This paper proposes two kinds of approximate proximal point algorithms （APPA） for monotone variational inequalities, both of which can be viewed as two extended versions of Solodov and Svaiter＇s APPA in the paper ...This paper proposes two kinds of approximate proximal point algorithms （APPA） for monotone variational inequalities, both of which can be viewed as two extended versions of Solodov and Svaiter＇s APPA in the paper ＂Error bounds for proximal point subproblems and associated inexact proximal point algorithms＂ published in 2000. They are both prediction- correction methods which use the same inexactness restriction; the only difference is that they use different search directions in the correction steps. This paper also chooses an optimal step size in the two versions of the APPA to improve the profit at each iteration. Analysis also shows that the two APPAs are globally convergent under appropriate assumptions, and we can expect algorithm 2 to get more progress in every iteration than algorithm 1. Numerical experiments indicate that algorithm 2 is more efficient than algorithm 1 with the same correction step size,展开更多
In order to find roots of maximal monotone operators, this paper introduces and studies the modified approximate proximal point algorithm with an error sequence {e k} such that || ek || \leqslant hk || xk - [(x)\tilde...In order to find roots of maximal monotone operators, this paper introduces and studies the modified approximate proximal point algorithm with an error sequence {e k} such that || ek || \leqslant hk || xk - [(x)\tilde]k ||\left\| { e^k } \right\| \leqslant \eta _k \left\| { x^k - \tilde x^k } \right\| with ?k = 0￥ ( hk - 1 ) < + ￥\sum\limits_{k = 0}^\infty {\left( {\eta _k - 1} \right)} and infk \geqslant 0 hk = m\geqslant 1\mathop {\inf }\limits_{k \geqslant 0} \eta _k = \mu \geqslant 1 . Here, the restrictions on {η k} are very different from the ones on {η k}, given by He et al (Science in China Ser. A, 2002, 32 (11): 1026–1032.) that supk \geqslant 0 hk = v < 1\mathop {\sup }\limits_{k \geqslant 0} \eta _k = v . Moreover, the characteristic conditions of the convergence of the modified approximate proximal point algorithm are presented by virtue of the new technique very different from the ones given by He et al.展开更多
The Quantum Approximate Optimization Algorithm(QAOA)is an algorithmic framework for finding approximate solutions to combinatorial optimization problems.It consists of interleaved unitary transformations induced by tw...The Quantum Approximate Optimization Algorithm(QAOA)is an algorithmic framework for finding approximate solutions to combinatorial optimization problems.It consists of interleaved unitary transformations induced by two operators labelled the mixing and problem Hamiltonians.To fit this framework,one needs to transform the original problem into a suitable form and embed it into these two Hamiltonians.In this paper,for the well-known NP-hard Traveling Salesman Problem(TSP),we encode its constraints into the mixing Hamiltonian rather than the conventional approach of adding penalty terms to the problem Hamiltonian.Moreover,we map edges(routes)connecting each pair of cities to qubits,which decreases the search space significantly in comparison to other approaches.As a result,our method can achieve a higher probability for the shortest round-trip route with only half the number of qubits consumed compared to IBM Q’s approach.We argue the formalization approach presented in this paper would lead to a generalized framework for finding,in the context of QAOA,high-quality approximate solutions to NP optimization problems.展开更多
develop a mentation This paper considers the priority facility primal-dual 3-approximation algorithm for procedure, the authors further improve the location problem with penalties： The authors this problem. Combining...develop a mentation This paper considers the priority facility primal-dual 3-approximation algorithm for procedure, the authors further improve the location problem with penalties： The authors this problem. Combining with the greedy aug- previous ratio 3 to 1.8526.展开更多
This paper presents two one-pass algorithms for dynamically computing frequency counts in sliding window over a data stream-computing frequency counts exceeding user-specified threshold ε. The first algorithm constru...This paper presents two one-pass algorithms for dynamically computing frequency counts in sliding window over a data stream-computing frequency counts exceeding user-specified threshold ε. The first algorithm constructs subwindows and deletes expired sub-windows periodically in sliding window, and each sub-window maintains a summary data structure. The first algorithm outputs at most 1/ε ＋ 1 elements for frequency queries over the most recent N elements. The second algorithm adapts multiple levels method to deal with data stream. Once the sketch of the most recent N elements has been constructed, the second algorithm can provides the answers to the frequency queries over the most recent n （ n≤N） elements. The second algorithm outputs at most 1/ε ＋ 2 elements. The analytical and experimental results show that our algorithms are accurate and effective.展开更多
