For enhancing the control effectiveness,we firstly design a fuzzy logic based sliding mode controller(FSMC)for nonlinear crane systems.On basis of overhead crane dynamic characteristic,the sliding mode function with r...For enhancing the control effectiveness,we firstly design a fuzzy logic based sliding mode controller(FSMC)for nonlinear crane systems.On basis of overhead crane dynamic characteristic,the sliding mode function with regard to trolley position and payload angle.Additionally,in order to eliminate the chattering problem of sliding mode control,the fuzzy logic theory is adopted to soften the control performance.Moreover,aiming at the FSMC parameter setting problem,a DE algorithm based optimization scheme is proposed for enhancing the control performance.Finally,by implementing the computer simulation,the DE based FSMC can effectively tackle the overhead crane sway problem and avoid unexpected accident greatly.展开更多
Cracking furnace is the core device for ethylene production. In practice, multiple ethylene furnaces are usually run in parallel. The scheduling of the entire cracking furnace system has great significance when multip...Cracking furnace is the core device for ethylene production. In practice, multiple ethylene furnaces are usually run in parallel. The scheduling of the entire cracking furnace system has great significance when multiple feeds are simultaneously processed in multiple cracking furnaces with the changing of operating cost and yield of product. In this paper, given the requirements of both profit and energy saving in actual production process, a multi-objective optimization model contains two objectives, maximizing the average benefits and minimizing the average coking amount was proposed. The model can be abstracted as a multi-objective mixed integer non- linear programming problem. Considering the mixed integer decision variables of this multi-objective problem, an improved hybrid encoding non-dominated sorting genetic algorithm with mixed discrete variables （MDNSGA-II） is used to solve the Pareto optimal front of this model, the algorithm adopted crossover and muta- tion strategy with multi-operators, which overcomes the deficiency that normal genetic algorithm cannot handle the optimization problem with mixed variables. Finally, using an ethylene plant with multiple cracking furnaces as an example to illustrate the effectiveness of the scheduling results by comparing the optimization results of multi-objective and single objective model.展开更多
Due to the importance and role of systems engineering in space mission developments, optimization of Omid＇s systems engineering as a milestone to its current and future generations is focused. In this regard systems ...Due to the importance and role of systems engineering in space mission developments, optimization of Omid＇s systems engineering as a milestone to its current and future generations is focused. In this regard systems engineering management organization as the basis of optimization work flow in the conceptual design phase is proposed for improvement. To improve the systems engineering management, an agile enhanced organization chart is developed that defines various system duties. This is a type of concurrent engineering approach that promotes direct communication and data interchange between the team members. Due to the importance of decision making in the conceptual design phase, two design matrices are constructed that portray merits of various design options in terms of improved satellite life as well as specific choices of remote sensing capability for the Omid second generation（Omid-2）. Conceptual design optimization is explored considering several structural objectives as well as optimal solar energy absorption utilizing a multiple criteria decision making approach. The Eigenvector method is utilized to formulate the objective function via expert judgment. This approach is robust with respect to designer probable miss-judgment. The optimized version of Omid-2 turned out to be a passive Z-axis spin stabilized satellite made of hexagonal honeycomb configuration with carbon-epoxy side panels and Aluminum bottom plate.展开更多
I.I NTRODUCTION W ITH the advent of low-carbon economy,there has been a growing interest in harnessing renewable energy resources particularly for electricity generation.Renewable energy resources are advocated for th...I.I NTRODUCTION W ITH the advent of low-carbon economy,there has been a growing interest in harnessing renewable energy resources particularly for electricity generation.Renewable energy resources are advocated for the economic and environ-展开更多
This paper focuses on the simulation and test of the switched reluctance starter/generator systems. Through the emulational analysis of the initial starting torque, the optimal turn-on section of the power switches is...This paper focuses on the simulation and test of the switched reluctance starter/generator systems. Through the emulational analysis of the initial starting torque, the optimal turn-on section of the power switches is discovered. The fundamental theory of the generating operation is analyzed with the linearity model, and a new method is presented based on voltage pulse width modulation for the generating mode control. Through the steady-state and optimized emulation of the output power and system efficiency, the optimizational control approach for the generating mode over a wide speed range is introduced. At last, the test of the 3KW prototype system shows that the dynamic and static performance of this system is fine.展开更多
