In this paper, some necessary and sufficient optimality conditions are obtained for a fractional multiple objective programming involving semilocal E-convex and related functions. Also, some dual results are establish...In this paper, some necessary and sufficient optimality conditions are obtained for a fractional multiple objective programming involving semilocal E-convex and related functions. Also, some dual results are established under this kind of generalized convex functions. Our results generalize the ones obtained by Preda[J Math Anal Appl, 288（2003） 365-382].展开更多
The principal-subordinate hierarchical multi-objective programming model of initial water rights allocation was developed based on the principle of coordinated and sustainable development of different regions and wate...The principal-subordinate hierarchical multi-objective programming model of initial water rights allocation was developed based on the principle of coordinated and sustainable development of different regions and water sectors within a basin. With the precondition of strictly controlling maximum emissions rights, initial water rights were allocated between the first and the second levels of the hierarchy in order to promote fair and coordinated development across different regions of the basin and coordinated and efficient water use across different water sectors, realize the maximum comprehensive benefits to the basin, promote the unity of quantity and quality of initial water rights allocation, and eliminate water conflict across different regions and water sectors. According to interactive decision-making theory, a principal-subordinate hierarchical interactive iterative algorithm based on the satisfaction degree was developed and used to solve the initial water rights allocation model. A case study verified the validity of the model.展开更多
An uncertain multi-objective programming problem is a special type of mathematical multi-objective programming involving uncertain variables. This type of problem is important because there are several uncertain varia...An uncertain multi-objective programming problem is a special type of mathematical multi-objective programming involving uncertain variables. This type of problem is important because there are several uncertain variables in real-world problems.Therefore, research on the uncertain multi-objective programming problem is highly relevant, particularly those problems whose objective functions are correlated. In this paper, an approach that solves an uncertain multi-objective programming problem under the expected-variance value criterion is proposed. First, we define the basic framework of the approach and review concepts such as a Pareto efficient solution and expected-variance value criterion using an order relation between various uncertain variables.Second, the uncertain multi-objective problem is converted into an uncertain single-objective programming problem via a linear weighted method or ideal point method. Then the problem is transformed into a deterministic single objective programming problem under the expected-variance value criterion. Third, four lemmas and two theorems are proved to illustrate that the optimal solution of the deterministic single-objective programming problem is an efficient solution to the original uncertainty problem. Finally, two numerical examples are presented to validate the effectiveness of the proposed approach.展开更多
Program slice has many applications such as program debugging, testing, maintenance, and complexity measurement. A static slice consists of all statements in program P that may effect the value of variable v a...Program slice has many applications such as program debugging, testing, maintenance, and complexity measurement. A static slice consists of all statements in program P that may effect the value of variable v at some point p , and a dynamic slice consists only of statements that influence the value of variable occurrence for specific program inputs. In this paper, we concern the problem of dynamic slicing of object oriented programs which, to our knowledge, has not been addressed in the literatures. To solve this problem, we present the dynamic object oriented dependence graph (DODG)which is an arc classified digraph to explicitly represent various dynamic dependence between statement instances for a particular execution of an object oriented program. Based on the DODG, we present a two phase backward algorithm for computing a dynamic slice of an object oriented program.展开更多
To simulate the process of cold roll-forming process, a new method isadopted. The theoretical foundation of this method is an elastic-plastic large deformation splinefinite strip method based on object-oriented progra...To simulate the process of cold roll-forming process, a new method isadopted. The theoretical foundation of this method is an elastic-plastic large deformation splinefinite strip method based on object-oriented programming. Combined with the computer graphicstechnology, the visual simulation of cold roll-forming is completed and the system is established.By analyzing common channel steel, the process is shown and explained including theory method, modeland result display. So the simulation system is already a kind of mature and effective tool toanalyze the process of cold roll forming.展开更多