The connected dominating set （CDS） problem, which consists of finding a smallest connected dominating set for graphs is an NP-hard problem in the unit disk graphs （UDGs）. This paper focuses on the CDS problem in w...The connected dominating set （CDS） problem, which consists of finding a smallest connected dominating set for graphs is an NP-hard problem in the unit disk graphs （UDGs）. This paper focuses on the CDS problem in wireless networks. Investigation of some properties of independent set （IS） in UDGs shows that geometric features of nodes distribution like angle and area can be used to design efficient heuristics for the approximation algorithms. Several constant factor approximation algorithms are presented for the CDS problem in UDGs. Simulation results show that the proposed algorithms perform better than some known ones.展开更多
In this paper,we address the k-Chinese postman problem under interdiction budget constraints(the k-CPIBC problem,for short),which is a further generalization of the k-Chinese postman problem and has many practical app...In this paper,we address the k-Chinese postman problem under interdiction budget constraints(the k-CPIBC problem,for short),which is a further generalization of the k-Chinese postman problem and has many practical applications in real life.Specifically,given a weighted graph G=(V,E;w,c;v_(1))equipped with a weight function w:E→R^(+)that satisfies the triangle inequality,an interdiction cost function c:E→Z^(+),a fixed depot v_(1)∈V,an integer k∈^Z^(+)and a budget B∈N,we are asked to find a subset S_(K)■E such that c(S_(K))=∑_(e∈S_(k)c_(e))≤B and that the subgraph G\S_(k)is connected,the objective is to minimize the value min_(C_(E)\S_(k))max{w(C_(i))|C_(i)∈C_(E)\S_(K)}among such all aforementioned subsets S_(k),where C_(E)S_(k)is a set of k-tours(of G\S_(k))starting and ending at the depot v_(1),jointly traversing each edge in G\S_(k)at least once,and w(C_(i))=∑e∈C_(i)w(e)for each tour C_(i)∈C_(E)\S_(k).We obtain the following main results:(1)Given an-approximation algorithm to solve the minimization knapsack problem,we design an(α+β)-approximation algorithm to solve the k-CPIBC problem,whereβ=7/2-1/k-[1/k].(2)We present aβ-approximation algorithm to solve the special version of the k-CPIBC problem,where c(e)1 for each edge e in G and is defined in(1).展开更多
We study scheduling problems with rejection on parallel-machine.Each job consists of a processing time,a rejection cost,and a release date.The goal is to minimize the makespan of the jobs accepted when the total rejec...We study scheduling problems with rejection on parallel-machine.Each job consists of a processing time,a rejection cost,and a release date.The goal is to minimize the makespan of the jobs accepted when the total rejection cost is not larger than a given threshold.Firstly,we verify that these problems are NP-hard.Secondly,for the multiprocessor scheduling problem with rejection,we give a pseudo-polynomial algorithm and two fully polynomial approximation schemes(FPTAS for short)for fixed positive integer m,where m is the number of machines.For the scheduling problem with rejection and the job with non-identical release time on m machines,we also design a pseudo-polynomial algorithm and a fully polynomial approximation scheme when m is a fixed positive integer.We provide an approximation algorithm with the worst case performance 2 for arbitrary positive integer m.Finally,we discuss the online scheduling problem with rejection.We show that even if there are just two distinct arrive times for the jobs,there is not any online algorithm whose competitive ratio is constant for it.展开更多
Li transient concentration distribution in spherical active material particles can affect the maximum power density and the safe operating regime of the electric vehicles(EVs). On one hand, the quasiexact/exact soluti...Li transient concentration distribution in spherical active material particles can affect the maximum power density and the safe operating regime of the electric vehicles(EVs). On one hand, the quasiexact/exact solution obtained in the time/frequency domain is time-consuming and just as a reference value for approximate solutions;on the other hand, calculation errors and application range of approximate solutions not only rely on approximate algorithms but also on discharge modes. For the purpose to track the transient dynamics for Li solid-phase diffusion in spherical active particles with a tolerable error range and for a wide applicable range, it is necessary to choose optimal approximate algorithms in terms of discharge modes and the nature of active material particles. In this study, approximation methods,such as diffusion length method, polynomial profile approximation method, Padé approximation method,pseudo steady state method, eigenfunction-based Galerkin collocation method, and separation of variables method for solving Li solid-phase diffusion in spherical active particles are compared from calculation fundamentals to algorithm implementation. Furthermore, these approximate solutions are quantitatively compared to the quasi-exact/exact solution in the time/frequency domain under typical discharge modes, i.e., start-up, slow-down, and speed-up. The results obtained from the viewpoint of time-frequency analysis offer a theoretical foundation on how to track Li transient concentration profile in spherical active particles with a high precision and for a wide application range. In turn, optimal solutions of Li solid diffusion equations for spherical active particles can improve the reliability in predicting safe operating regime and estimating maximum power for automotive batteries.展开更多
