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A Two-Step Iterative Local Search for the Harvester Scheduling Problem With Splittable Workloads 认领 引用
1
作者 Hongyu Lin Jing Liang +2 位作者 Bo Jin Caitong Yue Yaonan Wang 《IEEE/CAA Journal of Automatica Sinica》 SCIE EI CSCD 2026年第7期1584-1599,共16页
With the growing emphasis on intelligent agriculture,scheduling problems involving multiple harvesters in largescale croplands have attracted increasing attention.In these scenarios,harvesters collaboratively perform ... With the growing emphasis on intelligent agriculture,scheduling problems involving multiple harvesters in largescale croplands have attracted increasing attention.In these scenarios,harvesters collaboratively perform tasks in expansive croplands,with each harvester taking on a portion of the workload.This study defines such problems as the harvester scheduling problem with splittable workloads(HSPSW).Unlike most multi-robot task allocation problems,HSPSW requires collaboration among several harvesters and involves more harvesters than croplands.These features increase the complexity of harvester-cropland interactions.To address these challenges,this paper proposes a novel two-step iterative local search(TSILS)algorithm.A greedy strategy that prioritizes croplands with higher workloads is proposed to generate initial solutions.Subsequently,a two-step iterative search strategy is employed to obtain high-quality solutions:the first step uses a predefined objective to facilitate rapid workload allocation for feasible solutions,and the second step integrates specific neighborhood operators and finegrained local search to improve its search capability.Experimental results demonstrate that the proposed method TSILS significantly outperforms existing approaches in both algorithmic performance and computational efficiency. 展开更多
关键词 Cooperative operations heuristic local search multi-harvester scheduling
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Mixed Local and Nonlocal Elliptic Problem with Concave-Convex and Discontinuous Nonlinearities 认领 引用
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作者 Yiru WANG Shuibo HUANG Qiaoyu TIAN 《Journal of Mathematical Research with Applications》 CSCD 2026年第1期40-56,共17页
This paper investigates the following mixed local and nonlocal elliptic problem fea-turing concave-convex nonlinearities and a discontinuous right-hand side:{L(u)=H(u−μ)|u|p−2u+λ|u|q−2u,x∈Ω,u≥0,x∈Ω,u=0,x... This paper investigates the following mixed local and nonlocal elliptic problem fea-turing concave-convex nonlinearities and a discontinuous right-hand side:{L(u)=H(u−μ)|u|p−2u+λ|u|q−2u,x∈Ω,u≥0,x∈Ω,u=0,x∈RN\Ω,where Ω ⊂RN(N>2)is a bounded domain,μ≥0 and λ>0 are real parameters,H denotes the Heaviside function(H(t)=0 for t0),and the mixed local and nolocal operator is defined as L(u)=−Δu+(−Δ)su with(−Δ)s being the restricted fractional Laplace(0<s<1).The exponents satisfy 1<q<2<p.By employing a novel non-smooth variational principle,we establish the existence of an M-solution for this problem and identify a range for the exponent p. 展开更多
关键词 mixed local and nonlocal operator discontinuous non-smooth variational principle M-solution
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On the Riemann-Hilbert problem for the reverse space-time nonlocal Hirota equation with step-like initial data 认领 引用
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作者 Bei-Bei Hu Ling Zhang +1 位作者 Zu-Yi Shen Ji Lin 《Communications in Theoretical Physics》 SCIE CAS CSCD 2025年第2期30-38,共9页
In this paper,we use the Riemann-Hilbert(RH)method to investigate the Cauchy problem of the reverse space-time nonlocal Hirota equation with step-like initial data:q(z,0)=o(1)as z→-∞and q(z,0)=δ+o(1)as z→∞,where... In this paper,we use the Riemann-Hilbert(RH)method to investigate the Cauchy problem of the reverse space-time nonlocal Hirota equation with step-like initial data:q(z,0)=o(1)as z→-∞and q(z,0)=δ+o(1)as z→∞,whereδis an arbitrary positive constant.We show that the solution of the Cauchy problem can be determined by the solution of the corresponding matrix RH problem established on the plane of complex spectral parameterλ.As an example,we construct an exact solution of the reverse space-time nonlocal Hirota equation in a special case via this RH problem. 展开更多
关键词 nonlocal Hirota equation Cauchy problem Riemann-Hilbert problem step-like initial data