Detecting well-known design patterns in object-oriented program source code can help maintainers understand the design of a program. Through the detection, the understandability, maintainability, and reusability of ob...Detecting well-known design patterns in object-oriented program source code can help maintainers understand the design of a program. Through the detection, the understandability, maintainability, and reusability of object-oriented programs can be improved. There are automated detection techniques;however, many existing techniques are based on static analysis and use strict conditions composed on class structure data. Hence, it is difficult for them to detect and distinguish design patterns in which the class structures are similar. Moreover, it is difficult for them to deal with diversity in design pattern applications. To solve these problems in existing techniques, we propose a design pattern detection technique using source code metrics and machine learning. Our technique judges candidates for the roles that compose design patterns by using machine learning and measurements of several metrics, and it detects design patterns by analyzing the relations between candidates. It suppresses false negatives and distinguishes patterns in which the class structures are similar. As a result of experimental evaluations with a set of programs, we confirmed that our technique is more accurate than two conventional techniques.展开更多
An object oriented multi robotic graphic simulation environment is described in this paper. Object oriented programming is used to model the physical objects of the robotic workcell in the form of software objects ...An object oriented multi robotic graphic simulation environment is described in this paper. Object oriented programming is used to model the physical objects of the robotic workcell in the form of software objects or classes. The virtual objects are defined to provide the user with a user friendly interface including realistic graphic simulation and clarify the software architecture. The programming method of associating the task object with active object effectively increases the software reusability, maintainability and modifiability. Task level programming is also demonstrated through a multi robot welding task that allows the user to concentrate on the most important aspects of the tasks. The multi thread programming technique is used to simulate the interaction of multiple tasks. Finally, a virtual test is carried out in the graphic simulation environment to observe design and program errors and fix them before downloading the software to the real workcell.展开更多
A primal-dual infeasible interior point algorithm for multiple objective linear programming(MOLP)problems was presented.In contrast to the current MOLP algorithm.moving through the interior of polytope but not confini...A primal-dual infeasible interior point algorithm for multiple objective linear programming(MOLP)problems was presented.In contrast to the current MOLP algorithm.moving through the interior of polytope but not confining the iterates within the feasible region in our proposed algorithm result in a solution approach that is quite different and less sensitive to problem size,so providing the potential to dramatically improve the practical computation effectiveness.展开更多
In this paper, a modified method to find the efficient solutions of multi-objective linear fractional programming (MOLFP) problems is presented. While some of the previously proposed methods provide only one efficient...In this paper, a modified method to find the efficient solutions of multi-objective linear fractional programming (MOLFP) problems is presented. While some of the previously proposed methods provide only one efficient solution to the MOLFP problem, this modified method provides multiple efficient solutions to the problem. As a result, it provides the decision makers flexibility to choose a better option from alternatives according to their financial position and their level of satisfaction of objectives. A numerical example is provided to illustrate the modified method and also a real life oriented production problem is modeled and solved.展开更多
Students often face difficulties while taking basic programming courses due to several factors. In response, research has presented subjective assessments for diagnosing learning problems to improve the teaching of pr...Students often face difficulties while taking basic programming courses due to several factors. In response, research has presented subjective assessments for diagnosing learning problems to improve the teaching of programming in higher education. In this paper, the authors propose an Object Oriented conceptual map model and organize this approach into three levels： constructing a Concept Effect Propagation Table, constructing Test Item-Concept Relationships and diagnosing Student Learning Problems with Matrix Composition. The authors＇ work is a modification of the approaches of Chert and Bai as well as Chu et al., as the authors use statistical methods, rather than fuzzy sets, for the authors＇ analysis. This paper includes a statistical summary, which has been tested on a small sample of students in King Abdulaziz University, Jeddah, Saudi Arabia, illustrating the learning problems in an Object Oriented course. The experimental results have demonstrated that this approach might aid learning and teaching in an effective way.展开更多