In this paper,a two-stage semi-hybrid flowshop problem which appears in graphics processing is studied. For this problem, there are two machines M1 and M2, and a set of independent jobs J= {J1 ,J2 ,…,Jn }. Each Ji co...In this paper,a two-stage semi-hybrid flowshop problem which appears in graphics processing is studied. For this problem, there are two machines M1 and M2, and a set of independent jobs J= {J1 ,J2 ,…,Jn }. Each Ji consists of two tasks Ai and Bi ,and task Ai must be completed before task Bi can start. Furthermore ,task Ai can be processed on M1 for ai time units ,or on Mw for ai^J time units ,while task Bi can only be processed on M2 for bi time units. Jobs and machines are available at time zero and no preemption is allowed. The objective is to minimize the maximum job completion time. It is showed that this problem is NP-hard. And a pseudo-polynomial time optimal algorithm is presented. A polynomial time approximation algorithm with worst-case ratio 2 is also presented.展开更多
This paper presents an economic lot-sizing problem with perishable inventory and general economies of scale cost functions. For the case with backlogging allowed, a mathematical model is formulated, and several proper...This paper presents an economic lot-sizing problem with perishable inventory and general economies of scale cost functions. For the case with backlogging allowed, a mathematical model is formulated, and several properties of the optimal solutions are explored. With the help of these optimality properties, a polynomial time approximation algorithm is developed by a new method. The new method adopts a shift technique to obtain a feasible solution of subproblem and takes the optimal solution of the subproblem as an approximation solution of our problem. The worst case performance for the approximation algorithm is proven to be （4√2 ＋ 5）/7. Finally, an instance illustrates that the bound is tight.展开更多
The electrical system of CNC machine tool is very complex which involves many uncertain factors and dynamic stochastic characteristics when failure occurs.Therefore,the traditional system reliability analysis method,f...The electrical system of CNC machine tool is very complex which involves many uncertain factors and dynamic stochastic characteristics when failure occurs.Therefore,the traditional system reliability analysis method,fault tree analysis(FTA)method,based on static logic and static failure mechanism is no longer applicable for dynamic systems reliability analysis.Dynamic fault tree(DFT)analysis method can solve this problem effectively.In this method,DFT first should be pretreated to get a simplified fault tree(FT);then the FT was modularized to get the independent static subtrees and dynamic subtrees.Binary decision diagram(BDD)analysis method was used to analyze static subtrees,while an approximation algorithm was used to deal with dynamic subtrees.When the scale of each subtree is smaller than the system scale,the analysis efficiency can be improved significantly.At last,the usefulness of this DFT analysis method was proved by applying it to analyzing the reliability of electrical system.展开更多
In this paper, we investigate the/-preemptive scheduling on parallel machines to maximize the minimum machine completion time, i.e., machine covering problem with limited number of preemptions. It is aimed to obtain t...In this paper, we investigate the/-preemptive scheduling on parallel machines to maximize the minimum machine completion time, i.e., machine covering problem with limited number of preemptions. It is aimed to obtain the worst case ratio of the objective value of the optimal schedule with unlimited preemptions and that of the schedule allowed to be preempted at most i times. For the m identical machines case, we show the worst case ratio is 2m-i-1/m and we present a polynomial time algorithm which can guarantee the ratio for any 0 〈 i 〈2 m - 1. For the /-preemptive scheduling on two uniform machines case, we only need to consider the cases of i = 0 and i = 1. For both cases, we present two linear time algorithms and obtain the worst case ratios with respect to s, i.e., the ratio of the speeds of two machines.展开更多
