We introduce Quafu-Qcover,an open-source cloud-based software package developed for solving combinatorial optimization problems using quantum simulators and hardware backends.Quafu-Qcover provides a standardized and c...We introduce Quafu-Qcover,an open-source cloud-based software package developed for solving combinatorial optimization problems using quantum simulators and hardware backends.Quafu-Qcover provides a standardized and comprehensive workflow that utilizes the quantum approximate optimization algorithm(QAOA).It facilitates the automatic conversion of the original problem into a quadratic unconstrained binary optimization(QUBO)model and its corresponding Ising model,which can be subsequently transformed into a weight graph.The core of Qcover relies on a graph decomposition-based classical algorithm,which efficiently derives the optimal parameters for the shallow QAOA circuit.Quafu-Qcover incorporates a dedicated compiler capable of translating QAOA circuits into physical quantum circuits that can be executed on Quafu cloud quantum computers.Compared to a general-purpose compiler,our compiler demonstrates the ability to generate shorter circuit depths,while also exhibiting superior speed performance.Additionally,the Qcover compiler has the capability to dynamically create a library of qubits coupling substructures in real-time,utilizing the most recent calibration data from the superconducting quantum devices.This ensures that computational tasks can be assigned to connected physical qubits with the highest fidelity.The Quafu-Qcover allows us to retrieve quantum computing sampling results using a task ID at any time,enabling asynchronous processing.Moreover,it incorporates modules for results preprocessing and visualization,facilitating an intuitive display of solutions for combinatorial optimization problems.We hope that Quafu-Qcover can serve as an instructive illustration for how to explore application problems on the Quafu cloud quantum computers.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
In this paper, we address one of the issues in the frequency assignment problem for cellular mobile networks in which we intend to minimize the interference levels when assigning frequencies from a limited frequency s...In this paper, we address one of the issues in the frequency assignment problem for cellular mobile networks in which we intend to minimize the interference levels when assigning frequencies from a limited frequency spectrum. In order to satisfy the increasing demand in such cellular mobile networks, we use a hybrid approach consisting of a Particle Swarm Optimization(PSO) combined with a Tabu Search(TS) algorithm. This approach takes both advantages of PSO efficiency in global optimization and TS in avoiding the premature convergence that would lead PSO to stagnate in a local minimum. Moreover, we propose a new efficient, simple, and inexpensive model for storing and evaluating solution's assignment. The purpose of this model reduces the solution's storage volume as well as the computations required to evaluate thesesolutions in comparison with the classical model. Our simulation results on the most known benchmarking instances prove the effectiveness of our proposed algorithm in comparison with previous related works in terms of convergence rate, the number of iterations, the solution storage volume and the running time required to converge to the optimal solution.展开更多
A bicubic B-spline finite element method is proposed to solve optimal control problems governed by fourth-order semilinear parabolic partial differential equations.Its key feature is the selection of bicubic B-splines...A bicubic B-spline finite element method is proposed to solve optimal control problems governed by fourth-order semilinear parabolic partial differential equations.Its key feature is the selection of bicubic B-splines as trial functions to approximate the state and costate variables in two space dimensions.A Crank-Nicolson difference scheme is constructed for time discretization.The resulting numerical solutions belong to C2in space,and the order of the coefficient matrix is low.Moreover,the Bogner-Fox-Schmit element is considered for comparison.Two numerical experiments demonstrate the feasibility and effectiveness of the proposed method.展开更多
This paper deals with the problem of recreating horizontal alignments of existing railway lines.The main objective is to propose a simple method for automatically obtaining optimized recreated alignments located as cl...This paper deals with the problem of recreating horizontal alignments of existing railway lines.The main objective is to propose a simple method for automatically obtaining optimized recreated alignments located as close as possible to an existing one.Based on a previously defined geometric model,two different constrained optimization problems are formulated.The first problem uses only the information provided by a set of points representing the track centerline while the second one also considers additional data about the existing alignment.The proposed methodology consists of a two-stage process in which both problems are solved consecutively using numerical techniques.The main results obtained applying this methodology are presented to show its performance and to prove its practical usefulness:an academic example used to compare with other methods,and a case study of a railway section located in Parga(Spain)in which the geometry of its horizontal alignment is successfully recovered.展开更多
