In this paper, both Fritz John and Karush-Kuhn-Tucker necessary optimality conditions are established for a （weakly） LU-efficient solution in the considered nonsmooth multiobjective programming problem with the mult...In this paper, both Fritz John and Karush-Kuhn-Tucker necessary optimality conditions are established for a （weakly） LU-efficient solution in the considered nonsmooth multiobjective programming problem with the multiple interval-objective function. Further, the sufficient optimality conditions for a （weakly） LU-efficient solution and several duality results in Mond-Weir sense are proved under assumptions that the functions constituting the considered nondifferentiable multiobjective programming problem with the multiple interval- objective function are convex.展开更多
Formalizing complex processes and phenomena of a real-world problem may require a large number of variables and constraints,resulting in what is termed a large-scale optimization problem.Nowadays,such large-scale opti...Formalizing complex processes and phenomena of a real-world problem may require a large number of variables and constraints,resulting in what is termed a large-scale optimization problem.Nowadays,such large-scale optimization problems are solved using computing machines,leading to an enormous computational time being required,which may delay deriving timely solutions.Decomposition methods,which partition a large-scale optimization problem into lower-dimensional subproblems,represent a key approach to addressing time-efficiency issues.There has been significant progress in both applied mathematics and emerging artificial intelligence approaches on this front.This work aims at providing an overview of the decomposition methods from both the mathematics and computer science points of view.We also remark on the state-of-the-art developments and recent applications of the decomposition methods,and discuss the future research and development perspectives.展开更多
Ant colony optimization （ACO） is a new heuristic algo- rithm which has been proven a successful technique and applied to a number of combinatorial optimization problems. The traveling salesman problem （TSP） is amo...Ant colony optimization （ACO） is a new heuristic algo- rithm which has been proven a successful technique and applied to a number of combinatorial optimization problems. The traveling salesman problem （TSP） is among the most important combinato- rial problems. An ACO algorithm based on scout characteristic is proposed for solving the stagnation behavior and premature con- vergence problem of the basic ACO algorithm on TSP. The main idea is to partition artificial ants into two groups： scout ants and common ants. The common ants work according to the search manner of basic ant colony algorithm, but scout ants have some differences from common ants, they calculate each route＇s muta- tion probability of the current optimal solution using path evaluation model and search around the optimal solution according to the mutation probability. Simulation on TSP shows that the improved algorithm has high efficiency and robustness.展开更多
There are three common types of predictability problems in weather and climate, which each involve different constrained nonlinear optimization problems： the lower bound of maximum predictable time, the upper bound o...There are three common types of predictability problems in weather and climate, which each involve different constrained nonlinear optimization problems： the lower bound of maximum predictable time, the upper bound of maximum prediction error, and the lower bound of maximum allowable initial error and parameter error. Highly effcient algorithms have been developed to solve the second optimization problem. And this optimization problem can be used in realistic models for weather and climate to study the upper bound of the maximum prediction error. Although a filtering strategy has been adopted to solve the other two problems, direct solutions are very time-consuming even for a very simple model, which therefore limits the applicability of these two predictability problems in realistic models. In this paper, a new strategy is designed to solve these problems, involving the use of the existing highly effcient algorithms for the second predictability problem in particular. Furthermore, a series of comparisons between the older filtering strategy and the new method are performed. It is demonstrated that the new strategy not only outputs the same results as the old one, but is also more computationally effcient. This would suggest that it is possible to study the predictability problems associated with these two nonlinear optimization problems in realistic forecast models of weather or climate.展开更多
As power systems expand,solving the unit commitment problem(UCP)becomes increasingly challenging due to the curse of dimensionality,and traditional methods often struggle to balance computational efficiency and soluti...As power systems expand,solving the unit commitment problem(UCP)becomes increasingly challenging due to the curse of dimensionality,and traditional methods often struggle to balance computational efficiency and solution optimality.To tackle this issue,we propose a problem-structure-informed quantum approximate optimization algorithm(QAOA)framework that fully exploits the quantum advantage under extremely limited quantum resources.Specifically,we leverage the inherent topological structure of power systems to decompose large-scale UCP instances into smaller subproblems,which are solvable in parallel by limited number of qubits.This decomposition not only circumvents the current hardware limitations of quantum computing but also achieves higher performance as the graph structure of the power system becomes more sparse.Consequently,our approach can be extended to future power systems that are larger and more complex.展开更多