A hybrid two-stage flowshop scheduling problem was considered which involves m identical parallel machines at Stage 1 and a burn-in processor M at Stage 2, and the makespan was taken as the minimization objective. Thi...A hybrid two-stage flowshop scheduling problem was considered which involves m identical parallel machines at Stage 1 and a burn-in processor M at Stage 2, and the makespan was taken as the minimization objective. This scheduling problem is NP-hard in general. We divide it into eight subcases. Except for the following two subcases： （1） b≥ an, max{m, B} 〈 n; （2） a1 ≤ b ≤ an, m ≤ B 〈 n, for all other subcases, their NP-hardness was proved or pointed out, corresponding approximation algorithms were conducted and their worst-case performances were estimated. In all these approximation algorithms, the Multifit and PTAS algorithms were respectively used, as the jobs were scheduled in m identical parallel machines.展开更多
A parallel related uniform machine system consists of m machines with different processing speeds. The speed of any machine is independent on jobs. In this paper, we consider online scheduling for jobs with arbitrary ...A parallel related uniform machine system consists of m machines with different processing speeds. The speed of any machine is independent on jobs. In this paper, we consider online scheduling for jobs with arbitrary release times on the parallel uniform machine system. The jobs appear over list in terms of order. An order includes the processing size and releasing time of a job. For this model, an algorithm with competitive ratio of 12 is addressed in this paper.展开更多
The multiple knapsack problem denoted by MKP (B,S,m,n) can be defined as fol- lows.A set B of n items and a set Sof m knapsacks are given such thateach item j has a profit pjand weightwj,and each knapsack i has a ca...The multiple knapsack problem denoted by MKP (B,S,m,n) can be defined as fol- lows.A set B of n items and a set Sof m knapsacks are given such thateach item j has a profit pjand weightwj,and each knapsack i has a capacity Ci.The goal is to find a subset of items of maximum profit such that they have a feasible packing in the knapsacks.MKP(B,S,m,n) is strongly NP- Complete and no polynomial- time approximation algorithm can have an approxima- tion ratio better than0 .5 .In the last ten years,semi- definite programming has been empolyed to solve some combinatorial problems successfully.This paper firstly presents a semi- definite re- laxation algorithm (MKPS) for MKP (B,S,m,n) .It is proved that MKPS have a approxima- tion ratio better than 0 .5 for a subclass of MKP (B,S,m,n) with n≤ 1 0 0 ,m≤ 5 and maxnj=1{ wj} minmi=1{ Ci} ≤ 2 3 .展开更多
A novel underwater localization algorithm for autonomous underwater vehicle(AUVs) is proposed. Taking aim at the high cost of the traditional "leader-follower" positioning,a "parallel" model is ado...A novel underwater localization algorithm for autonomous underwater vehicle(AUVs) is proposed. Taking aim at the high cost of the traditional "leader-follower" positioning,a "parallel" model is adopted to describe the localization problem. Under an unknown-but-bounded assumption for sensor noise,bearing and range measurements can be modeled as linear constraints on the configuration space of the AUVs. Merged these constraints,a convex polyhedron representing the set of all configurations consistent with the sensor measurements can be induced. Estimates for the uncertainty in the position of a single AUV or the relative positions of two or more AUVs can then be obtained by projecting this polyhedron into appropriate subspaces of the configuration space. The localization uncertain region for each AUV can be recovered by an approximation algorithm to realize underwater localization for multiple AUVs. The deduced theoretically and the simulated results show that it is an economical and practical localization method for the AUV swarm.展开更多
A novel approach that integrates occlusion culling within the view-dependent rendering framework is proposed. The algorithm uses the prioritized-layered projection（PLP） algorithm to occlude those obscured objects, a...A novel approach that integrates occlusion culling within the view-dependent rendering framework is proposed. The algorithm uses the prioritized-layered projection（PLP） algorithm to occlude those obscured objects, and uses an approximate visibility technique to accurately and efficiently determine which objects will be visible in the coming future and prefetch those objects from disk before they are rendered, view-dependent rendering technique provides the ability to change level of detail over the surface seamlessly and smoothly in real-time according to cell solidity value.展开更多
