The optimal control problem with a long run average cost is investigated for unknown linear discrete-time systems with additive noise.The authors propose a value iteration-based stochastic adaptive dynamic programming...The optimal control problem with a long run average cost is investigated for unknown linear discrete-time systems with additive noise.The authors propose a value iteration-based stochastic adaptive dynamic programming(VI-based SADP)algorithm,based on which the optimal controller is obtained.Different from the existing relevant work,the algorithm does not need to estimate the expectation(conditional expectation)and variance(conditional variance)of states or other relevant variables,and the convergence of the algorithm can be proved rigorously.A simulation example is given to verify the effectiveness of the proposed approach.展开更多
The aim of this paper is to establish a fundamental theory of convex analysis for the sets and functions over a discrete domain.By introducing conjugate/biconjugate functions and a discrete duality notion for the cone...The aim of this paper is to establish a fundamental theory of convex analysis for the sets and functions over a discrete domain.By introducing conjugate/biconjugate functions and a discrete duality notion for the cones over discrete domains,we study duals of optimization problems whose decision parameters are integers.In particular,we construct duality theory for integer linear programming,provide a discrete version of Slater’s condition that implies the strong duality and discuss the relationship between integrality and discrete convexity.展开更多
Discrete Tomography(DT)is a technology that uses image projection to reconstruct images.Its reconstruction problem,especially the binary image(0–1matrix)has attracted strong attention.In this study,a fixed point iter...Discrete Tomography(DT)is a technology that uses image projection to reconstruct images.Its reconstruction problem,especially the binary image(0–1matrix)has attracted strong attention.In this study,a fixed point iterative method of integer programming based on intelligent optimization is proposed to optimize the reconstructedmodel.The solution process can be divided into two procedures.First,the DT problem is reformulated into a polyhedron judgment problembased on lattice basis reduction.Second,the fixed-point iterativemethod of Dang and Ye is used to judge whether an integer point exists in the polyhedron of the previous program.All the programs involved in this study are written in MATLAB.The final experimental data show that this method is obviously better than the branch and bound method in terms of computational efficiency,especially in the case of high dimension.The branch and bound method requires more branch operations and takes a long time.It also needs to store a large number of leaf node boundaries and the corresponding consumptionmatrix,which occupies a largememory space.展开更多
In this paper we consider modeling techniques for the mathematical puzzle KenKen. It is an interesting puzzle from modeling point of view since it has different kind of mathematical restrictions that are not trivial t...In this paper we consider modeling techniques for the mathematical puzzle KenKen. It is an interesting puzzle from modeling point of view since it has different kind of mathematical restrictions that are not trivial to express as linear constraints. We give an integer program for solving KenKen and and its implementation on modeling language AMPL. Our integer program uses an innovative way for converting product restrictions into linear constraints. It can be also used for teaching various integer programming techniques in an Operations Research course.展开更多
Deadlock resolution strategies based on siphon control are widely investigated.Their computational efficiency largely depends on siphon computation.Mixed-integer programming(MIP)can be utilized for the computation of ...Deadlock resolution strategies based on siphon control are widely investigated.Their computational efficiency largely depends on siphon computation.Mixed-integer programming(MIP)can be utilized for the computation of an emptiable siphon in a Petri net(PN).Based on it,deadlock resolution strategies can be designed without requiring complete siphon enumeration that has exponential complexity.Due to this reason,various MIP methods are proposed for various subclasses of PNs.This work proposes an innovative MIP method to compute an emptiable minimal siphon(EMS)for a subclass of PNs named S^(4)PR.In particular,many particular structural characteristics of EMS in S4 PR are formalized as constraints,which greatly reduces the solution space.Experimental results show that the proposed MIP method has higher computational efficiency.Furthermore,the proposed method allows one to determine the liveness of an ordinary S^(4)PR.展开更多
Fluctuations in commodity prices should influence mining operations to continually update and adjust their mine plans in order to capture additional value under new market conditions. One of the adjustments is the cha...Fluctuations in commodity prices should influence mining operations to continually update and adjust their mine plans in order to capture additional value under new market conditions. One of the adjustments is the change in production sequencing. This paper seeks to present a method for quantifying the net present value(NPV) that may be directly attributed to the change in commodity prices. The evaluation is conducted across ten copper price scenarios. Discrete event simulation combined with mixed integer programming was used to attain a viable production strategy and to generate optimal mine plans. The analysis indicates that an increase in prices results in an increased in the NPV from$96.57M to $755.65M. In an environment where mining operations must be striving to gain as much value as possible from the rights to exploit a finite resource, it is not appropriate to keep operating under the same mine plan if commodity prices alter during the course of operations.展开更多
The paper gives an optimization model for a special type of exercise session, circuit training. Circuit training involves a series of exercises performed in rotation with minimal rest. The goal of our model is to mini...The paper gives an optimization model for a special type of exercise session, circuit training. Circuit training involves a series of exercises performed in rotation with minimal rest. The goal of our model is to minimize the total circuit time while accomplishing a number of training goals. Our primary model is a linear integer program;additional constraints are added for muscle group and intensity requirements. The model is implemented and tested on algebraic modeling language AMPL. Our computational results show that the model can return an exercise schedule for a typical real-life data set within a few seconds.展开更多
基金supported by the National Natural Science Foundation of China under Grant No.61673284the Science Development Project of Sichuan University under Grant No.2020SCUNL201。
文摘The optimal control problem with a long run average cost is investigated for unknown linear discrete-time systems with additive noise.The authors propose a value iteration-based stochastic adaptive dynamic programming(VI-based SADP)algorithm,based on which the optimal controller is obtained.Different from the existing relevant work,the algorithm does not need to estimate the expectation(conditional expectation)and variance(conditional variance)of states or other relevant variables,and the convergence of the algorithm can be proved rigorously.A simulation example is given to verify the effectiveness of the proposed approach.