According to Hainan Island's biological characteristics, and existing structure of productivity of tropical crops and local climatic conditions, this paper carries on regional division of tropical crops by fuzzy m...According to Hainan Island's biological characteristics, and existing structure of productivity of tropical crops and local climatic conditions, this paper carries on regional division of tropical crops by fuzzy mathematics. Based on calculation of basic parameters for tl1e formation of production, near-tem optimum models of tropical crops structure of each region was established by means of multi-objective programming, and a far-term grey programming model was set up through the above-mentioned near-term model and prediction of future parameters. Conclusion shows that the near-term programming may raise the profit by 5. 1-55.7 percent and far-tem programming by 54-90 percent, both gainingobvious economic benefits.展开更多
The traditional linear programming model is deterministic. The way that uncertainty is handled is to compute the range of optimality. After the optimal solution is obtained, typically by the simplex method, one consid...The traditional linear programming model is deterministic. The way that uncertainty is handled is to compute the range of optimality. After the optimal solution is obtained, typically by the simplex method, one considers the effect of varying each objective function coefficient, one at a time. This yields the range of optimality within which the decision variables remain constant. This sensitivity analysis is useful for helping the analyst get a sense for the problem. However, it is unrealistic because objective function coefficients tend not to stand still. They are typically profit contributions from products sold and are subject to randomly varying selling prices. In this paper, a realistic linear program is created for simultaneously randomizing the coefficients from any probability distribution. Furthermore, we present a novel approach for designing a copula of random objective function coefficients according to a specified rank correlation. The corresponding distribution of objective function values is created. This distribution is examined directly for central tendency, spread, skewness and extreme values for the purpose of risk analysis. This enables risk analysis and business analytics, emerging topics in education and preparation for the knowledge economy.展开更多
To improve the efficiency of gate reassignment and optimize the plan of gate reassignment,the concept of disruption management is introduced,and a multi-objective programming model for airport gate reassignment is pro...To improve the efficiency of gate reassignment and optimize the plan of gate reassignment,the concept of disruption management is introduced,and a multi-objective programming model for airport gate reassignment is proposed.Considering the interests of passengers and the airport,the model minimizes the total flight delay,the total passengers′walking distance and the number of flights reassigned to other gates different from the planned ones.According to the characteristics of the gate reassignment,the model is simplified.As the multi-objective programming model is hard to reach the optimal solutions simultaneously,a threshold of satisfactory solutions of the model is set.Then a simulated annealing algorithm is designed for the model.Case studies show that the model decreases the total flight delay to the satisfactory solutions,and minimizes the total passengers′walking distance.The least change of planned assignment is also reached.The results achieve the goals of disruption management.Therefore,the model is verified to be effective.展开更多
In this paper, we present an algorithm to solve the inequality constrained multi-objective programming (MP) by using a penalty function with objective parameters and constraint penalty parameter. First, the penalty fu...In this paper, we present an algorithm to solve the inequality constrained multi-objective programming (MP) by using a penalty function with objective parameters and constraint penalty parameter. First, the penalty function with objective parameters and constraint penalty parameter for MP and the corresponding unconstraint penalty optimization problem (UPOP) is defined. Under some conditions, a Pareto efficient solution (or a weakly-efficient solution) to UPOP is proved to be a Pareto efficient solution (or a weakly-efficient solution) to MP. The penalty function is proved to be exact under a stable condition. Then, we design an algorithm to solve MP and prove its convergence. Finally, numerical examples show that the algorithm may help decision makers to find a satisfactory solution to MP.展开更多