This paper considers the semi-resumable model of single machine scheduling with anon-availability period. The machine is not available for processing during a given time interval.A job cannot be completed before the n...This paper considers the semi-resumable model of single machine scheduling with anon-availability period. The machine is not available for processing during a given time interval.A job cannot be completed before the non-availability period will have to partially restartafter the machine has become available again. For the problem with objective of minimizingmakespan, the tight worst-case ratio of algorithm LPT is given, and an FPTAS is also proposed.For the problem with objective of minimizing total weighted completion time, an approximationalgorithm with worst-case ratio smaller than 2 is presented. Two special cases of the latterproblem are also considered, and improved algorithms are given.展开更多
文摘This paper proposes two kinds of approximate proximal point algorithms （APPA） for monotone variational inequalities, both of which can be viewed as two extended versions of Solodov and Svaiter＇s APPA in the paper ＂Error bounds for proximal point subproblems and associated inexact proximal point algorithms＂ published in 2000. They are both prediction- correction methods which use the same inexactness restriction; the only difference is that they use different search directions in the correction steps. This paper also chooses an optimal step size in the two versions of the APPA to improve the profit at each iteration. Analysis also shows that the two APPAs are globally convergent under appropriate assumptions, and we can expect algorithm 2 to get more progress in every iteration than algorithm 1. Numerical experiments indicate that algorithm 2 is more efficient than algorithm 1 with the same correction step size,
基金Supported both by the Teaching and Research Award Fund for Outstanding Young Teachers inHigher Educational Institutions of MOEChinaand by the Dawn Program Fund in Shanghai
文摘In order to find roots of maximal monotone operators, this paper introduces and studies the modified approximate proximal point algorithm with an error sequence {e k} such that || ek || \leqslant hk || xk - [(x)\tilde]k ||\left\| { e^k } \right\| \leqslant \eta _k \left\| { x^k - \tilde x^k } \right\| with ?k = 0￥ ( hk - 1 ) < + ￥\sum\limits_{k = 0}^\infty {\left( {\eta _k - 1} \right)} and infk \geqslant 0 hk = m\geqslant 1\mathop {\inf }\limits_{k \geqslant 0} \eta _k = \mu \geqslant 1 . Here, the restrictions on {η k} are very different from the ones on {η k}, given by He et al (Science in China Ser. A, 2002, 32 (11): 1026–1032.) that supk \geqslant 0 hk = v < 1\mathop {\sup }\limits_{k \geqslant 0} \eta _k = v . Moreover, the characteristic conditions of the convergence of the modified approximate proximal point algorithm are presented by virtue of the new technique very different from the ones given by He et al.
基金This work is supported by the Natural Science Foundation,China(Grant No.61802002)Natural Science Foundation of Anhui Province,China(Grant No.1708085MF162).
文摘The Quantum Approximate Optimization Algorithm(QAOA)is an algorithmic framework for finding approximate solutions to combinatorial optimization problems.It consists of interleaved unitary transformations induced by two operators labelled the mixing and problem Hamiltonians.To fit this framework,one needs to transform the original problem into a suitable form and embed it into these two Hamiltonians.In this paper,for the well-known NP-hard Traveling Salesman Problem(TSP),we encode its constraints into the mixing Hamiltonian rather than the conventional approach of adding penalty terms to the problem Hamiltonian.Moreover,we map edges(routes)connecting each pair of cities to qubits,which decreases the search space significantly in comparison to other approaches.As a result,our method can achieve a higher probability for the shortest round-trip route with only half the number of qubits consumed compared to IBM Q’s approach.We argue the formalization approach presented in this paper would lead to a generalized framework for finding,in the context of QAOA,high-quality approximate solutions to NP optimization problems.
基金supported by the National Natural Science Foundation of China under Grant No.11371001
文摘develop a mentation This paper considers the priority facility primal-dual 3-approximation algorithm for procedure, the authors further improve the location problem with penalties： The authors this problem. Combining with the greedy aug- previous ratio 3 to 1.8526.
基金Supported by the National Natural Science Foun-dation of China (60403027)
文摘This paper presents two one-pass algorithms for dynamically computing frequency counts in sliding window over a data stream-computing frequency counts exceeding user-specified threshold ε. The first algorithm constructs subwindows and deletes expired sub-windows periodically in sliding window, and each sub-window maintains a summary data structure. The first algorithm outputs at most 1/ε ＋ 1 elements for frequency queries over the most recent N elements. The second algorithm adapts multiple levels method to deal with data stream. Once the sketch of the most recent N elements has been constructed, the second algorithm can provides the answers to the frequency queries over the most recent n （ n≤N） elements. The second algorithm outputs at most 1/ε ＋ 2 elements. The analytical and experimental results show that our algorithms are accurate and effective.
