An integer linear bi-level programming problem is firstly transformed into a binary linear bi-level programming problem, and then converted into a single-level binary implicit programming. An orthogonal genetic algorithm is developed for solving the binary linear implicit programming problem based on the orthogonal design. The orthogonal design with the factor analysis, an experimental design method is applied to the genetic algorithm to make the algorithm more robust, statistically sound and quickly convergent. A crossover operator formed by the orthogonal array and the factor analysis is presented. First, this crossover operator can generate a small but representative sample of points as offspring. After all of the better genes of these offspring are selected, a best combination among these offspring is then generated. The simulation results show the effectiveness of the proposed algorithm.
We present genetic algorithm for solving bi-level quadratic fractional programming problem by constructing the fitness function of the upper-level programming problem based on the definition of the feasible degree. This GA avoids the use of penalty function to deal with the constraints, by changing the randomly generated initial population into an initial population satisfying the constraints in order to improve the ability of the GA to deal with the constraints. The method has no special requirement for the characters of the function and overcome the difficulty discussing the conditions and the algorithms of the optimal solution with the definition of the differentiability of the function. Finally, the feasibility and effectiveness of the proposed approach is demonstrated by the numerical example.
A three-level fractional programming problem is presented in this paper with a random rough coefficient in constraints at the first phase of the solution approach and to avoid the complexity of this problem we begin with converting fractional programming problem into linear problem using Charnes & Cooper method, Then interval technique is used to convert the rough nature in constraints into equivalent crisp model. At the final phase, a membership function is constructed to develop a fuzzy model for obtaining a compromised solution of the three-level programming problem. Finally, results are illustrated by a numerical example.
A new Homotopy Perturbation Method (HPM) is used to find exact solutions for the system of Linear Fractional Programming Problem (LFPP).The Homotopy Perturbation method (HPM) and factorization technique are used together to build a new method. A new technique is also used to convert LFPP to Linear programming problem (LPP). Numerical experiments are given to show the ability of the method. The results betray that our new method is very easy and effective and compares good with the original result which possess a special attraction to the people working in the field of applied mathematics.
A new Homotopy Perturbation Method (HPM) is used to find exact solutions for the system of Linear Fractional Programming Problem (LFPP).The Homotopy Perturbation method (HPM) and factorization technique are used together to build a new method. A new technique is also used to convert LFPP to Linear programming problem (LPP). Numerical experiments are given to show the ability of the method. The results betray that our new method is very easy and effective and compares good with the original result which possess a special attraction to the people working in the field of applied mathematics.
A new Homotopy Perturbation Method (HPM) is used to find exact solutions for the system of Quadratic Fractional Programming Problem (QFPP).The Homotopy Perturbation method (HPM) and factorization technique are used together to build a new method. A new technique is also used to convert QFPP to Linear Fractional programming problem (LFPP). Numerical experiments are given to show the ability of the method. The results betray that our new method is very easy and effective and compares good with the original result which possess a special attraction to the people working in the field of applied mathematics.