A novel chaotic search method is proposed,and a hybrid algorithm combining particle swarm optimization(PSO) with this new method,called CLSPSO,is put forward to solve 14 integer and mixed integer programming problems....A novel chaotic search method is proposed,and a hybrid algorithm combining particle swarm optimization(PSO) with this new method,called CLSPSO,is put forward to solve 14 integer and mixed integer programming problems.The performances of CLSPSO are compared with those of other five hybrid algorithms combining PSO with chaotic search methods.Experimental results indicate that in terms of robustness and final convergence speed,CLSPSO is better than other five algorithms in solving many of these problems.Furthermore,CLSPSO exhibits good performance in solving two high-dimensional problems,and it finds better solutions than the known ones.A performance index(PI) is introduced to fairly compare the above six algorithms,and the obtained values of(PI) in three cases demonstrate that CLSPSO is superior to all the other five algorithms under the same conditions.展开更多
Most material distribution-based topology optimization methods work on a relaxed form of the optimization problem and then push the solution toward the binary limits.However,when benchmarking these methods,researchers...Most material distribution-based topology optimization methods work on a relaxed form of the optimization problem and then push the solution toward the binary limits.However,when benchmarking these methods,researchers use known solutions to only a single form of benchmark problem.This paper proposes a comparison platform for systematic benchmarking of topology optimization methods using both binary and relaxed forms.A greyness measure is implemented to evaluate how far a solution is from the desired binary form.The well-known ZhouRozvany(ZR)problem is selected as the benchmarking problem here,making use of available global solutions for both its relaxed and binary forms.The recently developed non-penalization Smooth-edged Material Distribution for Optimizing Topology(SEMDOT),well-established Solid Isotropic Material with Penalization(SIMP),and continuation methods are studied on this platform.Interestingly,in most cases,the grayscale solutions obtained by SEMDOT demonstrate better performance in dealing with the ZR problem than SIMP.The reasons are investigated and attributed to the usage of two different regularization techniques,namely,the Heaviside smooth function in SEMDOT and the power-law penalty in SIMP.More importantly,a simple-to-use benchmarking graph is proposed for evaluating newly developed topology optimization methods.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 authors of this article are interested in characterization of efficient solutions for special classes of problems. These classes consider semi-strong E-convexity of involved functions. Sufficient and necessary con...The authors of this article are interested in characterization of efficient solutions for special classes of problems. These classes consider semi-strong E-convexity of involved functions. Sufficient and necessary conditions for a feasible solution to be an efficient or properly efficient solution are obtained.展开更多
This paper proposes a modified version of the Dwarf Mongoose Optimization Algorithm (IDMO) for constrained engineering design problems. This optimization technique modifies the base algorithm (DMO) in three simple but...This paper proposes a modified version of the Dwarf Mongoose Optimization Algorithm (IDMO) for constrained engineering design problems. This optimization technique modifies the base algorithm (DMO) in three simple but effective ways. First, the alpha selection in IDMO differs from the DMO, where evaluating the probability value of each fitness is just a computational overhead and contributes nothing to the quality of the alpha or other group members. The fittest dwarf mongoose is selected as the alpha, and a new operator ω is introduced, which controls the alpha movement, thereby enhancing the exploration ability and exploitability of the IDMO. Second, the scout group movements are modified by randomization to introduce diversity in the search process and explore unvisited areas. Finally, the babysitter's exchange criterium is modified such that once the criterium is met, the babysitters that are exchanged interact with the dwarf mongoose exchanging them to gain information about food sources and sleeping mounds, which could result in better-fitted mongooses instead of initializing them afresh as done in DMO, then the counter is reset to zero. The proposed IDMO was used to solve the classical and CEC 2020 benchmark functions and 12 continuous/discrete engineering optimization problems. The performance of the IDMO, using different performance metrics and statistical analysis, is compared with the DMO and eight other existing algorithms. In most cases, the results show that solutions achieved by the IDMO are better than those obtained by the existing algorithms.展开更多
