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
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
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
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
With the rapid development of highway construction and formation of the highway network in China,the man- agement of pavement maintenance and rehabilitation （MR） activities has become important.In this paper,four di...With the rapid development of highway construction and formation of the highway network in China,the man- agement of pavement maintenance and rehabilitation （MR） activities has become important.In this paper,four discrete optimization models are proposed for different parties involved in the management system： government,highway agent,con- tractor and the common users.These four optimal decision models are formulated as linear integer programming problems with binary decision variables.The objective function and constraints are based on the pavement performance and prediction model using the pavement condition index （PCI）.Numerical experiments are carried out with the data from a highway system in Sichuan Province which show the feasibility and effectiveness of the proposed models.展开更多
In this paper we develop modeling techniques for a social partitioning problem. Different social interaction regulations are imposed during pandemics to prevent the spread of diseases. We suggest partitioning a set of...In this paper we develop modeling techniques for a social partitioning problem. Different social interaction regulations are imposed during pandemics to prevent the spread of diseases. We suggest partitioning a set of company employees as an effective way to curb the spread, and use integer programming techniques to model it. The goal of the model is to maximize the number of direct interactions between employees who are essential for company’s work subject to the constraint that all employees should be partitioned into components of no more than a certain size implied by the regulations. Then we further develop the basic model to take into account different restrictions and provisions. We also give heuristics for solving the problem. Our computational results include sensitivity analysis on some of the models and analysis of the heuristic performance.展开更多
This work addresses the multiscale optimization of the puri cation processes of antibody fragments. Chromatography decisions in the manufacturing processes are optimized, including the number of chromatography columns...This work addresses the multiscale optimization of the puri cation processes of antibody fragments. Chromatography decisions in the manufacturing processes are optimized, including the number of chromatography columns and their sizes, the number of cycles per batch, and the operational ow velocities. Data-driven models of chromatography throughput are developed considering loaded mass, ow velocity, and column bed height as the inputs, using manufacturing-scale simulated datasets based on microscale experimental data. The piecewise linear regression modeling method is adapted due to its simplicity and better prediction accuracy in comparison with other methods. Two alternative mixed-integer nonlinear programming (MINLP) models are proposed to minimize the total cost of goods per gram of the antibody puri cation process, incorporating the data-driven models. These MINLP models are then reformulated as mixed-integer linear programming (MILP) models using linearization techniques and multiparametric disaggregation. Two industrially relevant cases with different chromatography column size alternatives are investigated to demonstrate the applicability of the proposed models.展开更多
Approaches based on integer linear programming have been recently proposed for topology optimization in wireless sensor networks. They are, however, based on over-theoretical, unrealistic models. Our aim is to show th...Approaches based on integer linear programming have been recently proposed for topology optimization in wireless sensor networks. They are, however, based on over-theoretical, unrealistic models. Our aim is to show that it is possible to accommodate realistic models for energy consumption and communication protocols into integer linear programming. We analyze the maximum lifetime broadcasting topology problem and we present realistic models that are also shown to provide efficient and practical solving tools. We present a strategy to substantially speed up the convergence of the solving process of our algorithm. This strategy introduces a practical drawback, however, in the characteristics of the optimal solutions retrieved. A method to overcome this drawback is discussed. Computational experiments are reported.展开更多
One of the most important responsibilities of a supply chain manager is to decide “how much” (or “many”) of inventory items to order and how to transport them. This paper presents four mixed-integer linear program...One of the most important responsibilities of a supply chain manager is to decide “how much” (or “many”) of inventory items to order and how to transport them. This paper presents four mixed-integer linear programming models to help supply chain managers make these decisions for multiple products subject to multiple constraints when suppliers offer quantity discounts and shippers offer freight discounts. Each model deals with one of the possible combinations of all-units, incremental quantity discounts, all-weight and incremental freight discounts. The models are based on a piecewise linear approximation of the number of orders function. They allow any number of linear constraints and determine if independent or common (fixed) cycle ordering has a lower total cost. Results of computational experiments on an example problem are also presented.展开更多
This paper gives integer linear programming models for scheduling doubles tennis group competitions. The goal is to build a fair and competitive schedule for all players. Our basic model achieves that for each player ...This paper gives integer linear programming models for scheduling doubles tennis group competitions. The goal is to build a fair and competitive schedule for all players. Our basic model achieves that for each player the average ranking of his partners in all matches is as close as possible to the average ranking of his opponents in all matches. One of the variations of the basic model provides that each matchup is fair and competitive. We also give models for the case when the number of players is 4n<span style="font-family:;" "=""> </span><span style="font-family:;" "="">+</span><span style="font-family:;" "=""> </span><span style="font-family:;" "="">2, and thus one of the matches has to be singles. Our models were implemented and tested using optimization software AMPL. Computational results along with schedules for some typical situations are also given the paper.</span>展开更多
This paper gives integer linear programming (ILP) models for scheduling the League Phase of one of the most popular professional club competitions in the world, UEFA Champion’s League. There are 36 teams in the compe...This paper gives integer linear programming (ILP) models for scheduling the League Phase of one of the most popular professional club competitions in the world, UEFA Champion’s League. There are 36 teams in the competition, but each team plays only 8 other teams in the League Phase. Thus, the difficulty or ease of a team’s opponents, known as strength of schedule (SOS), compared to other teams will be different. Our main ILP model aims to minimize the maximum difference between SOS of any two teams, thus making the schedule as fair as possible. We also give a model for creating a timetable of all the matchups obtained by the first model. The models were implemented and tested using optimization software AMPL. Our main model obtained a schedule with a difference 0.4 between the highest and the lowest SOS, while that difference is 19 for the actual 2024-2025 competition. Thus, our model returns a schedule that is significantly fairer compared to the actual competition.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.