Based on the uncertainty theory, this paper is devoted to the redundancy allocation problem in repairable parallel-series systems with uncertain factors, where the failure rate, repair rate and other relative coeffici...Based on the uncertainty theory, this paper is devoted to the redundancy allocation problem in repairable parallel-series systems with uncertain factors, where the failure rate, repair rate and other relative coefficients involved are considered as uncertain variables. The availability of the system and the corresponding designing cost are considered as two optimization objectives. A crisp multiobjective optimization formulation is presented on the basis of uncertainty theory to solve this resultant problem. For solving this problem efficiently, a new multiobjective artificial bee colony algorithm is proposed to search the Pareto efficient set, which introduces rank value and crowding distance in the greedy selection strategy, applies fast non-dominated sort procedure in the exploitation search and inserts tournament selection in the onlooker bee phase. It shows that the proposed algorithm outperforms NSGA-II greatly and can solve multiobjective redundancy allocation problem efficiently. Finally, a numerical example is provided to illustrate this approach.展开更多
The controlled objects are uncertain stable,but the optimal control systems which are constituted by the controlled objects under certain conditions are certain stable. This paper analyses stability of optimal control...The controlled objects are uncertain stable,but the optimal control systems which are constituted by the controlled objects under certain conditions are certain stable. This paper analyses stability of optimal control systems which have quadric performance index via Liapunov method.展开更多
A single intersection of two phases is selected as a model to put forward a new optimal time-planning scheme for traffic light based on the model of hybrid automata for single intersection. A method of optimization is...A single intersection of two phases is selected as a model to put forward a new optimal time-planning scheme for traffic light based on the model of hybrid automata for single intersection. A method of optimization is proposed for hybrid systems, and the average queue length over all queues is used as an objective function to find an optimal switching scheme for traffic light. It is illustrated that traffic light control for single intersection is a typical hybrid system, and the optimal planning-time scheme can be obtained using the optimal hybrid systems control based on the two stages method.展开更多
Under complex currents, the motion governing equations of marine cables are complex and nonlinear, and the calculations of cable configuration and tension become difficult compared with those under the uniform or simp...Under complex currents, the motion governing equations of marine cables are complex and nonlinear, and the calculations of cable configuration and tension become difficult compared with those under the uniform or simple currents. To obtain the numerical results, the usual Newton-Raphson iteration is often adopted, but its stability depends on the initial guessed solution to the governing equations. To improve the stability of numerical calculation, this paper proposed separated the particle swarm optimization, in which the variables are separated into several groups, and the dimension of search space is reduced to facilitate the particle swarm optimization. Via the separated particle swarm optimization, these governing nonlinear equations can be solved successfully with any initial solution, and the process of numerical calculation is very stable. For the calculations of cable configuration and tension of marine cables under complex currents, the proposed separated swarm particle optimization is more effective than the other particle swarm optimizations.展开更多
An optimal feedback guidance law with disturbance rejection objective is proposed for endoatmospheric powered descent.This guidance law with an affine form is derived by solving a novel problem called Endoatmospheric ...An optimal feedback guidance law with disturbance rejection objective is proposed for endoatmospheric powered descent.This guidance law with an affine form is derived by solving a novel problem called Endoatmospheric Powered Descent Guidance with Disturbance Rejection(Endo-PDG-DR).The key idea of formulating the Endo-PDG-DR problem is dividing disturbances into two parts,modeled and unmodeled disturbances:the modeled disturbance is proactively exploited by augmenting it as a new state of a dynamics model;the unmodeled disturbance is reactively attenuated in terms of its effect on the guidance performance by adjoining a parameterized time-varying quadratic performance index in the proposed optimal guidance problem.A Pseudospectral Differential Dynamic Programming(PDDP)method is developed to solve the Endo-PDG-DR problem,and correspondingly a robust neighboring optimal state feedback law is obtained,which has two synergistic functionalities.One is adaptive optimal steering to accommodate the modeled disturbance,and the other is disturbance attenuation to compensate for the state perturbation effect induced by the unmodeled disturbance.Using the derived feedback guidance law,a disturbance rejection level is quantified,and is correspondingly optimized by designing a quadratic weighting parameter tuning law.The numerical computations of interest are performed within a pseudospectral setting,ensuring polynomial analytical solution,high computational efficiency,and reliable convergence.展开更多
For the missile with blended aero-fin and lateral impulsive thrust, a blended control autopilot is designed, which comprises an optimal controller and a control allocation module. The combined optimal/classical approa...For the missile with blended aero-fin and lateral impulsive thrust, a blended control autopilot is designed, which comprises an optimal controller and a control allocation module. The combined optimal/classical approach is applied to designing the optimal controller to determine the virtual controls, and the control allocation module is used to distribute the desired vitlual controls onto the redundant control effectors. The autopilot holds some attractive characteristics, such as simple structure, good tracking performance and robustness; moreover the actual constraints of the control effectors can be taken into account. Based on this blended control autopilot, it is found that the conflict between stability and fast tracking performance is serious when using the total acceleration as feedback. In order to avoid this problem, the transient factors in total acceleration are eliminated, so the acceleration caused only by angle of attack is used as feedback, and obvious improvement is shown. Finally, how to get reasonable acceleration feedback is discussed, and conclusion is presented that after passing the low-pass filter, the total acceleration can also be used as feedback, and satisfied tracking performance can be obtained.展开更多
