During the use of robotics in applications such as antiterrorism or combat,a motion-constrained pursuer vehicle,such as a Dubins unmanned surface vehicle(USV),must get close enough(within a prescribed zero or positive...During the use of robotics in applications such as antiterrorism or combat,a motion-constrained pursuer vehicle,such as a Dubins unmanned surface vehicle(USV),must get close enough(within a prescribed zero or positive distance)to a moving target as quickly as possible,resulting in the extended minimum-time intercept problem(EMTIP).Existing research has primarily focused on the zero-distance intercept problem,MTIP,establishing the necessary or sufficient conditions for MTIP optimality,and utilizing analytic algorithms,such as root-finding algorithms,to calculate the optimal solutions.However,these approaches depend heavily on the properties of the analytic algorithm,making them inapplicable when problem settings change,such as in the case of a positive effective range or complicated target motions outside uniform rectilinear motion.In this study,an approach employing a high-accuracy and quality-guaranteed mixed-integer piecewise-linear program(QG-PWL)is proposed for the EMTIP.This program can accommodate different effective interception ranges and complicated target motions(variable velocity or complicated trajectories).The high accuracy and quality guarantees of QG-PWL originate from elegant strategies such as piecewise linearization and other developed operation strategies.The approximate error in the intercept path length is proved to be bounded to h^(2)/(4√2),where h is the piecewise length.展开更多
A novel Parsimonious Genetic Programming （PGP） algorithm together with a novel aero-engine optimum data-driven dynamic start process model based on PGP is proposed. In application of this method, first, the traditio...A novel Parsimonious Genetic Programming （PGP） algorithm together with a novel aero-engine optimum data-driven dynamic start process model based on PGP is proposed. In application of this method, first, the traditional Genetic Programming（GP） is used to generate the nonlinear input-output models that are represented in a binary tree structure; then, the Orthogonal Least Squares algorithm （OLS） is used to estimate the contribution of the branches of the tree （refer to basic function term that cannot be decomposed anymore according to special rule） to the accuracy of the model, which contributes to eliminate complex redundant subtrees and enhance GP＇s convergence speed; and finally, a simple, reliable and exact linear-in-parameter nonlinear model via GP evolution is obtained. The real aero-engine start process test data simulation and the comparisons with Support Vector Machines （SVM） validate that the proposed method can generate more applicable, interpretable models and achieve comparable, even superior results to SVM.展开更多
In this paper, a linear programming method is proposed to solve model predictive control for a class of hybrid systems. Firstly, using the （max, ＋） algebra, a typical subclass of hybrid systems called max-plus-line...In this paper, a linear programming method is proposed to solve model predictive control for a class of hybrid systems. Firstly, using the （max, ＋） algebra, a typical subclass of hybrid systems called max-plus-linear （MPL） systems is obtained. And then, model predictive control （MPC） framework is extended to MPL systems. In general, the nonlinear optimization approach or extended linear complementarity problem （ELCP） were applied to solve the MPL-MPC optimization problem. A new optimization method based on canonical forms for max-min-plus-scaling （MMPS） functions （using the operations maximization, minimization, addition and scalar multiplication） with linear constraints on the inputs is presented. The proposed approach consists in solving several linear programming problems and is more efficient than nonlinear optimization. The validity of the algorithm is illustrated by an example.展开更多
A Linear Programming DASH diet model for persons with hypertension has previously been formulated and daily minimum cost diet plans that satisfy the DASH diets’ tolerable intake level of the nutrients for 1500 mg a d...A Linear Programming DASH diet model for persons with hypertension has previously been formulated and daily minimum cost diet plans that satisfy the DASH diets’ tolerable intake level of the nutrients for 1500 mg a day Sodium level and different daily calorie levels were obtained using sample foods from the DASH diet eating plan chart. But the limitation in the use of linear programming model in selecting diet plans to meet specific nutritional requirements which normally results in the oversupply of certain nutrients was evident in the linear programming DASH diet plan obtained as the nutrient level of the diet plans obtained had wide deviations of from the DASH diets’ tolerable upper and