm(SPMOEA). Maximization of the static voltage stability margin(SVSM) and minimizations of real power losses(RPL) and load voltage deviation(LVD) are taken as the goals or three objective functions, when optimally locating multi-type FACTS devices. The performance and effectiveness of the proposed approach has been validated by the simulation results of the IEEE 30-bus and IEEE 118-bus test systems. The proposed approach is compared with non-dominated sorting particle swarm optimization(NSPSO) algorithm. This comparison confirms the usefulness of the multi-objective proposed technique that makes it promising for determination of combinatorial problems of FACTS devices location and setting in large scale power systems.
基金supported by the National Natural Science Foundation of China(Nos.11902065,11825202)the Fundamental Research Funds for the Central Universities,China(No.DUT21RC(3)013).
文摘To accelerate the multi-objective optimization for expensive engineering cases, a Knowledge-Extraction-based Variable-Fidelity Surrogate-assisted Covariance Matrix Adaptation Evolution Strategy(KE-VFS-CMA-ES) is presented. In the first part, the KE-VFS model is established. Firstly, the optimization is performed using the low-fidelity surrogate model to obtain the Low-Fidelity Non-Dominated Solutions(LF-NDS). Secondly, aiming to obtain the High-Fidelity(HF) sample points located in promising areas, the K-means clustering algorithm and the space-filling strategy are used to extract knowledge from the LF-NDS to the HF space. Finally,the KE-VFS model is established by means of the obtained HF and LF sample points. In the second part, a novel model management based on the Modified Hypervolume Improvement(MHVI) criterion and pre-screening strategy is proposed. In each generation of KE-VFS-CMA-ES, excessive candidate points are firstly generated and then calculated by the MHVI criterion to find out a few potential points, which will be evaluated by the HF model. Through the above two parts,the promising areas can be detected and the potential points can be screened out, which contributes to speeding up the optimization process twofold. Three classic benchmark functions and a time-consuming engineering case of the aerospace integrally stiffened shell are studied, and results illustrate the excellent efficiency, robustness and applicability of KE-VFS-CMA-ES compared with other four known multi-objective optimization algorithms.
文摘The traveling salesman problem has long been regarded as a challenging application for existing optimization methods as well as a benchmark application for the development of new optimization methods. As with many existing algorithms, a traditional genetic algorithm will have limited success with this problem class, particularly as the problem size increases. A rule based genetic algorithm is proposed and demonstrated on sets of traveling salesman problems of increasing size. The solution character as well as the solution efficiency is compared against a simulated annealing technique as well as a standard genetic algorithm. The rule based genetic algorithm is shown to provide superior performance for all problem sizes considered. Furthermore, a post optimal analysis provides insight into which rules were successfully applied during the solution process which allows for rule modification to further enhance performance.