The structure of the optimal solution set is derived for linear fractional programming with the representation theorem of polyhedral sets. Based on an adaptation of the convex simplex method credited to Gilmore and Go...The structure of the optimal solution set is derived for linear fractional programming with the representation theorem of polyhedral sets. Based on an adaptation of the convex simplex method credited to Gilmore and Gomory, we give the uniqueness condition of optimal solution and the computational procedures to find all optimal solutions if the uniqueness condition is not satisfied. Finally, an illustrative example is also given.展开更多
An optimal guidance law based on missile-target line-of-sight (LOS) angular rate is presented for intercepting a nonmaneuvering target. It is then integrated with sliding-mode control theory by using reaching-law of s...An optimal guidance law based on missile-target line-of-sight (LOS) angular rate is presented for intercepting a nonmaneuvering target. It is then integrated with sliding-mode control theory by using reaching-law of sliding-mode, in order to derive an optimal sliding-mode guidance law for intercepting a maneuvering target. The new guidance method's robustness against target maneuvers and good miss distance performance are proved by the second method of Lyapunov and simulation results. The presented guidance law is simple to implement in practical applications.展开更多
Returning to moon has become a top topic recently. Many studies have shown that soft landing is a challenging problem in lunar exploration. The lunar soft landing in this paper begins from a 100 km circular lunar park...Returning to moon has become a top topic recently. Many studies have shown that soft landing is a challenging problem in lunar exploration. The lunar soft landing in this paper begins from a 100 km circular lunar parking orbit. Once the landing area has been selected and it is time to deorbit for landing, a ΔV burn of 19.4 m/s is performed to establish a 100×15 km elliptical orbit. At perilune, the landing jets are ignited, and a propulsive landing is performed. A guidance and control scheme for lunar soft landing is proposed in the paper, which combines optimal theory with nonlinear neuro-control. Basically, an optimal nonlinear control law based on artificial neural network is presented, on the basis of the optimum trajectory from perilune to lunar surface in terms of Pontryagin's maximum principle according to the terminal boundary conditions and performance index. Therefore some optimal control laws can be carried out in the soft landing system due to the nonlinear mapping function of the neural network. The feasibility and validity of the control laws are verified in a simulation experiment.展开更多
This paper deals with the problem of planned lead time calculation in a Material Requirement Planning （MRP） environment under stochastic lead times. The objective is to minimize the sum of holding and backlogging co...This paper deals with the problem of planned lead time calculation in a Material Requirement Planning （MRP） environment under stochastic lead times. The objective is to minimize the sum of holding and backlogging costs. The proposed approach is based on discrete time inventory control where the decision variables are integer. Two types of systems are considered： multi-level serial-production and assembly systems. For the serial production systems （one type of component at each level）, a mathematical model is suggested. Then, it is proven that this model is equivalent to the well known discrete Newsboy Model. This directly provides the optimal values for the planned lead times. For multilevel assembly systems, a dedicated model is proposed and some properties of the decision variables and objective function are proven. These properties are used to calculate lower and upper limits on the decision variables and lower and upper bounds on the objective function. The obtained limits and bounds open the possibility to develop an efficient optimization algorithm using, for example, a Branch and Bound approach. The paper presents the proposed models in detail with corresponding proofs and se＇~eral numerical examples. Some advantages of the suggested models and perspectives of this research are discussed.展开更多
We systemically investigate the interchannel four-wave mixing (FWM) in dispersion-managed WDM systems with arbitrary launch position. We optimize the number of fiber sections, and the dispersion ratio for the system p...We systemically investigate the interchannel four-wave mixing (FWM) in dispersion-managed WDM systems with arbitrary launch position. We optimize the number of fiber sections, and the dispersion ratio for the system performance.展开更多
基金This work is supported by the Natural Science Foundation of Jiangsu Province(No.BK20160913)the Natural Science Foundation of the Jiangsu Higher Education Institutions of China(No.18KJB520035)+4 种基金the High Level Teacher Research Foundation of Nanjing University of Posts and Telecommunications(No.NY2016021)the Incubation Foundation of Nanjing University of Posts and Telecommunications(No.NY217055)Postdoctoral Foundation of Jiangsu Province(No.1701016A)Natural Science Foundation of China(No.61602259,No.61373135 and No.61672299)National Engineering Laboratory for Logistics Information Technology,YuanTong Express Co.LTD.