lower intake level for the given calorie and sodium levels. Hence the need for a model that gives diet plans with minimized nutrients’ level deviations from the DASH diets’ tolerable intake level for different daily calorie and sodium level at desired cost. A weighted Goal Programming DASH diet model that minimizes the daily cost of the DASH eating plan as well as deviations of the diets’ nutrients content from the DASH diet’s tolerable intake levels is hereby presented in this work. The formulated weighted goal programming DASH diet model is further illustrated using chosen sample foods from the DASH food chart as used in the work on the linear programming DASH diet model for a 1500 mg sodium level and 2000 calories a day diet plan as well as for 1800, 2200, 2400, 2600, 2800 and 3000 daily calorie levels. A comparison of the DASH nutrients’ composition of the weighted Goal Programming DASH diet plans and those of the linear programming DASH diet plans were carried out at this sodium level and the different daily calorie levels. It was evident from the results of the comparison that the weighted goal programming DASH diet plans has minimized deviations from the DASH diet’s tolerable intake levels than those of the linear programming DASH diet plans.展开更多
This paper aims to find unit cost of a product for firms. It establishes a linear cost model to find unit cost. Linear goal programs assume a direct relationship between independent variable and dependent variable. De...This paper aims to find unit cost of a product for firms. It establishes a linear cost model to find unit cost. Linear goal programs assume a direct relationship between independent variable and dependent variable. Dependent variable of linear model is unit cost. Independent variables are cost accounting variables. They are supply cost, labor cost, and administration cost. This study assumes a direct relationship between supply-labor-administration costs and unit cost. Therefore, it establishes a linear cost model. The major research question of this study is to apply linear goal programming to cost accounting. The goal of this linear program is to find unit cost of product. This study uses quantitative method and human capital method. The main research result is linear costing model itself.展开更多
The refugee immigration problem can be considered as a special “transportation problem”. Linear Programming Model is built, where two objectives with weight in the objective function, for the shortest routes that th...The refugee immigration problem can be considered as a special “transportation problem”. Linear Programming Model is built, where two objectives with weight in the objective function, for the shortest routes that the refugees go along and the minimum number of refugees stayed in each country. An example of EU is introduced and calculated on Lingo software. The results show that the model is available to solve the refugee immigration problem in different scale.展开更多
In this paper, we provide a new approach to solve approximately a system of fractional differential equations (FDEs). We extend this approach for approximately solving a fractional-order differential equation model of...In this paper, we provide a new approach to solve approximately a system of fractional differential equations (FDEs). We extend this approach for approximately solving a fractional-order differential equation model of HIV infection of CD4<sup>+</sup>T cells with therapy effect. The fractional derivative in our approach is in the sense of Riemann-Liouville. To solve the problem, we reduce the system of FDE to a discrete optimization problem. By obtaining the optimal solutions of new problem by minimization the total errors, we obtain the approximate solution of the original problem. The numerical solutions obtained from the proposed approach indicate that our approximation is easy to implement and accurate when it is applied to a systems of FDEs.展开更多
As one part of the Landstad International Metropolitan Area,Utrecht has become known as one of the best tourist destinations in recent years,with the rapid growth of worldwide travel trends.In this paper,through the a...As one part of the Landstad International Metropolitan Area,Utrecht has become known as one of the best tourist destinations in recent years,with the rapid growth of worldwide travel trends.In this paper,through the adaption of the linear programming model,the paper intends to not only quantify the optimum number of visitors to Utrecht but also formulate a number of policy recommendations based on the reconstruction of this optimum.The paper draws the following conclusions:(1) tourist carrying capacity of Utrecht is not yet exceeded;(2) restrictive accommodation policy does not currently seem necessary;(3) the cultural-historical attractions are not yet optimally used;(4) investing in strategic provisions is currently not necessary.And from the conclusion,the paper further puts forward the following suggestions on the city’s tourism development strategy:(1) to identify "tourist flood plains";(2) to encourage the tourist disclosure of these alternatives;(3) to invest even more explicitly in residential tourism and,where possible,curb day tourism;(4) to introduce a new business model.展开更多