基金supported by the National Natural Science Foundation of China under Grant No 60473090the National "11th Five-Year-Supporting-Plan" of China under Grant No 2006BAH02A0407
文摘The connected dominating set （CDS） problem, which consists of finding a smallest connected dominating set for graphs is an NP-hard problem in the unit disk graphs （UDGs）. This paper focuses on the CDS problem in wireless networks. Investigation of some properties of independent set （IS） in UDGs shows that geometric features of nodes distribution like angle and area can be used to design efficient heuristics for the approximation algorithms. Several constant factor approximation algorithms are presented for the CDS problem in UDGs. Simulation results show that the proposed algorithms perform better than some known ones.
基金supported by the National Natural Science Foundation of China(Nos.11861075,12101593)Project for Innovation Team(Cultivation)of Yunnan Province(No.202005AE-160006)+2 种基金Peng-Xiang Pan is also supported by Project of Yunnan Provincial Department of Education Science Research Fund(No.2020Y0040)Jun-Ran Lichen is also supported by Fundamental Research Funds for the Central Universities(No.buctrc202219)Jian-Ping Li is also supported by Project of Yunling Scholars Training of Yunnan Province(No.K264202011820).
文摘In this paper,we address the k-Chinese postman problem under interdiction budget constraints(the k-CPIBC problem,for short),which is a further generalization of the k-Chinese postman problem and has many practical applications in real life.Specifically,given a weighted graph G=(V,E;w,c;v_(1))equipped with a weight function w:E→R^(+)that satisfies the triangle inequality,an interdiction cost function c:E→Z^(+),a fixed depot v_(1)∈V,an integer k∈^Z^(+)and a budget B∈N,we are asked to find a subset S_(K)■E such that c(S_(K))=∑_(e∈S_(k)c_(e))≤B and that the subgraph G\S_(k)is connected,the objective is to minimize the value min_(C_(E)\S_(k))max{w(C_(i))|C_(i)∈C_(E)\S_(K)}among such all aforementioned subsets S_(k),where C_(E)S_(k)is a set of k-tours(of G\S_(k))starting and ending at the depot v_(1),jointly traversing each edge in G\S_(k)at least once,and w(C_(i))=∑e∈C_(i)w(e)for each tour C_(i)∈C_(E)\S_(k).We obtain the following main results:(1)Given an-approximation algorithm to solve the minimization knapsack problem,we design an(α+β)-approximation algorithm to solve the k-CPIBC problem,whereβ=7/2-1/k-[1/k].(2)We present aβ-approximation algorithm to solve the special version of the k-CPIBC problem,where c(e)1 for each edge e in G and is defined in(1).
基金supported by the National Natural Science Foundation of China(Nos.12271295 and 12371319)Shandong Province Natural Science Foundation(Nos.ZR2019MA061 and ZR2022MA038).
文摘We study scheduling problems with rejection on parallel-machine.Each job consists of a processing time,a rejection cost,and a release date.The goal is to minimize the makespan of the jobs accepted when the total rejection cost is not larger than a given threshold.Firstly,we verify that these problems are NP-hard.Secondly,for the multiprocessor scheduling problem with rejection,we give a pseudo-polynomial algorithm and two fully polynomial approximation schemes(FPTAS for short)for fixed positive integer m,where m is the number of machines.For the scheduling problem with rejection and the job with non-identical release time on m machines,we also design a pseudo-polynomial algorithm and a fully polynomial approximation scheme when m is a fixed positive integer.We provide an approximation algorithm with the worst case performance 2 for arbitrary positive integer m.Finally,we discuss the online scheduling problem with rejection.We show that even if there are just two distinct arrive times for the jobs,there is not any online algorithm whose competitive ratio is constant for it.