文摘For enhancing the control effectiveness,we firstly design a fuzzy logic based sliding mode controller(FSMC)for nonlinear crane systems.On basis of overhead crane dynamic characteristic,the sliding mode function with regard to trolley position and payload angle.Additionally,in order to eliminate the chattering problem of sliding mode control,the fuzzy logic theory is adopted to soften the control performance.Moreover,aiming at the FSMC parameter setting problem,a DE algorithm based optimization scheme is proposed for enhancing the control performance.Finally,by implementing the computer simulation,the DE based FSMC can effectively tackle the overhead crane sway problem and avoid unexpected accident greatly.
基金Supported by the National Natural Science Foundation of China(21276078)"Shu Guang"project of Shanghai Municipal Education Commission,973 Program of China(2012CB720500)the Shanghai Science and Technology Program(13QH1401200)
文摘Cracking furnace is the core device for ethylene production. In practice, multiple ethylene furnaces are usually run in parallel. The scheduling of the entire cracking furnace system has great significance when multiple feeds are simultaneously processed in multiple cracking furnaces with the changing of operating cost and yield of product. In this paper, given the requirements of both profit and energy saving in actual production process, a multi-objective optimization model contains two objectives, maximizing the average benefits and minimizing the average coking amount was proposed. The model can be abstracted as a multi-objective mixed integer non- linear programming problem. Considering the mixed integer decision variables of this multi-objective problem, an improved hybrid encoding non-dominated sorting genetic algorithm with mixed discrete variables （MDNSGA-II） is used to solve the Pareto optimal front of this model, the algorithm adopted crossover and muta- tion strategy with multi-operators, which overcomes the deficiency that normal genetic algorithm cannot handle the optimization problem with mixed variables. Finally, using an ethylene plant with multiple cracking furnaces as an example to illustrate the effectiveness of the scheduling results by comparing the optimization results of multi-objective and single objective model.
文摘Due to the importance and role of systems engineering in space mission developments, optimization of Omid＇s systems engineering as a milestone to its current and future generations is focused. In this regard systems engineering management organization as the basis of optimization work flow in the conceptual design phase is proposed for improvement. To improve the systems engineering management, an agile enhanced organization chart is developed that defines various system duties. This is a type of concurrent engineering approach that promotes direct communication and data interchange between the team members. Due to the importance of decision making in the conceptual design phase, two design matrices are constructed that portray merits of various design options in terms of improved satellite life as well as specific choices of remote sensing capability for the Omid second generation（Omid-2）. Conceptual design optimization is explored considering several structural objectives as well as optimal solar energy absorption utilizing a multiple criteria decision making approach. The Eigenvector method is utilized to formulate the objective function via expert judgment. This approach is robust with respect to designer probable miss-judgment. The optimized version of Omid-2 turned out to be a passive Z-axis spin stabilized satellite made of hexagonal honeycomb configuration with carbon-epoxy side panels and Aluminum bottom plate.