With the reform of the power system further deepening,the reliance on electricity and importance attached to the reliable power supply are increasing year by year,and the establishment of a high resilient power system...With the reform of the power system further deepening,the reliance on electricity and importance attached to the reliable power supply are increasing year by year,and the establishment of a high resilient power system has considerable economic,environmental and social benefits.Reconfiguring the network is one of the well-known tactics to enhance reliability.Accordingly,this paper proposes a reconfiguration method of distribution network considering the enhancement of reliability,which reconfigures the network structure both under normal operation conditions and outage scenarios,and considers factors such as power loss,load distribution and voltage quality considered in conventional reconfiguration methods.In this paper,the reliability assessment is integrated into the process of distribution network reconfiguration by using binary variables to represent the operating state of switchable devices.Based on the concept of fictitious fault flows,the reliability indices of distribution network are linearized expressed,and the network loss is reduced by minimizing the voltage deviation.A mixed integer linear programming(MILP)model is established for distribution network reconfiguration problem,which can guarantee the global optimal solution with high solution efficiency.Finally,the applicability and effectiveness of the proposed method are verified by numerical tests on a 54-node test system.展开更多
In this study, Simplex Method, a Linear Programming technique was used to create a mathematical model that optimized the financial portfolio of Golden Guinea Breweries Plc, Nigeria. This work was motivated by the obse...In this study, Simplex Method, a Linear Programming technique was used to create a mathematical model that optimized the financial portfolio of Golden Guinea Breweries Plc, Nigeria. This work was motivated by the observed and anticipated miscalculations which Golden Guinea Breweries was bound to face if appropriate linear programming techniques were not applied in determining the profit level. This study therefore aims at using Simplex Method to create a Mathematical Model that will optimize the production of brewed drinks for Golden Guinea Breweries Plc. The first methodology involved the collection of sample data from the company, analyzed and the relevant coefficients were deployed for the coding of the model. Secondly, the indices collected from the first method were deployed in the software model called PHP simplex, an online software for solving Linear Programming Problem to access the profitability of the organization. The study showed that Linear Programming Model would give a high profit coefficient of N9,190,862,833 when compared with the result obtained from the manual computation which gave a profit coefficient of N7,172,093,375. Also, Bergedoff Lager, Eagle Stout and Bergedoff Malta were found not to contribute to overall profitability of the company and it was therefore recommended that their productions should be discontinued. It also recommends that various quantities of Golden Guinea Lager (1 × 12) and Golden Guinea Lager (1 × 24) should be produced.展开更多
Plant invasion refers to the phenomenon that some plants grow too fast due to they are far away from the original living environment or predators, affecting the local environment. With the development of tourism and t...Plant invasion refers to the phenomenon that some plants grow too fast due to they are far away from the original living environment or predators, affecting the local environment. With the development of tourism and trade, the harm caused by invasive plants will be more and more serious. Therefore, it is necessary to ex- plore an effective method for controlling plant invasion through qualitative and quan- titative research. In this paper, the models were established for the early and late harmful plant invasion control. The huge computation was completed by the com- puter programming to obtain the optimal solutions of the models. The real meaning of the optimal solution was further discussed. Through numerical simulations and discussion, it could be concluded that the quantitative research on the invasive plant control had a certain application value.展开更多
