The multiple attribute decision making problems are studied, in which the information about attribute weights is partly known and the attribute values take the form of intuitionistic fuzzy numbers. The operational law...The multiple attribute decision making problems are studied, in which the information about attribute weights is partly known and the attribute values take the form of intuitionistic fuzzy numbers. The operational laws of intuitionistic fuzzy numbers are introduced, and the score function and accuracy function are presented to compare the intuitionistic fuzzy numbers. The intuitionistic fuzzy ordered weighted averaging （IFOWA） operator which is an extension of the well-known ordered weighted averaging （OWA） operator is investigated to aggregate the intuitionistic fuzzy information. In order to determine the weights of intuitionistic fuzzy ordered weighted averaging operator, a linear goal programming procedure is proposed for learning the weights from data. Finally, an example is illustrated to verify the effectiveness and practicability of the developed method.展开更多
In the last several years, there has been a marked improvement in the development of new algorithms for solving Linear Goal programming (LGP). This paper presents a survey of current methods for LGP.
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
An evolutionary nature-inspired Firefly Algorithm (FA) is employed to set the optimal osmotic dehydration parameters in a case study of papaya. In the case, the functional form of the dehydration model is established ...An evolutionary nature-inspired Firefly Algorithm (FA) is employed to set the optimal osmotic dehydration parameters in a case study of papaya. In the case, the functional form of the dehydration model is established via a response surface technique with the resulting optimization formulation being a non-linear goal programming model. For optimization, a computationally efficient, FA-driven method is employed and the resulting solution is shown to be superior to those from previous approaches for determining the osmotic process parameters. The final component of this study provides a computational experimentation performed on the FA to illustrate the relative sensitivity of this evolutionary metaheuristic approach over a range of the two key parameters that most influence its running time-the number of iterations and the number of fireflies. This sensitivity analysis revealed that for intermediate-to-high values of either of these two key parameters, the FA would always determine overall optimal solutions, while lower values of either parameter would generate greater variability in solution quality. Since the running time complexity of the FA is polynomial in the number of fireflies but linear in the number of iterations, this experimentation shows that it is more computationally practical to run the FA using a “reasonably small” number of fireflies together with a relatively larger number of iterations than the converse.展开更多
The Dantzig/Wolfe linear programming decomposition algorithm has had important economicinterpretations as well as a widespread impact on solving large scale linear programming problem.Inthis paper we consider a simila...The Dantzig/Wolfe linear programming decomposition algorithm has had important economicinterpretations as well as a widespread impact on solving large scale linear programming problem.Inthis paper we consider a similar underlying structure,where however there is only one couplinginequality or equation.With this simplification,we demonstrate how to achieve an equitable partitionof the overall coupling resource to individual subproblem constraints through a simple iterationprocedure which appears to be very efficient.展开更多
基金supported by the National Natural Science Foundation of China (70771025)the Fundamental Research Funds for the Central Universities of Hohai University (2009B04514)Humanities and Social Sciences Foundations of Ministry of Education of China(10YJA630067)
文摘The multiple attribute decision making problems are studied, in which the information about attribute weights is partly known and the attribute values take the form of intuitionistic fuzzy numbers. The operational laws of intuitionistic fuzzy numbers are introduced, and the score function and accuracy function are presented to compare the intuitionistic fuzzy numbers. The intuitionistic fuzzy ordered weighted averaging （IFOWA） operator which is an extension of the well-known ordered weighted averaging （OWA） operator is investigated to aggregate the intuitionistic fuzzy information. In order to determine the weights of intuitionistic fuzzy ordered weighted averaging operator, a linear goal programming procedure is proposed for learning the weights from data. Finally, an example is illustrated to verify the effectiveness and practicability of the developed method.
文摘In the last several years, there has been a marked improvement in the development of new algorithms for solving Linear Goal programming (LGP). This paper presents a survey of current methods for LGP.
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An evolutionary nature-inspired Firefly Algorithm (FA) is employed to set the optimal osmotic dehydration parameters in a case study of papaya. In the case, the functional form of the dehydration model is established via a response surface technique with the resulting optimization formulation being a non-linear goal programming model. For optimization, a computationally efficient, FA-driven method is employed and the resulting solution is shown to be superior to those from previous approaches for determining the osmotic process parameters. The final component of this study provides a computational experimentation performed on the FA to illustrate the relative sensitivity of this evolutionary metaheuristic approach over a range of the two key parameters that most influence its running time-the number of iterations and the number of fireflies. This sensitivity analysis revealed that for intermediate-to-high values of either of these two key parameters, the FA would always determine overall optimal solutions, while lower values of either parameter would generate greater variability in solution quality. Since the running time complexity of the FA is polynomial in the number of fireflies but linear in the number of iterations, this experimentation shows that it is more computationally practical to run the FA using a “reasonably small” number of fireflies together with a relatively larger number of iterations than the converse.
文摘The Dantzig/Wolfe linear programming decomposition algorithm has had important economicinterpretations as well as a widespread impact on solving large scale linear programming problem.Inthis paper we consider a similar underlying structure,where however there is only one couplinginequality or equation.With this simplification,we demonstrate how to achieve an equitable partitionof the overall coupling resource to individual subproblem constraints through a simple iterationprocedure which appears to be very efficient.