A novel hybrid algorithm named ABC-BBO, which integrates artificial bee colony(ABC) algorithm with biogeography-based optimization(BBO) algorithm, is proposed to solve constrained mechanical design problems. ABC-BBO c...A novel hybrid algorithm named ABC-BBO, which integrates artificial bee colony(ABC) algorithm with biogeography-based optimization(BBO) algorithm, is proposed to solve constrained mechanical design problems. ABC-BBO combined the exploration of ABC algorithm with the exploitation of BBO algorithm effectively, and hence it can generate the promising candidate individuals. The proposed hybrid algorithm speeds up the convergence and improves the algorithm's performance. Several benchmark test functions and mechanical design problems are applied to verifying the effects of these improvements and it is demonstrated that the performance of this proposed ABC-BBO is superior to or at least highly competitive with other population-based optimization approaches.展开更多
As a new-style stochastic algorithm, the electromagnetism-like mechanism（EM） method gains more and more attention from many researchers in recent years. A novel model based on EM（NMEM） for multiobjective optimizat...As a new-style stochastic algorithm, the electromagnetism-like mechanism（EM） method gains more and more attention from many researchers in recent years. A novel model based on EM（NMEM） for multiobjective optimization problems is proposed, which regards the charge of all particles as the constraints in the current population and the measure of the uniformity of non-dominated solutions as the objective function. The charge of the particle is evaluated based on the dominated concept, and its magnitude determines the direction of a force between two particles. Numerical studies are carried out on six complex test functions and the experimental results demonstrate that the proposed NMEM algorithm is a very robust method for solving the multiobjective optimization problems.展开更多
The aim of this paper is to study the relationship among Minty vector variational-like inequality problem, Stampacchia vector variational-like inequality problem and vector optimization problem involving (G, α)-invex...The aim of this paper is to study the relationship among Minty vector variational-like inequality problem, Stampacchia vector variational-like inequality problem and vector optimization problem involving (G, α)-invex functions. Furthermore, we establish equivalence among the solutions of weak formulations of Minty vector variational-like inequality problem, Stampacchia vector variational-like inequality problem and weak efficient solution of vector optimization problem under the assumption of (G, α)-invex functions. Examples are provided to elucidate our results.展开更多
A new trust region algorithm for solving convex LC 1 optimization problem is presented.It is proved that the algorithm is globally convergent and the rate of convergence is superlinear under some reasonable assum...A new trust region algorithm for solving convex LC 1 optimization problem is presented.It is proved that the algorithm is globally convergent and the rate of convergence is superlinear under some reasonable assumptions.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
Though vortex search（VS） algorithm has good performance in solving global numerical optimization problems, it cannot fully search the whole space occasionally. Combining the vortex search algorithm and the artificia...Though vortex search（VS） algorithm has good performance in solving global numerical optimization problems, it cannot fully search the whole space occasionally. Combining the vortex search algorithm and the artificial bee colony algorithm（ABC） which has good performance in exploration, we present a HVS（hybrid vortex search） algorithm to solve the numerical optimization problems. We first use the employed bees and onlooker bees of ABC algorithm to find a solution, and then adopt the VS algorithm to find the best solution. In the meantime, we cannot treat the best solution so far as the center of the algorithm all the time. The algorithm is tested by 50 benchmark functions. The numerical results show the HVS algorithm has superior performance over the ABC and the VS algorithms.展开更多
There are many optimization problems in different branches of science that should be solved using an appropriate methodology.Populationbased optimization algorithms are one of the most efficient approaches to solve th...There are many optimization problems in different branches of science that should be solved using an appropriate methodology.Populationbased optimization algorithms are one of the most efficient approaches to solve this type of problems.In this paper,a new optimization algorithm called All Members-Based Optimizer(AMBO)is introduced to solve various optimization problems.The main idea in designing the proposedAMBOalgorithm is to use more information from the population members of the algorithm instead of just a few specific members(such as best member and worst member)to update the