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Nonlocal Boundary Value Problems for Nonlinear Fractional Differential Equations with a Disturbance Parameter on the Infinite Interval 认领 引用
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作者 ZHENG Yanping YANG Hui WANG Wenxia 《应用数学》 北大核心 2026年第2期360-372,共13页
This paper is concerned with a class of nonlinear fractional differential equations with a disturbance parameter in the integral boundary conditions on the infinite interval.By using Guo-Krasnoselskii fixed point theo... This paper is concerned with a class of nonlinear fractional differential equations with a disturbance parameter in the integral boundary conditions on the infinite interval.By using Guo-Krasnoselskii fixed point theorem,fixed point index theory and the analytic technique,we give the bifurcation point of the parameter which divides the range of parameter for the existence of at least two,one and no positive solutions for the problem.And,by using a fixed point theorem of generalized concave operator and cone theory,we establish the maximum parameter interval for the existence of the unique positive solution for the problem and show that such a positive solution continuously depends on the parameter.In the end,some examples are given to illustrate our main results. 展开更多
关键词 Boundary value problem Disturbance parameter Infinite interval Bifurcation point Cone
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MODIFIED LANDWEBER ITERATIVE METHOD FOR A BACKWARD PROBLEM IN TIME OF THE DIFFUSION EQUATION WITH LOCAL AND NONLOCAL OPERATORS 认领 引用
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作者 Hongwu ZHANG Yanhui LI 《Acta Mathematica Scientia》 SCIE CSCD 2025年第3期1205-1222,共18页
In this article, we consider a backward problem in time of the diffusion equation with local and nonlocal operators. This inverse problem is ill-posed because the solution does not depend continuously on the measured ... In this article, we consider a backward problem in time of the diffusion equation with local and nonlocal operators. This inverse problem is ill-posed because the solution does not depend continuously on the measured data. Inspired by the classical Landweber iterative method and Fourier truncation technique, we develops a modified Landweber iterative regularization method to restore the continuous dependence of solution on the measurement data. Under the a-priori and a-posteriori choice rules for the regularized parameter, the convergence estimates for the regularization method are derived. Some results of numerical simulation are provided to verify the stability and feasibility of our method in dealing with the considered problem. 展开更多
关键词 backward problem in time diffusion equation with local and nonlocal operators modified Landweber regularization convergence estimate numerical simulation
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PINN for solving forward and inverse problems involving integrable two-dimensional nonlocal equations 认领 引用 被引量：1
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作者 Xi Chen Wei-Qi Peng 《Communications in Theoretical Physics》 SCIE CAS CSCD 2025年第2期13-20,共8页
In this paper,the physics informed neural network(PINN)deep learning method is applied to solve two-dimensional nonlocal equations,including the partial reverse space y-nonlocal Mel'nikov equation,the partial reve... In this paper,the physics informed neural network(PINN)deep learning method is applied to solve two-dimensional nonlocal equations,including the partial reverse space y-nonlocal Mel'nikov equation,the partial reverse space-time nonlocal Mel'nikov equation and the nonlocal twodimensional nonlinear Schr?dinger(NLS)equation.By the PINN method,we successfully derive a data-driven two soliton solution,lump solution and rogue wave solution.Numerical simulation results indicate that the error range between the data-driven solution and the exact solution is relatively small,which verifies the effectiveness of the PINN deep learning method for solving high dimensional nonlocal equations.Moreover,the parameter discovery of the partial reverse space-time nonlocal Mel'nikov equation is analysed in terms of its soliton solution for the first time. 展开更多
关键词 two dimensional nonlocal equations PINN soliton solution rogue wave inverse problems
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Reduced Basis Method Based on Fourier Transform for Time-Dependent Parameterized Nonlocal Problems 认领 引用 被引量：1