This article is devoted to the identification, from observations or field measurements, of the hydraulic conductivity K for the saltwater intrusion problem in confined aquifers. The involved PDE model is a coupled sys...This article is devoted to the identification, from observations or field measurements, of the hydraulic conductivity K for the saltwater intrusion problem in confined aquifers. The involved PDE model is a coupled system of nonlinear parabolic-elliptic equations completed by boundary and initial conditions. The main unknowns are the saltwater/freshwater interface depth and the freshwater hydraulic head. The inverse problem is formulated as an optimization problem where the cost function is a least square functional measuring the discrepancy between experimental data and those provided by the model.Considering the exact problem as a constraint for the optimization problem and introducing the Lagrangian associated with the cost function, we prove that the optimality system has at least one solution. Moreover, the first order necessary optimality conditions are established for this optimization problem.展开更多
We present in this paper a survey of recent results on the relation between time and norm optimality for linear systems and the infinite dimensional version of Pontryagin＇s maximum principle. In particular, we discus...We present in this paper a survey of recent results on the relation between time and norm optimality for linear systems and the infinite dimensional version of Pontryagin＇s maximum principle. In particular, we discuss optimality （or nonoptimality） of singular controls satisfying the maximum principle and smoothness of the costate in function of smoothness of the target.展开更多
This paper deals with the optimal control problems of systems governed by a parabolic variational inequality coupled with a semilinear parabolic differential equations. The maximum principle and some kind of approxima...This paper deals with the optimal control problems of systems governed by a parabolic variational inequality coupled with a semilinear parabolic differential equations. The maximum principle and some kind of approximate controllability are studied.展开更多
Secret key generation(SKG)is a promising solution to the problem of wireless communications security.As the first step of SKG,channel probing affects it significantly.Although there have been some probing schemes,ther...Secret key generation(SKG)is a promising solution to the problem of wireless communications security.As the first step of SKG,channel probing affects it significantly.Although there have been some probing schemes,there is a lack of research on the optimization of the probing process.This study investigates how to optimize correlated parameters to maximize the SKG rate(SKGR)in the time-division duplex(TDD)mode.First,we build a probing model which includes the effects of transmitting power,the probing period,and the dimension of sample vectors.Based on the model,the analytical expression of the SKGR is given.Next,we formulate an optimization problem for maximizing the SKGR and give an algorithm to solve it.We conclude the SKGR monotonically increases as the transmitting power increases.Relevant mathematical proofs are given in this study.From the simulation results,increasing appropriately the probing period and the dimension of the sample vector could increase the SKGR dramatically compared to a yardstick,which indicates the importance of optimizing the parameters related to the channel probing phase.展开更多
An inexact Halley＇s method-Halley-PCG（preconditioned conjugate gradient） method is proposed for solving the systems of linear equations for improved Halley method either by Cholesky factorization exactly or by prec...An inexact Halley＇s method-Halley-PCG（preconditioned conjugate gradient） method is proposed for solving the systems of linear equations for improved Halley method either by Cholesky factorization exactly or by preconditioned conjugate gradient method approximately. The convergence result is given and the efficiency of the method compared to the improved Halley＇s method is shown.展开更多
Out-door billboard advertising plays an important role in attracting potential customers.However,whether a customer can be attracted is influenced by many factors,such as the probability that he/she sees the billboard...Out-door billboard advertising plays an important role in attracting potential customers.However,whether a customer can be attracted is influenced by many factors,such as the probability that he/she sees the billboard,the degree of his/her interest,and the detour distance for buying the product.Taking the above factors into account,we propose advertising strategies for selecting an effective set of billboards under the advertising budget to maximize commercial profit.By using the data collected by Mobile Crowdsensing(MCS),we extract potential customers’implicit information,such as their trajectories and preferences.We then study the billboard selection problem under two situations,where the advertiser may have only one or multiple products.When only one kind of product needs advertising,the billboard selection problem is formulated as the probabilistic set coverage problem.We propose two heuristic advertising strategies to greedily select advertising billboards,which achieves the expected maximum commercial profit with the lowest cost.When the advertiser has multiple products,we formulate the problem as searching for an optimal solution and adopt the simulated annealing algorithm to search for global optimum instead of local optimum.Extensive experiments based on three real-world data sets verify that our proposed advertising strategies can achieve the superior commercial profit compared with the state-of-the-art strategies.展开更多