population matrix.Therefore,in AMBO,any member of the population can play a role in updating the population matrix.The theory of AMBO is described and then mathematically modeled for implementation on optimization problems.The performance of the proposed algorithm is evaluated on a set of twenty-three standard objective functions,which belong to three different categories:unimodal,high-dimensional multimodal,and fixed-dimensional multimodal functions.In order to analyze and compare the optimization results for the mentioned objective functions obtained by AMBO,eight other well-known algorithms have been also implemented.The optimization results demonstrate the ability of AMBO to solve various optimization problems.Also,comparison and analysis of the results show that AMBO is superior andmore competitive than the other mentioned algorithms in providing suitable solution.展开更多
To solve large-scale optimization problems,Fragrance coefficient and variant Particle Swarm local search Butterfly Optimization Algorithm(FPSBOA)is proposed.In the position update stage of Butterfly Optimization Algor...To solve large-scale optimization problems,Fragrance coefficient and variant Particle Swarm local search Butterfly Optimization Algorithm(FPSBOA)is proposed.In the position update stage of Butterfly Optimization Algorithm(BOA),the fragrance coefficient is designed to balance the exploration and exploitation of BOA.The variant particle swarm local search strategy is proposed to improve the local search ability of the current optimal butterfly and prevent the algorithm from falling into local optimality.192000-dimensional functions and 201000-dimensional CEC 2010 large-scale functions are used to verify FPSBOA for complex large-scale optimization problems.The experimental results are statistically analyzed by Friedman test and Wilcoxon rank-sum test.All attained results demonstrated that FPSBOA can better solve more challenging scientific and industrial real-world problems with thousands of variables.Finally,four mechanical engineering problems and one ten-dimensional process synthesis and design problem are applied to FPSBOA,which shows FPSBOA has the feasibility and effectiveness in real-world application problems.展开更多
In this paper, some theoretical notions of well-posedness and of well-posedness in the generalized sense for scalar optimization problems are presented and some important results are analysed. Similar notions of well-...In this paper, some theoretical notions of well-posedness and of well-posedness in the generalized sense for scalar optimization problems are presented and some important results are analysed. Similar notions of well-posedness, respectively for a vector optimization problem and for a variational inequality of differential type, are discussed subsequently and, among the various vector well-posedness notions known in the literature, the attention is focused on the concept of pointwise well-posedness. Moreover, after a review of well-posedness properties, the study is further extended to a scalarizing procedure that preserves well-posedness of the notions listed, namely to a result, obtained with a special scalarizing function, which links the notion of pontwise well-posedness to the well-posedness of a suitable scalar variational inequality of differential type.展开更多
Till now,several novel metaheuristic algorithms are proposed for global search.But only specific algorithms have become popular or attracted researchers,who are efficient in solving global optimization problems as wel...Till now,several novel metaheuristic algorithms are proposed for global search.But only specific algorithms have become popular or attracted researchers,who are efficient in solving global optimization problems as well as real-world application problems.The Social Group Optimization(SGO)algorithm is a new metaheuristic bioinspired algorithm inspired by human social behavior that attracted researchers due to its simplicity and problem-solving capability.In this study,to deal with the problems of low accuracy and local convergence in SGO,the chaos theory is introduced into the evolutionary process of SGO.Since chaotic mapping has certainty,ergodicity,and stochastic property,by replacing the constant value of the self-introspection parameter with chaotic maps,the proposed chaotic social group optimization algorithm increases its convergence rate and resulting precision.The proposal chaotic SGO is validated through 13 benchmark functions and after that 9 structural engineering design problems have been solved.The simulated results have been noticed as competent with that of state-of-art algorithms regarding convergence quality and accuracy,which certifies that improved SGO with chaos is valid and feasible.展开更多
文摘In this paper, both Fritz John and Karush-Kuhn-Tucker necessary optimality conditions are established for a （weakly） LU-efficient solution in the considered nonsmooth multiobjective programming problem with the multiple interval-objective function. Further, the sufficient optimality conditions for a （weakly） LU-efficient solution and several duality results in Mond-Weir sense are proved under assumptions that the functions constituting the considered nondifferentiable multiobjective programming problem with the multiple interval- objective function are convex.
