An improved genetic algorithm（IGA） based on a novel selection strategy to handle nonlinear programming problems is proposed.Each individual in selection process is represented as a three-dimensional feature vector w...An improved genetic algorithm（IGA） based on a novel selection strategy to handle nonlinear programming problems is proposed.Each individual in selection process is represented as a three-dimensional feature vector which is composed of objective function value,the degree of constraints violations and the number of constraints violations.It is easy to distinguish excellent individuals from general individuals by using an individuals＇ feature vector.Additionally,a local search（LS） process is incorporated into selection operation so as to find feasible solutions located in the neighboring areas of some infeasible solutions.The combination of IGA and LS should offer the advantage of both the quality of solutions and diversity of solutions.Experimental results over a set of benchmark problems demonstrate that IGA has better performance than other algorithms.展开更多
A quadratic bilevel programming problem is transformed into a single level complementarity slackness problem by applying Karush-Kuhn-Tucker（KKT） conditions.To cope with the complementarity constraints,a binary encod...A quadratic bilevel programming problem is transformed into a single level complementarity slackness problem by applying Karush-Kuhn-Tucker（KKT） conditions.To cope with the complementarity constraints,a binary encoding scheme is adopted for KKT multipliers,and then the complementarity slackness problem is simplified to successive quadratic programming problems,which can be solved by many algorithms available.Based on 0-1 binary encoding,an orthogonal genetic algorithm,in which the orthogonal experimental design with both two-level orthogonal array and factor analysis is used as crossover operator,is proposed.Numerical experiments on 10 benchmark examples show that the orthogonal genetic algorithm can find global optimal solutions of quadratic bilevel programming problems with high accuracy in a small number of iterations.展开更多
By applying Kuhn-Tucker condition the quadratic bilevel programming, a class of bilevel programming, is transformed into a single level programming problem, which can be simplified by some rule. So we can search the o...By applying Kuhn-Tucker condition the quadratic bilevel programming, a class of bilevel programming, is transformed into a single level programming problem, which can be simplified by some rule. So we can search the optimal solution in the feasible region, hence reduce greatly the searching space. Numerical experiments on several literature problems show that the new algorithm is both feasible and effective in practice.展开更多
In this paper, an Improved Affine-Scaling Interior Point Algorithm for Linear Programming has been proposed. Computational results of selected practical problems affirming the proposed algorithm have been provided. Th...In this paper, an Improved Affine-Scaling Interior Point Algorithm for Linear Programming has been proposed. Computational results of selected practical problems affirming the proposed algorithm have been provided. The proposed algorithm is accurate, faster and therefore reduces the number of iterations required to obtain an optimal solution of a given Linear Programming problem as compared to the already existing Affine-Scaling Interior Point Algorithm. The algorithm can be very useful for development of faster software packages for solving linear programming problems using the interior-point methods.展开更多
To relax convexity assumptions imposed on the functions in theorems on sufficient conditions and duality,new concepts of generalized dI-G-type Ⅰ invexity were introduced for nondifferentiable multiobjective programmi...To relax convexity assumptions imposed on the functions in theorems on sufficient conditions and duality,new concepts of generalized dI-G-type Ⅰ invexity were introduced for nondifferentiable multiobjective programming problems.Based upon these generalized invexity,G-Fritz-John （G-F-J） and G-Karnsh-Kuhn-Tucker （G-K-K-T） types sufficient optimality conditions were established for a feasible solution to be an efficient solution.Moreover,weak and strict duality results were derived for a G-Mond-Weir type dual under various types of generalized dI-G-type Ⅰ invexity assumptions.展开更多
In this paper, we focus on a class of nonlinear bilevel programming problems where the follower’s objective is a function of the linear expression of all variables, and the follower’s constraint functions are convex...In this paper, we focus on a class of nonlinear bilevel programming problems where the follower’s objective is a function of the linear expression of all variables, and the follower’s constraint functions are convex with respect to the follower’s variables. First, based on the features of the follower’s problem, we give a new decomposition scheme by which the follower’s optimal solution can be obtained easily. Then, to solve efficiently this class of problems by using evolutionary algorithm, novel evolutionary operators are designed by considering the best individuals and the diversity of individuals in the populations. Finally, based on these techniques, a new evolutionary algorithm is proposed. The numerical results on 20 test problems illustrate that the proposed algorithm is efficient and stable.展开更多
The purpose of this research paper is to introduce Easy Simplex Algorithm which is developed by author. The simplex algorithm first presented by G. B. Dantzing, is generally used for solving a Linear programming probl...The purpose of this research paper is to introduce Easy Simplex Algorithm which is developed by author. The simplex algorithm first presented by G. B. Dantzing, is generally used for solving a Linear programming problem (LPP). One of the important steps of the simplex algorithm is to convert all unequal constraints into equal form by adding slack variables then proceeds to basic solution. Our new algorithm i) solves the LPP without equalize the constraints and ii) leads to optimal solution definitely in lesser time. The goal of suggested algorithm is to improve the simplex algorithm so that the time of solving an LPP will be definitely lesser than the simplex algorithm. According to this Easy Simplex (AHA Simplex) Algorithm the use of Big M method is not required.展开更多
In this paper we use a compromise approach to identify a lexicographic optimal solution of a multiple objective programming (MOP) problem. With this solution concept, we first find the maximization of each objection f...In this paper we use a compromise approach to identify a lexicographic optimal solution of a multiple objective programming (MOP) problem. With this solution concept, we first find the maximization of each objection function as the ideal value. Then, we construct a lexicographic order for the compromise (differences) between the ideal values and objective functions. Based on the usually lexicographic optimality structure, we discuss some theoretical properties about our approach and derive a constructing algorithm to compute such a lexicographic optimal solution.展开更多
基金supported by the National Natural Science Foundation of China (60632050)National Basic Research Program of Jiangsu Province University (08KJB520003)
文摘An improved genetic algorithm（IGA） based on a novel selection strategy to handle nonlinear programming problems is proposed.Each individual in selection process is represented as a three-dimensional feature vector which is composed of objective function value,the degree of constraints violations and the number of constraints violations.It is easy to distinguish excellent individuals from general individuals by using an individuals＇ feature vector.Additionally,a local search（LS） process is incorporated into selection operation so as to find feasible solutions located in the neighboring areas of some infeasible solutions.The combination of IGA and LS should offer the advantage of both the quality of solutions and diversity of solutions.Experimental results over a set of benchmark problems demonstrate that IGA has better performance than other algorithms.