文摘I.I NTRODUCTION W ITH the advent of low-carbon economy,there has been a growing interest in harnessing renewable energy resources particularly for electricity generation.Renewable energy resources are advocated for the economic and environ-
基金supported by the Natural Sciences and Engineering Research Council of Canada(N00892)in part by National Natural Science Foundation of China(51405436,51375452,61573174)
文摘This paper focuses on the simulation and test of the switched reluctance starter/generator systems. Through the emulational analysis of the initial starting torque, the optimal turn-on section of the power switches is discovered. The fundamental theory of the generating operation is analyzed with the linearity model, and a new method is presented based on voltage pulse width modulation for the generating mode control. Through the steady-state and optimized emulation of the output power and system efficiency, the optimizational control approach for the generating mode over a wide speed range is introduced. At last, the test of the 3KW prototype system shows that the dynamic and static performance of this system is fine.
基金supported by National Natural Science Foundation of China (No. 71171199)Natural Science Foundation of Shaanxi Province of China (No. 2013JM1003)
文摘Based on the uncertainty theory, this paper is devoted to the redundancy allocation problem in repairable parallel-series systems with uncertain factors, where the failure rate, repair rate and other relative coefficients involved are considered as uncertain variables. The availability of the system and the corresponding designing cost are considered as two optimization objectives. A crisp multiobjective optimization formulation is presented on the basis of uncertainty theory to solve this resultant problem. For solving this problem efficiently, a new multiobjective artificial bee colony algorithm is proposed to search the Pareto efficient set, which introduces rank value and crowding distance in the greedy selection strategy, applies fast non-dominated sort procedure in the exploitation search and inserts tournament selection in the onlooker bee phase. It shows that the proposed algorithm outperforms NSGA-II greatly and can solve multiobjective redundancy allocation problem efficiently. Finally, a numerical example is provided to illustrate this approach.
文摘The controlled objects are uncertain stable,but the optimal control systems which are constituted by the controlled objects under certain conditions are certain stable. This paper analyses stability of optimal control systems which have quadric performance index via Liapunov method.
文摘A single intersection of two phases is selected as a model to put forward a new optimal time-planning scheme for traffic light based on the model of hybrid automata for single intersection. A method of optimization is proposed for hybrid systems, and the average queue length over all queues is used as an objective function to find an optimal switching scheme for traffic light. It is illustrated that traffic light control for single intersection is a typical hybrid system, and the optimal planning-time scheme can be obtained using the optimal hybrid systems control based on the two stages method.
基金supported by the National Natural Science Foundation of China(Grant Nos.51009092 and 51279107)the Scientific Research Foundation of State Education Ministry for the Returned Overseas Chinese Scholars
文摘Under complex currents, the motion governing equations of marine cables are complex and nonlinear, and the calculations of cable configuration and tension become difficult compared with those under the uniform or simple currents. To obtain the numerical results, the usual Newton-Raphson iteration is often adopted, but its stability depends on the initial guessed solution to the governing equations. To improve the stability of numerical calculation, this paper proposed separated the particle swarm optimization, in which the variables are separated into several groups, and the dimension of search space is reduced to facilitate the particle swarm optimization. Via the separated particle swarm optimization, these governing nonlinear equations can be solved successfully with any initial solution, and the process of numerical calculation is very stable. For the calculations of cable configuration and tension of marine cables under complex currents, the proposed separated swarm particle optimization is more effective than the other particle swarm optimizations.
基金co-supported by the National Natural Science Foundation of China(No.62103014)。
文摘An optimal feedback guidance law with disturbance rejection objective is proposed for endoatmospheric powered descent.This guidance law with an affine form is derived by solving a novel problem called Endoatmospheric Powered Descent Guidance with Disturbance Rejection(Endo-PDG-DR).The key idea of formulating the Endo-PDG-DR problem is dividing disturbances into two parts,modeled and unmodeled disturbances:the modeled disturbance is proactively exploited by augmenting it as a new state of a dynamics model;the unmodeled disturbance is reactively attenuated in terms of its effect on the guidance performance by adjoining a parameterized time-varying quadratic performance index in the proposed optimal guidance problem.A Pseudospectral Differential Dynamic Programming(PDDP)method is developed to solve the Endo-PDG-DR problem,and correspondingly a robust neighboring optimal state feedback law is obtained,which has two synergistic functionalities.One is adaptive optimal steering to accommodate the modeled disturbance,and the other is disturbance attenuation to compensate for the state perturbation effect induced by the unmodeled disturbance.Using the derived feedback guidance law,a disturbance rejection level is quantified,and is correspondingly optimized by designing a quadratic weighting parameter tuning law.The numerical computations of interest are performed within a pseudospectral setting,ensuring polynomial analytical solution,high computational efficiency,and reliable convergence.