Intelligent process planning(PP)is one of the most important components in an intelligent manufacturing system and acts as a bridge between product designing and practical manufacturing.PP is a nondeterministic polyno...Intelligent process planning(PP)is one of the most important components in an intelligent manufacturing system and acts as a bridge between product designing and practical manufacturing.PP is a nondeterministic polynomial-time(NP)-hard problem and,as existing mathematical models are not formulated in linear forms,they cannot be solved well to achieve exact solutions for PP problems.This paper proposes a novel mixed-integer linear programming(MILP)mathematical model by considering the network topology structure and the OR nodes that represent a type of OR logic inside the network.Precedence relationships between operations are discussed by raising three types of precedence relationship matrices.Furthermore,the proposed model can be programmed in commonly-used mathematical programming solvers,such as CPLEX,Gurobi,and so forth,to search for optimal solutions for most open problems.To verify the effectiveness and generality of the proposed model,five groups of numerical experiments are conducted on well-known benchmarks.The results show that the proposed model can solve PP problems effectively and can obtain better solutions than those obtained by the state-ofthe-art algorithms.展开更多
基金supported by the National Natural Sci‐ence Foundation of China(Grant No.62306325)。
文摘During the use of robotics in applications such as antiterrorism or combat,a motion-constrained pursuer vehicle,such as a Dubins unmanned surface vehicle(USV),must get close enough(within a prescribed zero or positive distance)to a moving target as quickly as possible,resulting in the extended minimum-time intercept problem(EMTIP).Existing research has primarily focused on the zero-distance intercept problem,MTIP,establishing the necessary or sufficient conditions for MTIP optimality,and utilizing analytic algorithms,such as root-finding algorithms,to calculate the optimal solutions.However,these approaches depend heavily on the properties of the analytic algorithm,making them inapplicable when problem settings change,such as in the case of a positive effective range or complicated target motions outside uniform rectilinear motion.In this study,an approach employing a high-accuracy and quality-guaranteed mixed-integer piecewise-linear program(QG-PWL)is proposed for the EMTIP.This program can accommodate different effective interception ranges and complicated target motions(variable velocity or complicated trajectories).The high accuracy and quality guarantees of QG-PWL originate from elegant strategies such as piecewise linearization and other developed operation strategies.The approximate error in the intercept path length is proved to be bounded to h^(2)/(4√2),where h is the piecewise length.
基金National Defense Advanced Research Foundation of China
文摘A novel Parsimonious Genetic Programming （PGP） algorithm together with a novel aero-engine optimum data-driven dynamic start process model based on PGP is proposed. In application of this method, first, the traditional Genetic Programming（GP） is used to generate the nonlinear input-output models that are represented in a binary tree structure; then, the Orthogonal Least Squares algorithm （OLS） is used to estimate the contribution of the branches of the tree （refer to basic function term that cannot be decomposed anymore according to special rule） to the accuracy of the model, which contributes to eliminate complex redundant subtrees and enhance GP＇s convergence speed; and finally, a simple, reliable and exact linear-in-parameter nonlinear model via GP evolution is obtained. The real aero-engine start process test data simulation and the comparisons with Support Vector Machines （SVM） validate that the proposed method can generate more applicable, interpretable models and achieve comparable, even superior results to SVM.
基金This work was supported by the National Science Foundation of China (No. 60474051)the program for New Century Excellent Talents in University of China (NCET).
文摘In this paper, a linear programming method is proposed to solve model predictive control for a class of hybrid systems. Firstly, using the （max, ＋） algebra, a typical subclass of hybrid systems called max-plus-linear （MPL） systems is obtained. And then, model predictive control （MPC） framework is extended to MPL systems. In general, the nonlinear optimization approach or extended linear complementarity problem （ELCP） were applied to solve the MPL-MPC optimization problem. A new optimization method based on canonical forms for max-min-plus-scaling （MMPS） functions （using the operations maximization, minimization, addition and scalar multiplication） with linear constraints on the inputs is presented. The proposed approach consists in solving several linear programming problems and is more efficient than nonlinear optimization. The validity of the algorithm is illustrated by an example.