This paper addresses a nonlinear partial differential control system arising in population dynamics.The system consist of three diffusion equations describing the evolutions of three biological species:prey,predator,a...This paper addresses a nonlinear partial differential control system arising in population dynamics.The system consist of three diffusion equations describing the evolutions of three biological species:prey,predator,and food for the prey or vegetation.The equation for the food density incorporates a hysteresis operator of generalized stop type accounting for underlying hysteresis effects occurring in the dynamical process.We study the problem of minimization of a given integral cost functional over solutions of the above system.The set-valued mapping defining the control constraint is state-dependent and its values are nonconvex as is the cost integrand as a function of the control variable.Some relaxationtype results for the minimization problem are obtained and the existence of a nearly optimal solution is established.展开更多
In this dissertation, un-powered gliding aircraft＇s optimal extended rangeproblem is discussed. The aircraft movement model was built. According to the degree of coupling, the model can be classified into a simple mo...In this dissertation, un-powered gliding aircraft＇s optimal extended rangeproblem is discussed. The aircraft movement model was built. According to the degree of coupling, the model can be classified into a simple model or a complicated model. Using an optimal control method, two different movement models gave out the aircraft＇s attitude angle optimal flight path. Complicated model＇s optimal solution can be found by the genetic algorithm. This method can transfer the analytic solution of complicated model to a numerical value solution. Comparing the simulation results of different methods, it showed that the genetic algorithm combined with the complicated model＇s numerical value solution had the best performance in control strategy. This method solved the problem in which the highly coupling complicated model＇s analytic solution was hard to obtain. It verified that the genetic algorithm has validity in the field of extended range solution searching.展开更多
基金supported by the National Natural Science Foundation of China(Grant No.92365206)the support of the China Postdoctoral Science Foundation(Certificate Number:2023M740272)+1 种基金supported by the National Natural Science Foundation of China(Grant No.12247168)China Postdoctoral Science Foundation(Certificate Number:2022TQ0036)。
文摘We introduce Quafu-Qcover,an open-source cloud-based software package developed for solving combinatorial optimization problems using quantum simulators and hardware backends.Quafu-Qcover provides a standardized and comprehensive workflow that utilizes the quantum approximate optimization algorithm(QAOA).It facilitates the automatic conversion of the original problem into a quadratic unconstrained binary optimization(QUBO)model and its corresponding Ising model,which can be subsequently transformed into a weight graph.The core of Qcover relies on a graph decomposition-based classical algorithm,which efficiently derives the optimal parameters for the shallow QAOA circuit.Quafu-Qcover incorporates a dedicated compiler capable of translating QAOA circuits into physical quantum circuits that can be executed on Quafu cloud quantum computers.Compared to a general-purpose compiler,our compiler demonstrates the ability to generate shorter circuit depths,while also exhibiting superior speed performance.Additionally,the Qcover compiler has the capability to dynamically create a library of qubits coupling substructures in real-time,utilizing the most recent calibration data from the superconducting quantum devices.This ensures that computational tasks can be assigned to connected physical qubits with the highest fidelity.The Quafu-Qcover allows us to retrieve quantum computing sampling results using a task ID at any time,enabling asynchronous processing.Moreover,it incorporates modules for results preprocessing and visualization,facilitating an intuitive display of solutions for combinatorial optimization problems.We hope that Quafu-Qcover can serve as an instructive illustration for how to explore application problems on the Quafu cloud quantum computers.
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In this paper, we address one of the issues in the frequency assignment problem for cellular mobile networks in which we intend to minimize the interference levels when assigning frequencies from a limited frequency spectrum. In order to satisfy the increasing demand in such cellular mobile networks, we use a hybrid approach consisting of a Particle Swarm Optimization(PSO) combined with a Tabu Search(TS) algorithm. This approach takes both advantages of PSO efficiency in global optimization and TS in avoiding the premature convergence that would lead PSO to stagnate in a local minimum. Moreover, we propose a new efficient, simple, and inexpensive model for storing and evaluating solution's assignment. The purpose of this model reduces the solution's storage volume as well as the computations required to evaluate thesesolutions in comparison with the classical model. Our simulation results on the most known benchmarking instances prove the effectiveness of our proposed algorithm in comparison with previous related works in terms of convergence rate, the number of iterations, the solution storage volume and the running time required to converge to the optimal solution.