The design of finite element analysis program using object-oriented programming (OOP) techniques is presented. The objects, classes and the subclasses used in the programming are explained. The system of classes libra...The design of finite element analysis program using object-oriented programming (OOP) techniques is presented. The objects, classes and the subclasses used in the programming are explained. The system of classes library of finite element analysis program and Windows-type Graphical User Interfaces by VC + + and its MFC are developed. The reliability, reusability and extensibility of program are enhanced. It is a reference to develop the large-scale, versatile and powerful systems of object-oriented finite element software.展开更多
In this paper, a cubic objective programming problem (COPP) is defined. Introduced a new modification to solve a cubic objective programming problem. Suggested an algorithm for its solution. Also reported the algorith...In this paper, a cubic objective programming problem (COPP) is defined. Introduced a new modification to solve a cubic objective programming problem. Suggested an algorithm for its solution. Also reported the algorithm of the usual simplex method. Application talks about how the developed algorithm can be used to unravel non-linear. The proposed technique, modification simplex technique, can be used with the constructed numerical examples an illustrative numerical problems are given to demonstrate the algorithms.展开更多
This paper presents the Pareto solutions in continuous multi-objective mathematical programming. We discuss the role of some assumptions on the objective functions and feasible domain, the relationship between them, a...This paper presents the Pareto solutions in continuous multi-objective mathematical programming. We discuss the role of some assumptions on the objective functions and feasible domain, the relationship between them, and compactness, contractibility and fixed point properties of the Pareto sets. The authors have tried to remove the concavity assumptions on the objective functions which are usually used in multi-objective maximization problems. The results are based on constructing a retraction from the feasible domain onto the Pareto-optimal set.展开更多
In this paper, we shall be interested in characterization of efficient solutions for special classes of problems. These classes consider roughly B-invexity of involved functions. Sufficient and necessary conditions fo...In this paper, we shall be interested in characterization of efficient solutions for special classes of problems. These classes consider roughly B-invexity of involved functions. Sufficient and necessary conditions for a feasible solution to be an efficient or properly efficient solution are obtained.展开更多
In this paper, we address bilevel multi-objective programming problems (BMPP) in which the decision maker at each level has multiple objective functions conflicting with each other. Given a BMPP, we show how to constr...In this paper, we address bilevel multi-objective programming problems (BMPP) in which the decision maker at each level has multiple objective functions conflicting with each other. Given a BMPP, we show how to construct two artificial multiobjective programming problems such that any point that is efficient for both the two problems is an efficient solution of the BMPP. Some necessary and sufficient conditions for which the obtained result is applicable are provided. A complete procedure of the implementation of an algorithm for generating efficient solutions for the linear case of BMPP is presented. A numerical example is provided to illustrate how the algorithm operates.展开更多
The aim of this study is to present an alternative approach for solving the multi-objective posynomial geometric programming problems. The proposed approach minimizes the weighted objective function comes from multi-o...The aim of this study is to present an alternative approach for solving the multi-objective posynomial geometric programming problems. The proposed approach minimizes the weighted objective function comes from multi-objective geometric programming problem subject to constraints which constructed by using Kuhn-Tucker Conditions. A new nonlinear problem formed by this approach is solved iteratively. The solution of this approach gives the Pareto optimal solution for the multi-objective posynomial geometric programming problem. To demonstrate the performance of this approach, a problem which was solved with a weighted mean method by Ojha and Biswal (2010) is used. The comparison of solutions between two methods shows that similar results are obtained. In this manner, the proposed approach can be used as an alternative of weighted mean method.展开更多
基金Foundation item： Supported by Hunan Provincial Natural Science Foundation of China（05JJ40103） Supported by Soft Science Research Fund of Hunan Province（2006ZK3028） Supported by Scientific Research Fund of Hunan Provincial Education Department（105B0707, 08C470）
文摘In this paper, some necessary and sufficient optimality conditions are obtained for a fractional multiple objective programming involving semilocal E-convex and related functions. Also, some dual results are established under this kind of generalized convex functions. Our results generalize the ones obtained by Preda[J Math Anal Appl, 288（2003） 365-382].