基金the financial support from the National Science Foundation of China(22078190 and 12002196)the National Key Research and Development Program of China(2020YFB1505802)。
文摘Li transient concentration distribution in spherical active material particles can affect the maximum power density and the safe operating regime of the electric vehicles(EVs). On one hand, the quasiexact/exact solution obtained in the time/frequency domain is time-consuming and just as a reference value for approximate solutions;on the other hand, calculation errors and application range of approximate solutions not only rely on approximate algorithms but also on discharge modes. For the purpose to track the transient dynamics for Li solid-phase diffusion in spherical active particles with a tolerable error range and for a wide applicable range, it is necessary to choose optimal approximate algorithms in terms of discharge modes and the nature of active material particles. In this study, approximation methods,such as diffusion length method, polynomial profile approximation method, Padé approximation method,pseudo steady state method, eigenfunction-based Galerkin collocation method, and separation of variables method for solving Li solid-phase diffusion in spherical active particles are compared from calculation fundamentals to algorithm implementation. Furthermore, these approximate solutions are quantitatively compared to the quasi-exact/exact solution in the time/frequency domain under typical discharge modes, i.e., start-up, slow-down, and speed-up. The results obtained from the viewpoint of time-frequency analysis offer a theoretical foundation on how to track Li transient concentration profile in spherical active particles with a high precision and for a wide application range. In turn, optimal solutions of Li solid diffusion equations for spherical active particles can improve the reliability in predicting safe operating regime and estimating maximum power for automotive batteries.
文摘In this paper,a two-stage semi-hybrid flowshop problem which appears in graphics processing is studied. For this problem, there are two machines M1 and M2, and a set of independent jobs J= {J1 ,J2 ,…,Jn }. Each Ji consists of two tasks Ai and Bi ,and task Ai must be completed before task Bi can start. Furthermore ,task Ai can be processed on M1 for ai time units ,or on Mw for ai^J time units ,while task Bi can only be processed on M2 for bi time units. Jobs and machines are available at time zero and no preemption is allowed. The objective is to minimize the maximum job completion time. It is showed that this problem is NP-hard. And a pseudo-polynomial time optimal algorithm is presented. A polynomial time approximation algorithm with worst-case ratio 2 is also presented.
基金supported by National Natural Science Foundation of China (No. 10671108 and 70971076)Found for the Doctoral Program of Higher Education of Ministry of Education of China (No. 20070446001)+1 种基金Innovation Planning Project of Shandong Province (No. SDYY06034)Foundation of Qufu Normal University (No. XJZ200849)
文摘This paper presents an economic lot-sizing problem with perishable inventory and general economies of scale cost functions. For the case with backlogging allowed, a mathematical model is formulated, and several properties of the optimal solutions are explored. With the help of these optimality properties, a polynomial time approximation algorithm is developed by a new method. The new method adopts a shift technique to obtain a feasible solution of subproblem and takes the optimal solution of the subproblem as an approximation solution of our problem. The worst case performance for the approximation algorithm is proven to be （4√2 ＋ 5）/7. Finally, an instance illustrates that the bound is tight.
文摘The electrical system of CNC machine tool is very complex which involves many uncertain factors and dynamic stochastic characteristics when failure occurs.Therefore,the traditional system reliability analysis method,fault tree analysis(FTA)method,based on static logic and static failure mechanism is no longer applicable for dynamic systems reliability analysis.Dynamic fault tree(DFT)analysis method can solve this problem effectively.In this method,DFT first should be pretreated to get a simplified fault tree(FT);then the FT was modularized to get the independent static subtrees and dynamic subtrees.Binary decision diagram(BDD)analysis method was used to analyze static subtrees,while an approximation algorithm was used to deal with dynamic subtrees.When the scale of each subtree is smaller than the system scale,the analysis efficiency can be improved significantly.At last,the usefulness of this DFT analysis method was proved by applying it to analyzing the reliability of electrical system.
基金Supported by the National Natural Science Foundation of China(11001242,11071220)
文摘In this paper, we investigate the/-preemptive scheduling on parallel machines to maximize the minimum machine completion time, i.e., machine covering problem with limited number of preemptions. It is aimed to obtain the worst case ratio of the objective value of the optimal schedule with unlimited preemptions and that of the schedule allowed to be preempted at most i times. For the m identical machines case, we show the worst case ratio is 2m-i-1/m and we present a polynomial time algorithm which can guarantee the ratio for any 0 〈 i 〈2 m - 1. For the /-preemptive scheduling on two uniform machines case, we only need to consider the cases of i = 0 and i = 1. For both cases, we present two linear time algorithms and obtain the worst case ratios with respect to s, i.e., the ratio of the speeds of two machines.