基金supported by the National Natural Science Foundation of China(11871312,12131014)the Natural Science Foundation of Shandong Province,China(ZR2023MA086)。
文摘A bicubic B-spline finite element method is proposed to solve optimal control problems governed by fourth-order semilinear parabolic partial differential equations.Its key feature is the selection of bicubic B-splines as trial functions to approximate the state and costate variables in two space dimensions.A Crank-Nicolson difference scheme is constructed for time discretization.The resulting numerical solutions belong to C2in space,and the order of the coefficient matrix is low.Moreover,the Bogner-Fox-Schmit element is considered for comparison.Two numerical experiments demonstrate the feasibility and effectiveness of the proposed method.
基金founded by project TED2021129324B-I00 of the Ministerio de Ciencia e Innovación(Spain)and NextGenerationEU(European Union)the Collaboration Agreement between Consellería de Educación,Formación Profesional e Universidades(Xunta de Galicia,Spain)and Universidade de Santiago de Compostela(Spain)which regulates the Specialization Campus Campus Terra under Grant number 2022-PU014support given by Xunta de Galicia(Spain)by means of the research projects 2023 GPC GI-2084 ED431B2023/17 and GRC GI-1563-ED431C 2021/15,respectively.
文摘This paper deals with the problem of recreating horizontal alignments of existing railway lines.The main objective is to propose a simple method for automatically obtaining optimized recreated alignments located as close as possible to an existing one.Based on a previously defined geometric model,two different constrained optimization problems are formulated.The first problem uses only the information provided by a set of points representing the track centerline while the second one also considers additional data about the existing alignment.The proposed methodology consists of a two-stage process in which both problems are solved consecutively using numerical techniques.The main results obtained applying this methodology are presented to show its performance and to prove its practical usefulness:an academic example used to compare with other methods,and a case study of a railway section located in Parga(Spain)in which the geometry of its horizontal alignment is successfully recovered.
基金supported by the Natural Science Foundation of Chongqing Municipal Education Commission(KJ1706167)and the Program for the introduction of High-Level Talents(1756006,1752003).
文摘This article is devoted to the identification, from observations or field measurements, of the hydraulic conductivity K for the saltwater intrusion problem in confined aquifers. The involved PDE model is a coupled system of nonlinear parabolic-elliptic equations completed by boundary and initial conditions. The main unknowns are the saltwater/freshwater interface depth and the freshwater hydraulic head. The inverse problem is formulated as an optimization problem where the cost function is a least square functional measuring the discrepancy between experimental data and those provided by the model.Considering the exact problem as a constraint for the optimization problem and introducing the Lagrangian associated with the cost function, we prove that the optimality system has at least one solution. Moreover, the first order necessary optimality conditions are established for this optimization problem.
文摘We present in this paper a survey of recent results on the relation between time and norm optimality for linear systems and the infinite dimensional version of Pontryagin＇s maximum principle. In particular, we discuss optimality （or nonoptimality） of singular controls satisfying the maximum principle and smoothness of the costate in function of smoothness of the target.
基金This work was partially supported by the NutionalNatural Science Foundation of China
文摘This paper deals with the optimal control problems of systems governed by a parabolic variational inequality coupled with a semilinear parabolic differential equations. The maximum principle and some kind of approximate controllability are studied.
基金supported in part by the national natural science foundation of China (NSFC) under Grant61871193in part by the R&D Program of key science and technology fields in Guangdong province under Grant 2019B090912001in part by the Guangzhou Key Field R&D Program under Grant 202206030005
文摘Secret key generation(SKG)is a promising solution to the problem of wireless communications security.As the first step of SKG,channel probing affects it significantly.Although there have been some probing schemes,there is a lack of research on the optimization of the probing process.This study investigates how to optimize correlated parameters to maximize the SKG rate(SKGR)in the time-division duplex(TDD)mode.First,we build a probing model which includes the effects of transmitting power,the probing period,and the dimension of sample vectors.Based on the model,the analytical expression of the SKGR is given.Next,we formulate an optimization problem for maximizing the SKGR and give an algorithm to solve it.We conclude the SKGR monotonically increases as the transmitting power increases.Relevant mathematical proofs are given in this study.From the simulation results,increasing appropriately the probing period and the dimension of the sample vector could increase the SKGR dramatically compared to a yardstick,which indicates the importance of optimizing the parameters related to the channel probing phase.