基金The Australian Research Council(DP200101197,DP230101107).
文摘Formalizing complex processes and phenomena of a real-world problem may require a large number of variables and constraints,resulting in what is termed a large-scale optimization problem.Nowadays,such large-scale optimization problems are solved using computing machines,leading to an enormous computational time being required,which may delay deriving timely solutions.Decomposition methods,which partition a large-scale optimization problem into lower-dimensional subproblems,represent a key approach to addressing time-efficiency issues.There has been significant progress in both applied mathematics and emerging artificial intelligence approaches on this front.This work aims at providing an overview of the decomposition methods from both the mathematics and computer science points of view.We also remark on the state-of-the-art developments and recent applications of the decomposition methods,and discuss the future research and development perspectives.
基金supported by the National Natural Science Foundation of China(60573159)
文摘Ant colony optimization （ACO） is a new heuristic algo- rithm which has been proven a successful technique and applied to a number of combinatorial optimization problems. The traveling salesman problem （TSP） is among the most important combinato- rial problems. An ACO algorithm based on scout characteristic is proposed for solving the stagnation behavior and premature con- vergence problem of the basic ACO algorithm on TSP. The main idea is to partition artificial ants into two groups： scout ants and common ants. The common ants work according to the search manner of basic ant colony algorithm, but scout ants have some differences from common ants, they calculate each route＇s muta- tion probability of the current optimal solution using path evaluation model and search around the optimal solution according to the mutation probability. Simulation on TSP shows that the improved algorithm has high efficiency and robustness.
基金sponsored by the Key Knowledge Innovation Program of the Chinese Academy of Sciences (Grant. No. KZCX2-YW-QN203)the National Basic Research Program of China(2007CB411800),the GYHY200906009 of China Meteorological Administration
文摘There are three common types of predictability problems in weather and climate, which each involve different constrained nonlinear optimization problems： the lower bound of maximum predictable time, the upper bound of maximum prediction error, and the lower bound of maximum allowable initial error and parameter error. Highly effcient algorithms have been developed to solve the second optimization problem. And this optimization problem can be used in realistic models for weather and climate to study the upper bound of the maximum prediction error. Although a filtering strategy has been adopted to solve the other two problems, direct solutions are very time-consuming even for a very simple model, which therefore limits the applicability of these two predictability problems in realistic models. In this paper, a new strategy is designed to solve these problems, involving the use of the existing highly effcient algorithms for the second predictability problem in particular. Furthermore, a series of comparisons between the older filtering strategy and the new method are performed. It is demonstrated that the new strategy not only outputs the same results as the old one, but is also more computationally effcient. This would suggest that it is possible to study the predictability problems associated with these two nonlinear optimization problems in realistic forecast models of weather or climate.
文摘As power systems expand,solving the unit commitment problem(UCP)becomes increasingly challenging due to the curse of dimensionality,and traditional methods often struggle to balance computational efficiency and solution optimality.To tackle this issue,we propose a problem-structure-informed quantum approximate optimization algorithm(QAOA)framework that fully exploits the quantum advantage under extremely limited quantum resources.Specifically,we leverage the inherent topological structure of power systems to decompose large-scale UCP instances into smaller subproblems,which are solvable in parallel by limited number of qubits.This decomposition not only circumvents the current hardware limitations of quantum computing but also achieves higher performance as the graph structure of the power system becomes more sparse.Consequently,our approach can be extended to future power systems that are larger and more complex.