基金supported by the Public Welfare Industry Special Fund Project of the Ministry of Water Resources of China (Grant No. 200701028)the Humanities and Social Science Foundation Program of Hohai University (Grant No. 2008421411)
文摘The principal-subordinate hierarchical multi-objective programming model of initial water rights allocation was developed based on the principle of coordinated and sustainable development of different regions and water sectors within a basin. With the precondition of strictly controlling maximum emissions rights, initial water rights were allocated between the first and the second levels of the hierarchy in order to promote fair and coordinated development across different regions of the basin and coordinated and efficient water use across different water sectors, realize the maximum comprehensive benefits to the basin, promote the unity of quantity and quality of initial water rights allocation, and eliminate water conflict across different regions and water sectors. According to interactive decision-making theory, a principal-subordinate hierarchical interactive iterative algorithm based on the satisfaction degree was developed and used to solve the initial water rights allocation model. A case study verified the validity of the model.
基金supported by the National Natural Science Foundation of China(71601183 71571190)
文摘An uncertain multi-objective programming problem is a special type of mathematical multi-objective programming involving uncertain variables. This type of problem is important because there are several uncertain variables in real-world problems.Therefore, research on the uncertain multi-objective programming problem is highly relevant, particularly those problems whose objective functions are correlated. In this paper, an approach that solves an uncertain multi-objective programming problem under the expected-variance value criterion is proposed. First, we define the basic framework of the approach and review concepts such as a Pareto efficient solution and expected-variance value criterion using an order relation between various uncertain variables.Second, the uncertain multi-objective problem is converted into an uncertain single-objective programming problem via a linear weighted method or ideal point method. Then the problem is transformed into a deterministic single objective programming problem under the expected-variance value criterion. Third, four lemmas and two theorems are proved to illustrate that the optimal solution of the deterministic single-objective programming problem is an efficient solution to the original uncertainty problem. Finally, two numerical examples are presented to validate the effectiveness of the proposed approach.
文摘Program slice has many applications such as program debugging, testing, maintenance, and complexity measurement. A static slice consists of all statements in program P that may effect the value of variable v at some point p , and a dynamic slice consists only of statements that influence the value of variable occurrence for specific program inputs. In this paper, we concern the problem of dynamic slicing of object oriented programs which, to our knowledge, has not been addressed in the literatures. To solve this problem, we present the dynamic object oriented dependence graph (DODG)which is an arc classified digraph to explicitly represent various dynamic dependence between statement instances for a particular execution of an object oriented program. Based on the DODG, we present a two phase backward algorithm for computing a dynamic slice of an object oriented program.
基金This project is supported by Provincial Natural Science Foundation of Hebei (No.502214).
文摘To simulate the process of cold roll-forming process, a new method isadopted. The theoretical foundation of this method is an elastic-plastic large deformation splinefinite strip method based on object-oriented programming. Combined with the computer graphicstechnology, the visual simulation of cold roll-forming is completed and the system is established.By analyzing common channel steel, the process is shown and explained including theory method, modeland result display. So the simulation system is already a kind of mature and effective tool toanalyze the process of cold roll forming.
文摘Detecting well-known design patterns in object-oriented program source code can help maintainers understand the design of a program. Through the detection, the understandability, maintainability, and reusability of object-oriented programs can be improved. There are automated detection techniques;however, many existing techniques are based on static analysis and use strict conditions composed on class structure data. Hence, it is difficult for them to detect and distinguish design patterns in which the class structures are similar. Moreover, it is difficult for them to deal with diversity in design pattern applications. To solve these problems in existing techniques, we propose a design pattern detection technique using source code metrics and machine learning. Our technique judges candidates for the roles that compose design patterns by using machine learning and measurements of several metrics, and it detects design patterns by analyzing the relations between candidates. It suppresses false negatives and distinguishes patterns in which the class structures are similar. As a result of experimental evaluations with a set of programs, we confirmed that our technique is more accurate than two conventional techniques.