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作者 Dou Dai Huailing Song Yuming Ba 《Communications in Mathematical Research》 CSCD 2025年第1期69-102,共34页
In the paper,a reduced basis(RB)method for time-dependent nonlocal problems with a special parameterized fractional Laplace kernel function is proposed.Because of the lack of sparsity of discretized nonlocal systems c... In the paper,a reduced basis(RB)method for time-dependent nonlocal problems with a special parameterized fractional Laplace kernel function is proposed.Because of the lack of sparsity of discretized nonlocal systems compared to corresponding local partial differential equation(PDE)systems,model reduction for nonlocal systems becomes more critical.The method of snapshots and greedy(MOS-greedy)algorithm of RB method is developed for nonlocal problems with random inputs,which provides an efficient and reliable approximation of the solution.A major challenge lies in the excessive influence of the time domain on the model reduction process.To address this,the Fourier transform is applied to convert the original time-dependent parabolic equation into a frequency-dependent elliptic equation,where variable frequencies are independent.This enables parallel computation for approximating the solution in the frequency domain.Finally,the proposed MOS-greedy algorithm is applied to the nonlocal diffusion problems.Numerical results demonstrate that it provides an accurate approximation of the full order problems and significantly improves computational efficiency. 展开更多
关键词 Nonlocal problems reduced basis method method of snapshots greedy algorithm Fourier transform
Direct and Inverse Problems for a Third-order Differential Operator with Anti-periodic Boundary Conditions and a Non-local Potential 认领 引用
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作者 ZHANG Mingming LIU Yixuan 《数学理论与应用》 2025年第1期62-80,共19页
This paper focuses on the direct and inverse problems for a third-order self-adjoint differential operator with non-local potential and anti-periodic boundary conditions.Firstly,we obtain the expressions for the chara... This paper focuses on the direct and inverse problems for a third-order self-adjoint differential operator with non-local potential and anti-periodic boundary conditions.Firstly,we obtain the expressions for the characteristic function and resolvent of this third-order differential operator.Secondly,by using the expression for the resolvent of the operator,we prove that the spectrum for this operator consists of simple eigenvalues and a finite number of eigenvalues with multiplicity 2.Finally,we solve the inverse problem for this operator,which states that the non-local potential function can be reconstructed from four spectra.Specially,we prove the Ambarzumyan theorem and indicate that odd or even potential functions can be reconstructed by three spectra. 展开更多
关键词 Direct problem Inverse problem Non-local potential Anti-periodic boundary condition
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Wavelet multiresolution interpolation Galerkin method for nonlinear boundary value problems with localized steep gradients 认领 引用 被引量：1
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作者 Xiaojing LIU Youhe ZHOU Jizeng WANG 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI CSCD 2022年第6期863-882,共20页
The wavelet multiresolution interpolation for continuous functions defined on a finite interval is developed in this study by using a simple alternative of transformation matrix.The wavelet multiresolution interpolati... The wavelet multiresolution interpolation for continuous functions defined on a finite interval is developed in this study by using a simple alternative of transformation matrix.The wavelet multiresolution interpolation Galerkin method that applies this interpolation to represent the unknown function and nonlinear terms independently is proposed to solve the boundary value problems with the mixed Dirichlet-Robin boundary conditions and various nonlinearities,including transcendental ones,in which the discretization process is as simple as that in solving linear problems,and only common two-term connection coefficients are needed.All matrices are independent of unknown node values and lead to high efficiency in the calculation of the residual and Jacobian matrices needed in Newton’s method,which does not require numerical integration in the resulting nonlinear discrete system.The validity of the proposed method is examined through several nonlinear problems with interior or boundary layers.The results demonstrate that the proposed wavelet method shows excellent accuracy and stability against nonuniform grids,and high resolution of localized steep gradients can be achieved by using local refined multiresolution grids.In addition,Newton’s method converges rapidly in solving the nonlinear discrete system created by the proposed wavelet method,including the initial guess far from real solutions. 展开更多