基金Project supported by the Science and Technology Development Fund of Shanghai University(Grant No.A.10-0101-06-0017)
文摘A hybrid two-stage flowshop scheduling problem was considered which involves m identical parallel machines at Stage 1 and a burn-in processor M at Stage 2, and the makespan was taken as the minimization objective. This scheduling problem is NP-hard in general. We divide it into eight subcases. Except for the following two subcases： （1） b≥ an, max{m, B} 〈 n; （2） a1 ≤ b ≤ an, m ≤ B 〈 n, for all other subcases, their NP-hardness was proved or pointed out, corresponding approximation algorithms were conducted and their worst-case performances were estimated. In all these approximation algorithms, the Multifit and PTAS algorithms were respectively used, as the jobs were scheduled in m identical parallel machines.
文摘A parallel related uniform machine system consists of m machines with different processing speeds. The speed of any machine is independent on jobs. In this paper, we consider online scheduling for jobs with arbitrary release times on the parallel uniform machine system. The jobs appear over list in terms of order. An order includes the processing size and releasing time of a job. For this model, an algorithm with competitive ratio of 12 is addressed in this paper.
基金Supported by the National Natural Science Foundation of China(1 9971 0 78)
文摘The multiple knapsack problem denoted by MKP (B,S,m,n) can be defined as fol- lows.A set B of n items and a set Sof m knapsacks are given such thateach item j has a profit pjand weightwj,and each knapsack i has a capacity Ci.The goal is to find a subset of items of maximum profit such that they have a feasible packing in the knapsacks.MKP(B,S,m,n) is strongly NP- Complete and no polynomial- time approximation algorithm can have an approxima- tion ratio better than0 .5 .In the last ten years,semi- definite programming has been empolyed to solve some combinatorial problems successfully.This paper firstly presents a semi- definite re- laxation algorithm (MKPS) for MKP (B,S,m,n) .It is proved that MKPS have a approxima- tion ratio better than 0 .5 for a subclass of MKP (B,S,m,n) with n≤ 1 0 0 ,m≤ 5 and maxnj=1{ wj} minmi=1{ Ci} ≤ 2 3 .
基金Sponsored by National Natural Foundation (50979093)High Technology Research and Development Program of China (2007AA809502C)Program for New Century Excellent Talents in University (NCET-06-0877)
文摘A novel underwater localization algorithm for autonomous underwater vehicle(AUVs) is proposed. Taking aim at the high cost of the traditional "leader-follower" positioning,a "parallel" model is adopted to describe the localization problem. Under an unknown-but-bounded assumption for sensor noise,bearing and range measurements can be modeled as linear constraints on the configuration space of the AUVs. Merged these constraints,a convex polyhedron representing the set of all configurations consistent with the sensor measurements can be induced. Estimates for the uncertainty in the position of a single AUV or the relative positions of two or more AUVs can then be obtained by projecting this polyhedron into appropriate subspaces of the configuration space. The localization uncertain region for each AUV can be recovered by an approximation algorithm to realize underwater localization for multiple AUVs. The deduced theoretically and the simulated results show that it is an economical and practical localization method for the AUV swarm.
文摘A novel approach that integrates occlusion culling within the view-dependent rendering framework is proposed. The algorithm uses the prioritized-layered projection（PLP） algorithm to occlude those obscured objects, and uses an approximate visibility technique to accurately and efficiently determine which objects will be visible in the coming future and prefetch those objects from disk before they are rendered, view-dependent rendering technique provides the ability to change level of detail over the surface seamlessly and smoothly in real-time according to cell solidity value.
基金Supported by the National Natural Science Foundation of China(10971191, 60021201)Fundamental Research Funds for the Central Universities(2010QNA3040)the China Postdoctoral Science Foundation
文摘This paper considers the semi-resumable model of single machine scheduling with anon-availability period. The machine is not available for processing during a given time interval.A job cannot be completed before the non-availability period will have to partially restartafter the machine has become available again. For the problem with objective of minimizingmakespan, the tight worst-case ratio of algorithm LPT is given, and an FPTAS is also proposed.For the problem with objective of minimizing total weighted completion time, an approximationalgorithm with worst-case ratio smaller than 2 is presented. Two special cases of the latterproblem are also considered, and improved algorithms are given.
