Let G be a stratified Lie group and let{X_(1)……,X_(n1)}be a basis of the first layer of the Lie algebra of G.The sub-Laplacian△G is defined by△G=-n_(1)∑j=1 X^(2)j,The operator defined by△G-n_(1)∑j=1 Xjp/pXj is ...Let G be a stratified Lie group and let{X_(1)……,X_(n1)}be a basis of the first layer of the Lie algebra of G.The sub-Laplacian△G is defined by△G=-n_(1)∑j=1 X^(2)j,The operator defined by△G-n_(1)∑j=1 Xjp/pXj is called the Ornstein-Uhlenbeck operator on G,where p is a heat kernel at time 1 on G.In this paper,we investigate Gaussian BV functions and Gaussian BV capacities associated with the Ornstein-Uhlenbeck operator on the stratified Lie group.展开更多
Nowadays,optimization techniques are required in various engineering domains to find optimal solutions for complex problems.As a result,there is a growing tendency among scientists to enhance existing nature-inspired ...Nowadays,optimization techniques are required in various engineering domains to find optimal solutions for complex problems.As a result,there is a growing tendency among scientists to enhance existing nature-inspired algorithms using various evolutionary strategies and to develop new nature-inspired optimization methods that can properly explore the feature space.The recently designed nature-inspired meta-heuristic,named the Golden Jackal Optimization(GJO),was inspired by the collaborative hunting actions of the golden jackal in nature to solve various challenging problems.However,like other approaches,the GJO has the limitations of poor exploitation ability,the ease of getting stuck in a local optimal region,and an improper balancing of exploration and exploitation.To overcome these limitations,this paper proposes an improved GJO algorithm based on multi-strategy mixing(LGJO).First,using a chaotic mapping strategy to initialize the population instead of using random parameters,this algorithm can generate initial solutions with good diversity in the search space.Second,a dynamic inertia weight based on cosine variation is proposed to make the search process more realistic and effectively balance the algorithm's global and local search capabilities.Finally,a position update strategy based on Gaussian mutation was introduced,fully utilizing the guidance role of the optimal individual to improve population diversity,effectively exploring unknown regions,and avoiding the algorithm falling into local optima.To evaluate the proposed algorithm,23 mathematical benchmark functions,CEC-2019 and CEC2021 tests are employed.The results are compared to high-quality,well-known optimization methods.The results of the proposed method are compared from different points of view,including the quality of the results,convergence behavior,and robustness.The superiority and high-quality performance of the proposed method are demonstrated by comparing the results.Furthermore,to demonstrate its applicability,it is employed to solve four constrained industrial applications.The outcomes of the experiment reveal that the proposed algorithm can solve challenging,constrained problems and is very competitive compared with other optimization algorithms.This article provides a new approach to solving real-world optimization problems.展开更多
基金supported by Fundamental Research Funds for the Central Universities(No.500421126)Pengtao Li was in part supported by Shandong Natural Science Foundation of China(No.ZR2017JL008)+2 种基金National Natural Science Foundation of China(Nos.11871293 and 12071272)Yu Liu was supported by National Natural Science Foundation of China(No.11671031)Beijing Municipal Science and Technology Project(No.Z17111000220000).
文摘Let G be a stratified Lie group and let{X_(1)……,X_(n1)}be a basis of the first layer of the Lie algebra of G.The sub-Laplacian△G is defined by△G=-n_(1)∑j=1 X^(2)j,The operator defined by△G-n_(1)∑j=1 Xjp/pXj is called the Ornstein-Uhlenbeck operator on G,where p is a heat kernel at time 1 on G.In this paper,we investigate Gaussian BV functions and Gaussian BV capacities associated with the Ornstein-Uhlenbeck operator on the stratified Lie group.
基金support of the special project for collaborative innovation of science and technology in 2021(No:202121206)Henan Province University Scientific and Technological Innovation Team(No:18IRTSTHN009).
文摘Nowadays,optimization techniques are required in various engineering domains to find optimal solutions for complex problems.As a result,there is a growing tendency among scientists to enhance existing nature-inspired algorithms using various evolutionary strategies and to develop new nature-inspired optimization methods that can properly explore the feature space.The recently designed nature-inspired meta-heuristic,named the Golden Jackal Optimization(GJO),was inspired by the collaborative hunting actions of the golden jackal in nature to solve various challenging problems.However,like other approaches,the GJO has the limitations of poor exploitation ability,the ease of getting stuck in a local optimal region,and an improper balancing of exploration and exploitation.To overcome these limitations,this paper proposes an improved GJO algorithm based on multi-strategy mixing(LGJO).First,using a chaotic mapping strategy to initialize the population instead of using random parameters,this algorithm can generate initial solutions with good diversity in the search space.Second,a dynamic inertia weight based on cosine variation is proposed to make the search process more realistic and effectively balance the algorithm's global and local search capabilities.Finally,a position update strategy based on Gaussian mutation was introduced,fully utilizing the guidance role of the optimal individual to improve population diversity,effectively exploring unknown regions,and avoiding the algorithm falling into local optima.To evaluate the proposed algorithm,23 mathematical benchmark functions,CEC-2019 and CEC2021 tests are employed.The results are compared to high-quality,well-known optimization methods.The results of the proposed method are compared from different points of view,including the quality of the results,convergence behavior,and robustness.The superiority and high-quality performance of the proposed method are demonstrated by comparing the results.Furthermore,to demonstrate its applicability,it is employed to solve four constrained industrial applications.The outcomes of the experiment reveal that the proposed algorithm can solve challenging,constrained problems and is very competitive compared with other optimization algorithms.This article provides a new approach to solving real-world optimization problems.