关键词 wavelet multiresolution interpolation transcendental nonlinearity localized steep gradient singularly perturbed boundary value problem Troesch’s problem
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RIEMANN-HILBERT PROBLEMS AND SOLITON SOLUTIONS OF NONLOCAL REVERSE-TIME NLS HIERARCHIES 认领 引用 被引量：4
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作者 Wenxiu MA 《Acta Mathematica Scientia》 SCIE CSCD 2022年第1期127-140,共14页
The paper aims at establishing Riemann-Hilbert problems and presenting soliton solutions for nonlocal reverse-time nonlinear Schrodinger(NLS) hierarchies associated with higher-order matrix spectral problems.The Sokho... The paper aims at establishing Riemann-Hilbert problems and presenting soliton solutions for nonlocal reverse-time nonlinear Schrodinger(NLS) hierarchies associated with higher-order matrix spectral problems.The Sokhotski-Plemelj formula is used to transform the Riemann-Hilbert problems into Gelfand-Levitan-Marchenko type integral equations.A new formulation of solutions to special Riemann-Hilbert problems with the identity jump matrix,corresponding to the reflectionless inverse scattering transforms,is proposed and applied to construction of soliton solutions to each system in the considered nonlocal reversetime NLS hierarchies. 展开更多
关键词 matrix spectral problem nonlocal reverse-time integrable equation integrable hierarchy Riemann-Hilbert problem inverse scattering transform soliton solution
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Nonlocal controllability for semilinear problems in Banach spaces 认领 引用
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作者 薛星美 吕忠 《Journal of Southeast University(English Edition)》 EI CAS 2008年第4期541-544,共4页
If A： D（A） X→X is a densely defined and closed linear operator, which generates a linear semigroup S （t） in Banach space X. The nonlocal control/ability for the following nonlocal semilinear problems： u＇ （t）... If A： D（A） X→X is a densely defined and closed linear operator, which generates a linear semigroup S （t） in Banach space X. The nonlocal control/ability for the following nonlocal semilinear problems： u＇ （t） = Au （t） ＋ Bx（ t） ＋ f（ t, u（t） ）, 0≤t ≤ T with nonlocal initial condition u（0） = u0 ＋ g（u） is discussed in Banach space X. The results show that if semigroup S（t） is strongly continuous, the functionsf and g are compact and the control B is bounded, then it is nonlocally controllable. The nonlocal controllability for the above nonlocal problem is also studied when B and W are unbounded and the semigroup S（t） is compact or strongly continuous. For illustration, a partial differential equation is worked out. 展开更多
关键词 nonlocal problem nonlocal controllability mild solution completely continuous
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LOCAL REGULARITY RESULT IN OBSTACLE PROBLEMS 认领 引用 被引量：6
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作者 高红亚 郭静 +1 位作者 左亚丽 褚玉明 《Acta Mathematica Scientia》 SCIE 2010年第1期208-214,共7页
We obtain a local regularity result for solutions to kφ,θ-obstacle problem of A-harmonic equation divA（x, u（x）, ↓△u（x）） = 0, where .A ： Ω ×R × Rn → Rn is aCarath^odory function satisfying some c... We obtain a local regularity result for solutions to kφ,θ-obstacle problem of A-harmonic equation divA（x, u（x）, ↓△u（x）） = 0, where .A ： Ω ×R × Rn → Rn is aCarath^odory function satisfying some coercivity and growth conditions with the naturalexponent 1 〈 p 〈 n, the obstacle function φ≥ 0, and the boundary data θ ∈ W1mp（Ω）. 展开更多
关键词 local regularity A-harmonic equation obstacle problem
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LOCAL REGULARITY RESULT FOR SOLUTIONS OF OBSTACLE PROBLEMS 认领 引用 被引量：22
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作者 高红亚 田会英 《Acta Mathematica Scientia》 SCIE 2004年第1期71-74,共4页
This paper gives the local regularity result for solutions to obstacle problems of A-harmonic equation divA(x, ξu(x)) = 0, |A.(x,ξ)|≈|?|p-1, when 1 < p < n and the obstacle function (?)≥0.