基金Projects(50275150,61173052) supported by the National Natural Science Foundation of ChinaProject(14FJ3112) supported by the Planned Science and Technology of Hunan Province,ChinaProject(14B033) supported by Scientific Research Fund Education Department of Hunan Province,China
文摘A novel chaotic search method is proposed,and a hybrid algorithm combining particle swarm optimization(PSO) with this new method,called CLSPSO,is put forward to solve 14 integer and mixed integer programming problems.The performances of CLSPSO are compared with those of other five hybrid algorithms combining PSO with chaotic search methods.Experimental results indicate that in terms of robustness and final convergence speed,CLSPSO is better than other five algorithms in solving many of these problems.Furthermore,CLSPSO exhibits good performance in solving two high-dimensional problems,and it finds better solutions than the known ones.A performance index(PI) is introduced to fairly compare the above six algorithms,and the obtained values of(PI) in three cases demonstrate that CLSPSO is superior to all the other five algorithms under the same conditions.
文摘Most material distribution-based topology optimization methods work on a relaxed form of the optimization problem and then push the solution toward the binary limits.However,when benchmarking these methods,researchers use known solutions to only a single form of benchmark problem.This paper proposes a comparison platform for systematic benchmarking of topology optimization methods using both binary and relaxed forms.A greyness measure is implemented to evaluate how far a solution is from the desired binary form.The well-known ZhouRozvany(ZR)problem is selected as the benchmarking problem here,making use of available global solutions for both its relaxed and binary forms.The recently developed non-penalization Smooth-edged Material Distribution for Optimizing Topology(SEMDOT),well-established Solid Isotropic Material with Penalization(SIMP),and continuation methods are studied on this platform.Interestingly,in most cases,the grayscale solutions obtained by SEMDOT demonstrate better performance in dealing with the ZR problem than SIMP.The reasons are investigated and attributed to the usage of two different regularization techniques,namely,the Heaviside smooth function in SEMDOT and the power-law penalty in SIMP.More importantly,a simple-to-use benchmarking graph is proposed for evaluating newly developed topology optimization methods.
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The authors of this article are interested in characterization of efficient solutions for special classes of problems. These classes consider semi-strong E-convexity of involved functions. Sufficient and necessary conditions for a feasible solution to be an efficient or properly efficient solution are obtained.
文摘This paper proposes a modified version of the Dwarf Mongoose Optimization Algorithm (IDMO) for constrained engineering design problems. This optimization technique modifies the base algorithm (DMO) in three simple but effective ways. First, the alpha selection in IDMO differs from the DMO, where evaluating the probability value of each fitness is just a computational overhead and contributes nothing to the quality of the alpha or other group members. The fittest dwarf mongoose is selected as the alpha, and a new operator ω is introduced, which controls the alpha movement, thereby enhancing the exploration ability and exploitability of the IDMO. Second, the scout group movements are modified by randomization to introduce diversity in the search process and explore unvisited areas. Finally, the babysitter's exchange criterium is modified such that once the criterium is met, the babysitters that are exchanged interact with the dwarf mongoose exchanging them to gain information about food sources and sleeping mounds, which could result in better-fitted mongooses instead of initializing them afresh as done in DMO, then the counter is reset to zero. The proposed IDMO was used to solve the classical and CEC 2020 benchmark functions and 12 continuous/discrete engineering optimization problems. The performance of the IDMO, using different performance metrics and statistical analysis, is compared with the DMO and eight other existing algorithms. In most cases, the results show that solutions achieved by the IDMO are better than those obtained by the existing algorithms.
基金Projects(61463009,11264005,11361014)supported by the National Natural Science Foundation of ChinaProject([2013]2082)supported by the Science Technology Foundation of Guizhou Province,China
文摘A novel hybrid algorithm named ABC-BBO, which integrates artificial bee colony(ABC) algorithm with biogeography-based optimization(BBO) algorithm, is proposed to solve constrained mechanical design problems. ABC-BBO combined the exploration of ABC algorithm with the exploitation of BBO algorithm effectively, and hence it can generate the promising candidate individuals. The proposed hybrid algorithm speeds up the convergence and improves the algorithm's performance. Several benchmark test functions and mechanical design problems are applied to verifying the effects of these improvements and it is demonstrated that the performance of this proposed ABC-BBO is superior to or at least highly competitive with other population-based optimization approaches.