文摘A Linear Programming DASH diet model for persons with hypertension has previously been formulated and daily minimum cost diet plans that satisfy the DASH diets’ tolerable intake level of the nutrients for 1500 mg a day Sodium level and different daily calorie levels were obtained using sample foods from the DASH diet eating plan chart. But the limitation in the use of linear programming model in selecting diet plans to meet specific nutritional requirements which normally results in the oversupply of certain nutrients was evident in the linear programming DASH diet plan obtained as the nutrient level of the diet plans obtained had wide deviations of from the DASH diets’ tolerable upper and lower intake level for the given calorie and sodium levels. Hence the need for a model that gives diet plans with minimized nutrients’ level deviations from the DASH diets’ tolerable intake level for different daily calorie and sodium level at desired cost. A weighted Goal Programming DASH diet model that minimizes the daily cost of the DASH eating plan as well as deviations of the diets’ nutrients content from the DASH diet’s tolerable intake levels is hereby presented in this work. The formulated weighted goal programming DASH diet model is further illustrated using chosen sample foods from the DASH food chart as used in the work on the linear programming DASH diet model for a 1500 mg sodium level and 2000 calories a day diet plan as well as for 1800, 2200, 2400, 2600, 2800 and 3000 daily calorie levels. A comparison of the DASH nutrients’ composition of the weighted Goal Programming DASH diet plans and those of the linear programming DASH diet plans were carried out at this sodium level and the different daily calorie levels. It was evident from the results of the comparison that the weighted goal programming DASH diet plans has minimized deviations from the DASH diet’s tolerable intake levels than those of the linear programming DASH diet plans.
文摘This paper aims to find unit cost of a product for firms. It establishes a linear cost model to find unit cost. Linear goal programs assume a direct relationship between independent variable and dependent variable. Dependent variable of linear model is unit cost. Independent variables are cost accounting variables. They are supply cost, labor cost, and administration cost. This study assumes a direct relationship between supply-labor-administration costs and unit cost. Therefore, it establishes a linear cost model. The major research question of this study is to apply linear goal programming to cost accounting. The goal of this linear program is to find unit cost of product. This study uses quantitative method and human capital method. The main research result is linear costing model itself.
文摘The refugee immigration problem can be considered as a special “transportation problem”. Linear Programming Model is built, where two objectives with weight in the objective function, for the shortest routes that the refugees go along and the minimum number of refugees stayed in each country. An example of EU is introduced and calculated on Lingo software. The results show that the model is available to solve the refugee immigration problem in different scale.
文摘In this paper, we provide a new approach to solve approximately a system of fractional differential equations (FDEs). We extend this approach for approximately solving a fractional-order differential equation model of HIV infection of CD4<sup>+</sup>T cells with therapy effect. The fractional derivative in our approach is in the sense of Riemann-Liouville. To solve the problem, we reduce the system of FDE to a discrete optimization problem. By obtaining the optimal solutions of new problem by minimization the total errors, we obtain the approximate solution of the original problem. The numerical solutions obtained from the proposed approach indicate that our approximation is easy to implement and accurate when it is applied to a systems of FDEs.
文摘As one part of the Landstad International Metropolitan Area,Utrecht has become known as one of the best tourist destinations in recent years,with the rapid growth of worldwide travel trends.In this paper,through the adaption of the linear programming model,the paper intends to not only quantify the optimum number of visitors to Utrecht but also formulate a number of policy recommendations based on the reconstruction of this optimum.The paper draws the following conclusions:(1) tourist carrying capacity of Utrecht is not yet exceeded;(2) restrictive accommodation policy does not currently seem necessary;(3) the cultural-historical attractions are not yet optimally used;(4) investing in strategic provisions is currently not necessary.And from the conclusion,the paper further puts forward the following suggestions on the city’s tourism development strategy:(1) to identify "tourist flood plains";(2) to encourage the tourist disclosure of these alternatives;(3) to invest even more explicitly in residential tourism and,where possible,curb day tourism;(4) to introduce a new business model.
基金supported by the Natural Science Foundation of Jiangsu Province(Grant No.BK20221165).