关键词 Local regularity obstacle problem A-harmonic equation
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ON TRANSMISSION PROBLEM FOR KIRCHHOFF TYPE WAVE EQUATION WITH A LOCALIZED NONLINEAR DISSIPATION IN BOUNDED DOMAIN 认领 引用 被引量：1
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作者 Jeong Ja Bae 《Acta Mathematica Scientia》 SCIE CSCD 2012年第3期893-906,共14页
In this article, we consider the global existence and decay rates of solutions for the transmission problem of Kirchhoff type wave equations consisting of two physi- cally different types of materials, one component i... In this article, we consider the global existence and decay rates of solutions for the transmission problem of Kirchhoff type wave equations consisting of two physi- cally different types of materials, one component is a Kirchhoff type wave equation with nonlinear time dependent localized dissipation which is effective only on a neighborhood of certain part of the boundary, while the other is a Kirchhoff type wave equation with nonlinear memory. 展开更多
关键词 Existence of solution uniform decay transmission problem Kirchhoff type wave equation boundary value problem localized dissipation
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An Improved Artificial Rabbits Optimization Algorithm with Chaotic Local Search and Opposition-Based Learning for Engineering Problems and Its Applications in Breast Cancer Problem 认领 引用 被引量：6
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作者 Feyza AltunbeyÖzbay ErdalÖzbay Farhad Soleimanian Gharehchopogh 《Computer Modeling in Engineering & Sciences》 SCIE EI 2024年第11期1067-1110,共44页
Artificial rabbits optimization(ARO)is a recently proposed biology-based optimization algorithm inspired by the detour foraging and random hiding behavior of rabbits in nature.However,for solving optimization problems... Artificial rabbits optimization(ARO)is a recently proposed biology-based optimization algorithm inspired by the detour foraging and random hiding behavior of rabbits in nature.However,for solving optimization problems,the ARO algorithm shows slow convergence speed and can fall into local minima.To overcome these drawbacks,this paper proposes chaotic opposition-based learning ARO(COARO),an improved version of the ARO algorithm that incorporates opposition-based learning(OBL)and chaotic local search(CLS)techniques.By adding OBL to ARO,the convergence speed of the algorithm increases and it explores the search space better.Chaotic maps in CLS provide rapid convergence by scanning the search space efficiently,since their ergodicity and non-repetitive properties.The proposed COARO algorithm has been tested using thirty-three distinct benchmark functions.The outcomes have been compared with the most recent optimization algorithms.Additionally,the COARO algorithm’s problem-solving capabilities have been evaluated using six different engineering design problems and compared with various other algorithms.This study also introduces a binary variant of the continuous COARO algorithm,named BCOARO.The performance of BCOARO was evaluated on the breast cancer dataset.The effectiveness of BCOARO has been compared with different feature selection algorithms.The proposed BCOARO outperforms alternative algorithms,according to the findings obtained for real applications in terms of accuracy performance,and fitness value.Extensive experiments show that the COARO and BCOARO algorithms achieve promising results compared to other metaheuristic algorithms. 展开更多
关键词 Artificial rabbit optimization binary optimization breast cancer chaotic local search engineering design problem opposition-based learning
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LOCAL EXISTENCE OF SOLUTION TO FREE BOUNDARY VALUE PROBLEM FOR COMPRESSIBLE NAVIER-STOKES EQUATIONS 认领 引用 被引量：4
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作者 刘健 《Acta Mathematica Scientia》 SCIE CSCD 2012年第4期1298-1320,共23页
This paper is concerned with the free boundary value problem for multidimensional Navier-Stokes equations with density-dependent viscosity where the flow density vanishes continuously across the free boundary. Local ... This paper is concerned with the free boundary value problem for multidimensional Navier-Stokes equations with density-dependent viscosity where the flow density vanishes continuously across the free boundary. Local （in time） existence of a weak solution is established; in particular, the density is positive and the solution is regular away from the free boundary. 展开更多
关键词 Navier-Stokes equations free boundary value problem local existence