基金supported by the National Natural Science Foundation of China(60873099)the Fundamental Research Funds for the Central Universities(2011QNA29)
文摘As a new-style stochastic algorithm, the electromagnetism-like mechanism（EM） method gains more and more attention from many researchers in recent years. A novel model based on EM（NMEM） for multiobjective optimization problems is proposed, which regards the charge of all particles as the constraints in the current population and the measure of the uniformity of non-dominated solutions as the objective function. The charge of the particle is evaluated based on the dominated concept, and its magnitude determines the direction of a force between two particles. Numerical studies are carried out on six complex test functions and the experimental results demonstrate that the proposed NMEM algorithm is a very robust method for solving the multiobjective optimization problems.
文摘The aim of this paper is to study the relationship among Minty vector variational-like inequality problem, Stampacchia vector variational-like inequality problem and vector optimization problem involving (G, α)-invex functions. Furthermore, we establish equivalence among the solutions of weak formulations of Minty vector variational-like inequality problem, Stampacchia vector variational-like inequality problem and weak efficient solution of vector optimization problem under the assumption of (G, α)-invex functions. Examples are provided to elucidate our results.
基金Supported by the National Natural Science Foundation of P.R.China(1 9971 0 0 2 ) and the Subject ofBeijing Educational Committ
文摘A new trust region algorithm for solving convex LC 1 optimization problem is presented.It is proved that the algorithm is globally convergent and the rate of convergence is superlinear under some reasonable assumptions.
基金supported in part by the National Natural Science Foundation of China(72171172,62088101)in part by the Shanghai Science and Technology Major Special Project of Shanghai Development and Reform Commission(2021SHZDZX0100)+2 种基金in part by the Shanghai Commission of Science and Technology(19511132100,19511132101)in part by the China Scholarship Councilin part by the Deanship of Scientific Research(DSR)at King Abdulaziz University(KAU),Jeddah,Saudi Arabia(FP-146-43)。
文摘This study presents an autoencoder-embedded optimization(AEO)algorithm which involves a bi-population cooperative strategy for medium-scale expensive problems(MEPs).A huge search space can be compressed to an informative lowdimensional space by using an autoencoder as a dimension reduction tool.The search operation conducted in this low space facilitates the population with fast convergence towards the optima.To strike the balance between exploration and exploitation during optimization,two phases of a tailored teaching-learning-based optimization(TTLBO)are adopted to coevolve solutions in a distributed fashion,wherein one is assisted by an autoencoder and the other undergoes a regular evolutionary process.Also,a dynamic size adjustment scheme according to problem dimension and evolutionary progress is proposed to promote information exchange between these two phases and accelerate evolutionary convergence speed.The proposed algorithm is validated by testing benchmark functions with dimensions varying from 50 to 200.As indicated in our experiments,TTLBO is suitable for dealing with medium-scale problems and thus incorporated into the AEO framework as a base optimizer.Compared with the state-of-the-art algorithms for MEPs,AEO shows extraordinarily high efficiency for these challenging problems,t hus opening new directions for various evolutionary algorithms under AEO to tackle MEPs and greatly advancing the field of medium-scale computationally expensive optimization.
基金Supported by the National Natural Science Foundation of China(71471140)
文摘Though vortex search（VS） algorithm has good performance in solving global numerical optimization problems, it cannot fully search the whole space occasionally. Combining the vortex search algorithm and the artificial bee colony algorithm（ABC） which has good performance in exploration, we present a HVS（hybrid vortex search） algorithm to solve the numerical optimization problems. We first use the employed bees and onlooker bees of ABC algorithm to find a solution, and then adopt the VS algorithm to find the best solution. In the meantime, we cannot treat the best solution so far as the center of the algorithm all the time. The algorithm is tested by 50 benchmark functions. The numerical results show the HVS algorithm has superior performance over the ABC and the VS algorithms.
基金PT(corresponding author)was supported by the Excelence project PˇrF UHK No.2202/2020-2022 and Long-term development plan of UHK for year 2021,University of Hradec Králové,Czech Republic,https://www.uhk.cz/en/faculty-of-science/about-faculty/officialboard/internal-regulations-and-governing-acts/governing-acts/deans-decision/2020#grant-competition-of-fos-uhk-excellence-for-2020.