文摘An object oriented multi robotic graphic simulation environment is described in this paper. Object oriented programming is used to model the physical objects of the robotic workcell in the form of software objects or classes. The virtual objects are defined to provide the user with a user friendly interface including realistic graphic simulation and clarify the software architecture. The programming method of associating the task object with active object effectively increases the software reusability, maintainability and modifiability. Task level programming is also demonstrated through a multi robot welding task that allows the user to concentrate on the most important aspects of the tasks. The multi thread programming technique is used to simulate the interaction of multiple tasks. Finally, a virtual test is carried out in the graphic simulation environment to observe design and program errors and fix them before downloading the software to the real workcell.
基金Supported by the Doctoral Educational Foundation of China of the Ministry of Education(20020486035)
文摘A primal-dual infeasible interior point algorithm for multiple objective linear programming(MOLP)problems was presented.In contrast to the current MOLP algorithm.moving through the interior of polytope but not confining the iterates within the feasible region in our proposed algorithm result in a solution approach that is quite different and less sensitive to problem size,so providing the potential to dramatically improve the practical computation effectiveness.
文摘In this paper, a modified method to find the efficient solutions of multi-objective linear fractional programming (MOLFP) problems is presented. While some of the previously proposed methods provide only one efficient solution to the MOLFP problem, this modified method provides multiple efficient solutions to the problem. As a result, it provides the decision makers flexibility to choose a better option from alternatives according to their financial position and their level of satisfaction of objectives. A numerical example is provided to illustrate the modified method and also a real life oriented production problem is modeled and solved.
文摘Students often face difficulties while taking basic programming courses due to several factors. In response, research has presented subjective assessments for diagnosing learning problems to improve the teaching of programming in higher education. In this paper, the authors propose an Object Oriented conceptual map model and organize this approach into three levels： constructing a Concept Effect Propagation Table, constructing Test Item-Concept Relationships and diagnosing Student Learning Problems with Matrix Composition. The authors＇ work is a modification of the approaches of Chert and Bai as well as Chu et al., as the authors use statistical methods, rather than fuzzy sets, for the authors＇ analysis. This paper includes a statistical summary, which has been tested on a small sample of students in King Abdulaziz University, Jeddah, Saudi Arabia, illustrating the learning problems in an Object Oriented course. The experimental results have demonstrated that this approach might aid learning and teaching in an effective way.
文摘According to Hainan Island's biological characteristics, and existing structure of productivity of tropical crops and local climatic conditions, this paper carries on regional division of tropical crops by fuzzy mathematics. Based on calculation of basic parameters for tl1e formation of production, near-tem optimum models of tropical crops structure of each region was established by means of multi-objective programming, and a far-term grey programming model was set up through the above-mentioned near-term model and prediction of future parameters. Conclusion shows that the near-term programming may raise the profit by 5. 1-55.7 percent and far-tem programming by 54-90 percent, both gainingobvious economic benefits.
文摘The traditional linear programming model is deterministic. The way that uncertainty is handled is to compute the range of optimality. After the optimal solution is obtained, typically by the simplex method, one considers the effect of varying each objective function coefficient, one at a time. This yields the range of optimality within which the decision variables remain constant. This sensitivity analysis is useful for helping the analyst get a sense for the problem. However, it is unrealistic because objective function coefficients tend not to stand still. They are typically profit contributions from products sold and are subject to randomly varying selling prices. In this paper, a realistic linear program is created for simultaneously randomizing the coefficients from any probability distribution. Furthermore, we present a novel approach for designing a copula of random objective function coefficients according to a specified rank correlation. The corresponding distribution of objective function values is created. This distribution is examined directly for central tendency, spread, skewness and extreme values for the purpose of risk analysis. This enables risk analysis and business analytics, emerging topics in education and preparation for the knowledge economy.