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NON-LOCAL CONTINUUM MODEL AND ITS NUMERICAL SIMULATION FOR LOCALIZATION PROBLEM 认领 引用 被引量：1
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作者 Feng Jili Zhong Tieyi Wen Kewei 《Acta Mechanica Solida Sinica》 SCIE 1999年第1期51-62,共12页
A non-local continuum model for strain-softening simply takingplastic strain or damage vari- able as a non-local variable isderived by using the additive decomposition principle of finitedeformation gra- dient. At the... A non-local continuum model for strain-softening simply takingplastic strain or damage vari- able as a non-local variable isderived by using the additive decomposition principle of finitedeformation gra- dient. At the same time, variational equations,their finite element formulations and numerical convolutedintegration algorithm of the model in current configuration usuallycalled co-moving coordinate system are given. stability andconvergence of the model are proven by means of the weak convergencetheorem of gen- eral function and the convoluted integration theory. 展开更多
关键词 non-local model localization finite deformation
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ON TRANSMISSION PROBLEM FOR VISCOELASTIC WAVE EQUATION WITH A LOCALIZED A NONLINEAR DISSIPATION 认领 引用
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作者 Jeong Ja BAE Seong Sik KIM 《Acta Mathematica Scientia》 SCIE CSCD 2013年第2期362-374,共13页
In this article, we consider the global existence and decay rates of solutions for the transmission problem of Kirchhoff type wave equations consisting of two physically different types of materials, one component bei... In this article, we consider the global existence and decay rates of solutions for the transmission problem of Kirchhoff type wave equations consisting of two physically different types of materials, one component being a Kirchhoff type wave equation with time dependent localized dissipation which is effective only on a neighborhood of certain part of boundary, while the other being a Kirchhoff type viscoelastic wave equation with nonlinear memory 展开更多
关键词 Existence of solution uniform decay transmission problem boundary valueproblem localized dissipation
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EXISTENCE OF SOLUTIONS OF NONLOCAL PERTURBATIONS OF DIRICHLET DISCRETE NONLINEAR PROBLEMS 认领 引用 被引量：1
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作者 Alberto CABADA Nikolay D.DIMITROV 《Acta Mathematica Scientia》 SCIE CSCD 2017年第4期911-926,共16页
This paper is devoted to the study of second order nonlinear difference equations. A Nonlocal Perturbation of a Dirichlet Boundary Value Problem is considered. An exhaustive study of the related Green＇s function to t... This paper is devoted to the study of second order nonlinear difference equations. A Nonlocal Perturbation of a Dirichlet Boundary Value Problem is considered. An exhaustive study of the related Green＇s function to the linear part is done. The exact expression of the function is given, moreover the range of parameter for which it has constant sign is obtained. Using this, some existence results for the nonlinear problem are deduced from monotone iterative techniques, the classical Krasnoselski fixed point theorem or by application of recent fixed point theorems that combine both theories. 展开更多
关键词 Dirichlet boundary value problem nonlocal perturbations Green＇s function parameter dependence
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A GLOBAL LINEAR AND LOCAL QUADRATIC SINGLE-STEP NONINTERIOR CONTINUATION METHOD FOR MONOTONE SEMIDEFINITE COMPLEMENTARITY PROBLEMS 认领 引用 被引量：1
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作者 张立平 《Acta Mathematica Scientia》 SCIE 2007年第2期243-253,共11页
A noninterior continuation method is proposed for semidefinite complementarity problem （SDCP）. This method improves the noninterior continuation methods recently developed for SDCP by Chen and Tseng. The main proper... A noninterior continuation method is proposed for semidefinite complementarity problem （SDCP）. This method improves the noninterior continuation methods recently developed for SDCP by Chen and Tseng. The main properties of our method are： （i） it is well d.efined for the monotones SDCP; （ii） it has to solve just one linear system of equations at each step; （iii） it is shown to be both globally linearly convergent and locally quadratically convergent under suitable assumptions. 展开更多
关键词 Semidefinite complementarity problem noninterior continuation method,global convergence local quadratic convergence
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