文摘There are many optimization problems in different branches of science that should be solved using an appropriate methodology.Populationbased optimization algorithms are one of the most efficient approaches to solve this type of problems.In this paper,a new optimization algorithm called All Members-Based Optimizer(AMBO)is introduced to solve various optimization problems.The main idea in designing the proposedAMBOalgorithm is to use more information from the population members of the algorithm instead of just a few specific members(such as best member and worst member)to update the population matrix.Therefore,in AMBO,any member of the population can play a role in updating the population matrix.The theory of AMBO is described and then mathematically modeled for implementation on optimization problems.The performance of the proposed algorithm is evaluated on a set of twenty-three standard objective functions,which belong to three different categories:unimodal,high-dimensional multimodal,and fixed-dimensional multimodal functions.In order to analyze and compare the optimization results for the mentioned objective functions obtained by AMBO,eight other well-known algorithms have been also implemented.The optimization results demonstrate the ability of AMBO to solve various optimization problems.Also,comparison and analysis of the results show that AMBO is superior andmore competitive than the other mentioned algorithms in providing suitable solution.
基金funded by the National Natural Science Foundation of China(No.72104069)the Science and Technology Department of Henan Province,China(No.182102310886 and 162102110109)the Postgraduate Meritocracy Scheme,hina(No.SYL19060145).
文摘To solve large-scale optimization problems,Fragrance coefficient and variant Particle Swarm local search Butterfly Optimization Algorithm(FPSBOA)is proposed.In the position update stage of Butterfly Optimization Algorithm(BOA),the fragrance coefficient is designed to balance the exploration and exploitation of BOA.The variant particle swarm local search strategy is proposed to improve the local search ability of the current optimal butterfly and prevent the algorithm from falling into local optimality.192000-dimensional functions and 201000-dimensional CEC 2010 large-scale functions are used to verify FPSBOA for complex large-scale optimization problems.The experimental results are statistically analyzed by Friedman test and Wilcoxon rank-sum test.All attained results demonstrated that FPSBOA can better solve more challenging scientific and industrial real-world problems with thousands of variables.Finally,four mechanical engineering problems and one ten-dimensional process synthesis and design problem are applied to FPSBOA,which shows FPSBOA has the feasibility and effectiveness in real-world application problems.
文摘In this paper, some theoretical notions of well-posedness and of well-posedness in the generalized sense for scalar optimization problems are presented and some important results are analysed. Similar notions of well-posedness, respectively for a vector optimization problem and for a variational inequality of differential type, are discussed subsequently and, among the various vector well-posedness notions known in the literature, the attention is focused on the concept of pointwise well-posedness. Moreover, after a review of well-posedness properties, the study is further extended to a scalarizing procedure that preserves well-posedness of the notions listed, namely to a result, obtained with a special scalarizing function, which links the notion of pontwise well-posedness to the well-posedness of a suitable scalar variational inequality of differential type.
文摘Till now,several novel metaheuristic algorithms are proposed for global search.But only specific algorithms have become popular or attracted researchers,who are efficient in solving global optimization problems as well as real-world application problems.The Social Group Optimization(SGO)algorithm is a new metaheuristic bioinspired algorithm inspired by human social behavior that attracted researchers due to its simplicity and problem-solving capability.In this study,to deal with the problems of low accuracy and local convergence in SGO,the chaos theory is introduced into the evolutionary process of SGO.Since chaotic mapping has certainty,ergodicity,and stochastic property,by replacing the constant value of the self-introspection parameter with chaotic maps,the proposed chaotic social group optimization algorithm increases its convergence rate and resulting precision.The proposal chaotic SGO is validated through 13 benchmark functions and after that 9 structural engineering design problems have been solved.The simulated results have been noticed as competent with that of state-of-art algorithms regarding convergence quality and accuracy,which certifies that improved SGO with chaos is valid and feasible.