文摘An inexact Halley＇s method-Halley-PCG（preconditioned conjugate gradient） method is proposed for solving the systems of linear equations for improved Halley method either by Cholesky factorization exactly or by preconditioned conjugate gradient method approximately. The convergence result is given and the efficiency of the method compared to the improved Halley＇s method is shown.
基金This work is supported by Jilin Science and Technology Department Key Technology Project(20190304127YY)the National Natural Science Foundations of China(1772230,61972450 and 62072209)+4 种基金Natural Science Foundations of Jilin Province(20190201022JC)National Science Key Lab Fund Project(61421010418),Innovation Capacity Building Project of Jilin Province Development and Reform Commission(2020C017-2)Changchun Science and Technology Development Project(18DY005)Key Laboratory of Defense Science and Technology Foundations(61421010418)Jilin Province Young Talents Lifting Projec(3D4196993421).
文摘Out-door billboard advertising plays an important role in attracting potential customers.However,whether a customer can be attracted is influenced by many factors,such as the probability that he/she sees the billboard,the degree of his/her interest,and the detour distance for buying the product.Taking the above factors into account,we propose advertising strategies for selecting an effective set of billboards under the advertising budget to maximize commercial profit.By using the data collected by Mobile Crowdsensing(MCS),we extract potential customers’implicit information,such as their trajectories and preferences.We then study the billboard selection problem under two situations,where the advertiser may have only one or multiple products.When only one kind of product needs advertising,the billboard selection problem is formulated as the probabilistic set coverage problem.We propose two heuristic advertising strategies to greedily select advertising billboards,which achieves the expected maximum commercial profit with the lowest cost.When the advertiser has multiple products,we formulate the problem as searching for an optimal solution and adopt the simulated annealing algorithm to search for global optimum instead of local optimum.Extensive experiments based on three real-world data sets verify that our proposed advertising strategies can achieve the superior commercial profit compared with the state-of-the-art strategies.
基金supported by National Natural Science Foundation of China(12071165 and 62076104)Natural Science Foundation of Fujian Province(2020J01072)+2 种基金Program for Innovative Research Team in Science and Technology in Fujian Province University,Quanzhou High-Level Talents Support Plan(2017ZT012)Scientific Research Funds of Huaqiao University(605-50Y 19017,605-50Y14040)supported by Ministry of Science and Higher Education of Russian Federation(075-15-2020-787,large scientific project"Fundamentals,methods and technologies for digital monitoring and forecasting of the environmental situation on the Baikal natural territory")。
文摘This paper addresses a nonlinear partial differential control system arising in population dynamics.The system consist of three diffusion equations describing the evolutions of three biological species:prey,predator,and food for the prey or vegetation.The equation for the food density incorporates a hysteresis operator of generalized stop type accounting for underlying hysteresis effects occurring in the dynamical process.We study the problem of minimization of a given integral cost functional over solutions of the above system.The set-valued mapping defining the control constraint is state-dependent and its values are nonconvex as is the cost integrand as a function of the control variable.Some relaxationtype results for the minimization problem are obtained and the existence of a nearly optimal solution is established.
基金Supported by the National Natural Science Foundation of China(11172071)
文摘In this dissertation, un-powered gliding aircraft＇s optimal extended rangeproblem is discussed. The aircraft movement model was built. According to the degree of coupling, the model can be classified into a simple model or a complicated model. Using an optimal control method, two different movement models gave out the aircraft＇s attitude angle optimal flight path. Complicated model＇s optimal solution can be found by the genetic algorithm. This method can transfer the analytic solution of complicated model to a numerical value solution. Comparing the simulation results of different methods, it showed that the genetic algorithm combined with the complicated model＇s numerical value solution had the best performance in control strategy. This method solved the problem in which the highly coupling complicated model＇s analytic solution was hard to obtain. It verified that the genetic algorithm has validity in the field of extended range solution searching.