基金Project supported by the National Natural Science Foundation of China (Grant No.70671064)
文摘With the rapid development of highway construction and formation of the highway network in China,the man- agement of pavement maintenance and rehabilitation （MR） activities has become important.In this paper,four discrete optimization models are proposed for different parties involved in the management system： government,highway agent,con- tractor and the common users.These four optimal decision models are formulated as linear integer programming problems with binary decision variables.The objective function and constraints are based on the pavement performance and prediction model using the pavement condition index （PCI）.Numerical experiments are carried out with the data from a highway system in Sichuan Province which show the feasibility and effectiveness of the proposed models.
文摘In this paper we develop modeling techniques for a social partitioning problem. Different social interaction regulations are imposed during pandemics to prevent the spread of diseases. We suggest partitioning a set of company employees as an effective way to curb the spread, and use integer programming techniques to model it. The goal of the model is to maximize the number of direct interactions between employees who are essential for company’s work subject to the constraint that all employees should be partitioned into components of no more than a certain size implied by the regulations. Then we further develop the basic model to take into account different restrictions and provisions. We also give heuristics for solving the problem. Our computational results include sensitivity analysis on some of the models and analysis of the heuristic performance.
文摘This work addresses the multiscale optimization of the puri cation processes of antibody fragments. Chromatography decisions in the manufacturing processes are optimized, including the number of chromatography columns and their sizes, the number of cycles per batch, and the operational ow velocities. Data-driven models of chromatography throughput are developed considering loaded mass, ow velocity, and column bed height as the inputs, using manufacturing-scale simulated datasets based on microscale experimental data. The piecewise linear regression modeling method is adapted due to its simplicity and better prediction accuracy in comparison with other methods. Two alternative mixed-integer nonlinear programming (MINLP) models are proposed to minimize the total cost of goods per gram of the antibody puri cation process, incorporating the data-driven models. These MINLP models are then reformulated as mixed-integer linear programming (MILP) models using linearization techniques and multiparametric disaggregation. Two industrially relevant cases with different chromatography column size alternatives are investigated to demonstrate the applicability of the proposed models.
文摘Approaches based on integer linear programming have been recently proposed for topology optimization in wireless sensor networks. They are, however, based on over-theoretical, unrealistic models. Our aim is to show that it is possible to accommodate realistic models for energy consumption and communication protocols into integer linear programming. We analyze the maximum lifetime broadcasting topology problem and we present realistic models that are also shown to provide efficient and practical solving tools. We present a strategy to substantially speed up the convergence of the solving process of our algorithm. This strategy introduces a practical drawback, however, in the characteristics of the optimal solutions retrieved. A method to overcome this drawback is discussed. Computational experiments are reported.
文摘One of the most important responsibilities of a supply chain manager is to decide “how much” (or “many”) of inventory items to order and how to transport them. This paper presents four mixed-integer linear programming models to help supply chain managers make these decisions for multiple products subject to multiple constraints when suppliers offer quantity discounts and shippers offer freight discounts. Each model deals with one of the possible combinations of all-units, incremental quantity discounts, all-weight and incremental freight discounts. The models are based on a piecewise linear approximation of the number of orders function. They allow any number of linear constraints and determine if independent or common (fixed) cycle ordering has a lower total cost. Results of computational experiments on an example problem are also presented.
文摘This paper gives integer linear programming models for scheduling doubles tennis group competitions. The goal is to build a fair and competitive schedule for all players. Our basic model achieves that for each player the average ranking of his partners in all matches is as close as possible to the average ranking of his opponents in all matches. One of the variations of the basic model provides that each matchup is fair and competitive. We also give models for the case when the number of players is 4n<span style="font-family:;" "=""> </span><span style="font-family:;" "="">+</span><span style="font-family:;" "=""> </span><span style="font-family:;" "="">2, and thus one of the matches has to be singles. Our models were implemented and tested using optimization software AMPL. Computational results along with schedules for some typical situations are also given the paper.</span>
文摘This paper gives integer linear programming (ILP) models for scheduling the League Phase of one of the most popular professional club competitions in the world, UEFA Champion’s League. There are 36 teams in the competition, but each team plays only 8 other teams in the League Phase. Thus, the difficulty or ease of a team’s opponents, known as strength of schedule (SOS), compared to other teams will be different. Our main ILP model aims to minimize the maximum difference between SOS of any two teams, thus making the schedule as fair as possible. We also give a model for creating a timetable of all the matchups obtained by the first model. The models were implemented and tested using optimization software AMPL. Our main model obtained a schedule with a difference 0.4 between the highest and the lowest SOS, while that difference is 19 for the actual 2024-2025 competition. Thus, our model returns a schedule that is significantly fairer compared to the actual competition.