基金supported by the National Natural Science Foundation of China (60873099)
文摘A quadratic bilevel programming problem is transformed into a single level complementarity slackness problem by applying Karush-Kuhn-Tucker（KKT） conditions.To cope with the complementarity constraints,a binary encoding scheme is adopted for KKT multipliers,and then the complementarity slackness problem is simplified to successive quadratic programming problems,which can be solved by many algorithms available.Based on 0-1 binary encoding,an orthogonal genetic algorithm,in which the orthogonal experimental design with both two-level orthogonal array and factor analysis is used as crossover operator,is proposed.Numerical experiments on 10 benchmark examples show that the orthogonal genetic algorithm can find global optimal solutions of quadratic bilevel programming problems with high accuracy in a small number of iterations.
基金Supported by the National Natural Science Foundation of China (70371032,60574071)
文摘By applying Kuhn-Tucker condition the quadratic bilevel programming, a class of bilevel programming, is transformed into a single level programming problem, which can be simplified by some rule. So we can search the optimal solution in the feasible region, hence reduce greatly the searching space. Numerical experiments on several literature problems show that the new algorithm is both feasible and effective in practice.
文摘In this paper, an Improved Affine-Scaling Interior Point Algorithm for Linear Programming has been proposed. Computational results of selected practical problems affirming the proposed algorithm have been provided. The proposed algorithm is accurate, faster and therefore reduces the number of iterations required to obtain an optimal solution of a given Linear Programming problem as compared to the already existing Affine-Scaling Interior Point Algorithm. The algorithm can be very useful for development of faster software packages for solving linear programming problems using the interior-point methods.
基金National Natural Science Foundation of China(No.11071110)
文摘To relax convexity assumptions imposed on the functions in theorems on sufficient conditions and duality,new concepts of generalized dI-G-type Ⅰ invexity were introduced for nondifferentiable multiobjective programming problems.Based upon these generalized invexity,G-Fritz-John （G-F-J） and G-Karnsh-Kuhn-Tucker （G-K-K-T） types sufficient optimality conditions were established for a feasible solution to be an efficient solution.Moreover,weak and strict duality results were derived for a G-Mond-Weir type dual under various types of generalized dI-G-type Ⅰ invexity assumptions.
文摘In this paper, we focus on a class of nonlinear bilevel programming problems where the follower’s objective is a function of the linear expression of all variables, and the follower’s constraint functions are convex with respect to the follower’s variables. First, based on the features of the follower’s problem, we give a new decomposition scheme by which the follower’s optimal solution can be obtained easily. Then, to solve efficiently this class of problems by using evolutionary algorithm, novel evolutionary operators are designed by considering the best individuals and the diversity of individuals in the populations. Finally, based on these techniques, a new evolutionary algorithm is proposed. The numerical results on 20 test problems illustrate that the proposed algorithm is efficient and stable.
文摘The purpose of this research paper is to introduce Easy Simplex Algorithm which is developed by author. The simplex algorithm first presented by G. B. Dantzing, is generally used for solving a Linear programming problem (LPP). One of the important steps of the simplex algorithm is to convert all unequal constraints into equal form by adding slack variables then proceeds to basic solution. Our new algorithm i) solves the LPP without equalize the constraints and ii) leads to optimal solution definitely in lesser time. The goal of suggested algorithm is to improve the simplex algorithm so that the time of solving an LPP will be definitely lesser than the simplex algorithm. According to this Easy Simplex (AHA Simplex) Algorithm the use of Big M method is not required.
文摘In this paper we use a compromise approach to identify a lexicographic optimal solution of a multiple objective programming (MOP) problem. With this solution concept, we first find the maximization of each objection function as the ideal value. Then, we construct a lexicographic order for the compromise (differences) between the ideal values and objective functions. Based on the usually lexicographic optimality structure, we discuss some theoretical properties about our approach and derive a constructing algorithm to compute such a lexicographic optimal solution.