基金Supported by the National Natural Science Foundation of China(71103034)the Natural Science Foundation of Jiangsu Province(bk2011084)
文摘To improve the efficiency of gate reassignment and optimize the plan of gate reassignment,the concept of disruption management is introduced,and a multi-objective programming model for airport gate reassignment is proposed.Considering the interests of passengers and the airport,the model minimizes the total flight delay,the total passengers′walking distance and the number of flights reassigned to other gates different from the planned ones.According to the characteristics of the gate reassignment,the model is simplified.As the multi-objective programming model is hard to reach the optimal solutions simultaneously,a threshold of satisfactory solutions of the model is set.Then a simulated annealing algorithm is designed for the model.Case studies show that the model decreases the total flight delay to the satisfactory solutions,and minimizes the total passengers′walking distance.The least change of planned assignment is also reached.The results achieve the goals of disruption management.Therefore,the model is verified to be effective.
文摘In this paper, we present an algorithm to solve the inequality constrained multi-objective programming (MP) by using a penalty function with objective parameters and constraint penalty parameter. First, the penalty function with objective parameters and constraint penalty parameter for MP and the corresponding unconstraint penalty optimization problem (UPOP) is defined. Under some conditions, a Pareto efficient solution (or a weakly-efficient solution) to UPOP is proved to be a Pareto efficient solution (or a weakly-efficient solution) to MP. The penalty function is proved to be exact under a stable condition. Then, we design an algorithm to solve MP and prove its convergence. Finally, numerical examples show that the algorithm may help decision makers to find a satisfactory solution to MP.
文摘The design of finite element analysis program using object-oriented programming (OOP) techniques is presented. The objects, classes and the subclasses used in the programming are explained. The system of classes library of finite element analysis program and Windows-type Graphical User Interfaces by VC + + and its MFC are developed. The reliability, reusability and extensibility of program are enhanced. It is a reference to develop the large-scale, versatile and powerful systems of object-oriented finite element software.
文摘In this paper, a cubic objective programming problem (COPP) is defined. Introduced a new modification to solve a cubic objective programming problem. Suggested an algorithm for its solution. Also reported the algorithm of the usual simplex method. Application talks about how the developed algorithm can be used to unravel non-linear. The proposed technique, modification simplex technique, can be used with the constructed numerical examples an illustrative numerical problems are given to demonstrate the algorithms.
文摘This paper presents the Pareto solutions in continuous multi-objective mathematical programming. We discuss the role of some assumptions on the objective functions and feasible domain, the relationship between them, and compactness, contractibility and fixed point properties of the Pareto sets. The authors have tried to remove the concavity assumptions on the objective functions which are usually used in multi-objective maximization problems. The results are based on constructing a retraction from the feasible domain onto the Pareto-optimal set.
文摘In this paper, we shall be interested in characterization of efficient solutions for special classes of problems. These classes consider roughly B-invexity of involved functions. Sufficient and necessary conditions for a feasible solution to be an efficient or properly efficient solution are obtained.
文摘In this paper, we address bilevel multi-objective programming problems (BMPP) in which the decision maker at each level has multiple objective functions conflicting with each other. Given a BMPP, we show how to construct two artificial multiobjective programming problems such that any point that is efficient for both the two problems is an efficient solution of the BMPP. Some necessary and sufficient conditions for which the obtained result is applicable are provided. A complete procedure of the implementation of an algorithm for generating efficient solutions for the linear case of BMPP is presented. A numerical example is provided to illustrate how the algorithm operates.
文摘The aim of this study is to present an alternative approach for solving the multi-objective posynomial geometric programming problems. The proposed approach minimizes the weighted objective function comes from multi-objective geometric programming problem subject to constraints which constructed by using Kuhn-Tucker Conditions. A new nonlinear problem formed by this approach is solved iteratively. The solution of this approach gives the Pareto optimal solution for the multi-objective posynomial geometric programming problem. To demonstrate the performance of this approach, a problem which was solved with a weighted mean method by Ojha and Biswal (2010) is used. The comparison of solutions between two methods shows that similar results are obtained. In this manner, the proposed approach can be used as an alternative of weighted mean method.