文摘With the reform of the power system further deepening,the reliance on electricity and importance attached to the reliable power supply are increasing year by year,and the establishment of a high resilient power system has considerable economic,environmental and social benefits.Reconfiguring the network is one of the well-known tactics to enhance reliability.Accordingly,this paper proposes a reconfiguration method of distribution network considering the enhancement of reliability,which reconfigures the network structure both under normal operation conditions and outage scenarios,and considers factors such as power loss,load distribution and voltage quality considered in conventional reconfiguration methods.In this paper,the reliability assessment is integrated into the process of distribution network reconfiguration by using binary variables to represent the operating state of switchable devices.Based on the concept of fictitious fault flows,the reliability indices of distribution network are linearized expressed,and the network loss is reduced by minimizing the voltage deviation.A mixed integer linear programming(MILP)model is established for distribution network reconfiguration problem,which can guarantee the global optimal solution with high solution efficiency.Finally,the applicability and effectiveness of the proposed method are verified by numerical tests on a 54-node test system.
文摘In this study, Simplex Method, a Linear Programming technique was used to create a mathematical model that optimized the financial portfolio of Golden Guinea Breweries Plc, Nigeria. This work was motivated by the observed and anticipated miscalculations which Golden Guinea Breweries was bound to face if appropriate linear programming techniques were not applied in determining the profit level. This study therefore aims at using Simplex Method to create a Mathematical Model that will optimize the production of brewed drinks for Golden Guinea Breweries Plc. The first methodology involved the collection of sample data from the company, analyzed and the relevant coefficients were deployed for the coding of the model. Secondly, the indices collected from the first method were deployed in the software model called PHP simplex, an online software for solving Linear Programming Problem to access the profitability of the organization. The study showed that Linear Programming Model would give a high profit coefficient of N9,190,862,833 when compared with the result obtained from the manual computation which gave a profit coefficient of N7,172,093,375. Also, Bergedoff Lager, Eagle Stout and Bergedoff Malta were found not to contribute to overall profitability of the company and it was therefore recommended that their productions should be discontinued. It also recommends that various quantities of Golden Guinea Lager (1 × 12) and Golden Guinea Lager (1 × 24) should be produced.
文摘Plant invasion refers to the phenomenon that some plants grow too fast due to they are far away from the original living environment or predators, affecting the local environment. With the development of tourism and trade, the harm caused by invasive plants will be more and more serious. Therefore, it is necessary to ex- plore an effective method for controlling plant invasion through qualitative and quan- titative research. In this paper, the models were established for the early and late harmful plant invasion control. The huge computation was completed by the com- puter programming to obtain the optimal solutions of the models. The real meaning of the optimal solution was further discussed. Through numerical simulations and discussion, it could be concluded that the quantitative research on the invasive plant control had a certain application value.
基金supported in part by the National Natural Science Foundation of China(51825502,51775216)in part by the Program for Huazhong University of Science and Technology(HUST)Academic Frontier Youth Team(2017QYTD04).
文摘Intelligent process planning(PP)is one of the most important components in an intelligent manufacturing system and acts as a bridge between product designing and practical manufacturing.PP is a nondeterministic polynomial-time(NP)-hard problem and,as existing mathematical models are not formulated in linear forms,they cannot be solved well to achieve exact solutions for PP problems.This paper proposes a novel mixed-integer linear programming(MILP)mathematical model by considering the network topology structure and the OR nodes that represent a type of OR logic inside the network.Precedence relationships between operations are discussed by raising three types of precedence relationship matrices.Furthermore,the proposed model can be programmed in commonly-used mathematical programming solvers,such as CPLEX,Gurobi,and so forth,to search for optimal solutions for most open problems.To verify the effectiveness and generality of the proposed model,five groups of numerical experiments are conducted on well-known benchmarks.The results show that the proposed model can solve PP problems effectively and can obtain better solutions than those obtained by the state-ofthe-art algorithms.