基金This work has been supported by US Army Research Office Grant(No.W911NF-15-1-0223)The Scientific and Technological Research Council of Turkey Grant(No.1059B191300653).
文摘The aim of this paper is to establish a fundamental theory of convex analysis for the sets and functions over a discrete domain.By introducing conjugate/biconjugate functions and a discrete duality notion for the cones over discrete domains,we study duals of optimization problems whose decision parameters are integers.In particular,we construct duality theory for integer linear programming,provide a discrete version of Slater’s condition that implies the strong duality and discuss the relationship between integrality and discrete convexity.
基金funded by the NSFC under Grant Nos.61803279,71471091,62003231 and 51874205in part by the Qing Lan Project of Jiangsu,in part by the China Postdoctoral Science Foundation under Grant Nos.2020M671596 and 2021M692369+2 种基金in part by the Suzhou Science and Technology Development Plan Project(Key Industry Technology Innovation)under Grant No.SYG202114in part by the Natural Science Foundation of Jiangsu Province under Grant No.BK20200989Postdoctoral Research Funding Program of Jiangsu Province.
文摘Discrete Tomography(DT)is a technology that uses image projection to reconstruct images.Its reconstruction problem,especially the binary image(0–1matrix)has attracted strong attention.In this study,a fixed point iterative method of integer programming based on intelligent optimization is proposed to optimize the reconstructedmodel.The solution process can be divided into two procedures.First,the DT problem is reformulated into a polyhedron judgment problembased on lattice basis reduction.Second,the fixed-point iterativemethod of Dang and Ye is used to judge whether an integer point exists in the polyhedron of the previous program.All the programs involved in this study are written in MATLAB.The final experimental data show that this method is obviously better than the branch and bound method in terms of computational efficiency,especially in the case of high dimension.The branch and bound method requires more branch operations and takes a long time.It also needs to store a large number of leaf node boundaries and the corresponding consumptionmatrix,which occupies a largememory space.
文摘In this paper we consider modeling techniques for the mathematical puzzle KenKen. It is an interesting puzzle from modeling point of view since it has different kind of mathematical restrictions that are not trivial to express as linear constraints. We give an integer program for solving KenKen and and its implementation on modeling language AMPL. Our integer program uses an innovative way for converting product restrictions into linear constraints. It can be also used for teaching various integer programming techniques in an Operations Research course.
基金supported in part by Zhejiang Provincial Key Research and Development Program(2018C01084)Zhejiang Natural Science Foundation(LQ20F020009)Zhejiang Gongshang University,Zhejiang Provincial Key Laboratory of New Network Standards and Technologies(2013E10012)。
文摘Deadlock resolution strategies based on siphon control are widely investigated.Their computational efficiency largely depends on siphon computation.Mixed-integer programming(MIP)can be utilized for the computation of an emptiable siphon in a Petri net(PN).Based on it,deadlock resolution strategies can be designed without requiring complete siphon enumeration that has exponential complexity.Due to this reason,various MIP methods are proposed for various subclasses of PNs.This work proposes an innovative MIP method to compute an emptiable minimal siphon(EMS)for a subclass of PNs named S^(4)PR.In particular,many particular structural characteristics of EMS in S4 PR are formalized as constraints,which greatly reduces the solution space.Experimental results show that the proposed MIP method has higher computational efficiency.Furthermore,the proposed method allows one to determine the liveness of an ordinary S^(4)PR.
文摘Fluctuations in commodity prices should influence mining operations to continually update and adjust their mine plans in order to capture additional value under new market conditions. One of the adjustments is the change in production sequencing. This paper seeks to present a method for quantifying the net present value(NPV) that may be directly attributed to the change in commodity prices. The evaluation is conducted across ten copper price scenarios. Discrete event simulation combined with mixed integer programming was used to attain a viable production strategy and to generate optimal mine plans. The analysis indicates that an increase in prices results in an increased in the NPV from$96.57M to $755.65M. In an environment where mining operations must be striving to gain as much value as possible from the rights to exploit a finite resource, it is not appropriate to keep operating under the same mine plan if commodity prices alter during the course of operations.
文摘The paper gives an optimization model for a special type of exercise session, circuit training. Circuit training involves a series of exercises performed in rotation with minimal rest. The goal of our model is to minimize the total circuit time while accomplishing a number of training goals. Our primary model is a linear integer program;additional constraints are added for muscle group and intensity requirements. The model is implemented and tested on algebraic modeling language AMPL. Our computational results show that the model can return an exercise schedule for a typical real-life data set within a few seconds.