文摘For the missile with blended aero-fin and lateral impulsive thrust, a blended control autopilot is designed, which comprises an optimal controller and a control allocation module. The combined optimal/classical approach is applied to designing the optimal controller to determine the virtual controls, and the control allocation module is used to distribute the desired vitlual controls onto the redundant control effectors. The autopilot holds some attractive characteristics, such as simple structure, good tracking performance and robustness; moreover the actual constraints of the control effectors can be taken into account. Based on this blended control autopilot, it is found that the conflict between stability and fast tracking performance is serious when using the total acceleration as feedback. In order to avoid this problem, the transient factors in total acceleration are eliminated, so the acceleration caused only by angle of attack is used as feedback, and obvious improvement is shown. Finally, how to get reasonable acceleration feedback is discussed, and conclusion is presented that after passing the low-pass filter, the total acceleration can also be used as feedback, and satisfied tracking performance can be obtained.
文摘The structure of the optimal solution set is derived for linear fractional programming with the representation theorem of polyhedral sets. Based on an adaptation of the convex simplex method credited to Gilmore and Gomory, we give the uniqueness condition of optimal solution and the computational procedures to find all optimal solutions if the uniqueness condition is not satisfied. Finally, an illustrative example is also given.
文摘An optimal guidance law based on missile-target line-of-sight (LOS) angular rate is presented for intercepting a nonmaneuvering target. It is then integrated with sliding-mode control theory by using reaching-law of sliding-mode, in order to derive an optimal sliding-mode guidance law for intercepting a maneuvering target. The new guidance method's robustness against target maneuvers and good miss distance performance are proved by the second method of Lyapunov and simulation results. The presented guidance law is simple to implement in practical applications.
基金Supported by the National Natural Science Foundation of China(Nos.11172197,11332008 and 11572215)the Natural Science Foundation of Tianjin through a key-project Grant(12JCZDJC30400)the UC MEXUS-CONACy T through the project Hybridizing Set Oriented Methods and Evolutionary Strategies to Obtain Fast and Reliable Multi-objective Optimization Algorithms
文摘Returning to moon has become a top topic recently. Many studies have shown that soft landing is a challenging problem in lunar exploration. The lunar soft landing in this paper begins from a 100 km circular lunar parking orbit. Once the landing area has been selected and it is time to deorbit for landing, a ΔV burn of 19.4 m/s is performed to establish a 100×15 km elliptical orbit. At perilune, the landing jets are ignited, and a propulsive landing is performed. A guidance and control scheme for lunar soft landing is proposed in the paper, which combines optimal theory with nonlinear neuro-control. Basically, an optimal nonlinear control law based on artificial neural network is presented, on the basis of the optimum trajectory from perilune to lunar surface in terms of Pontryagin's maximum principle according to the terminal boundary conditions and performance index. Therefore some optimal control laws can be carried out in the soft landing system due to the nonlinear mapping function of the neural network. The feasibility and validity of the control laws are verified in a simulation experiment.
文摘This paper deals with the problem of planned lead time calculation in a Material Requirement Planning （MRP） environment under stochastic lead times. The objective is to minimize the sum of holding and backlogging costs. The proposed approach is based on discrete time inventory control where the decision variables are integer. Two types of systems are considered： multi-level serial-production and assembly systems. For the serial production systems （one type of component at each level）, a mathematical model is suggested. Then, it is proven that this model is equivalent to the well known discrete Newsboy Model. This directly provides the optimal values for the planned lead times. For multilevel assembly systems, a dedicated model is proposed and some properties of the decision variables and objective function are proven. These properties are used to calculate lower and upper limits on the decision variables and lower and upper bounds on the objective function. The obtained limits and bounds open the possibility to develop an efficient optimization algorithm using, for example, a Branch and Bound approach. The paper presents the proposed models in detail with corresponding proofs and se＇~eral numerical examples. Some advantages of the suggested models and perspectives of this research are discussed.
文摘We systemically investigate the interchannel four-wave mixing (FWM) in dispersion-managed WDM systems with arbitrary launch position. We optimize the number of fiber sections, and the dispersion ratio for the system performance.
