In this paper, the present algorithm [4] to solve fractional programming problem for multi objective functions, investigate the algorithm to solve linear programming problem for multiobjective functions [2], the computer application of algorithm was tested on a number of numerical examples and modify the approach by using mean and median for values of objective functions, to combine objective function from objective functions for linear programming problem for multi objective functions then it has been improved the above algorithm to solve the problem and computer application of improvement algorithm has been demonstrated by a flow chart and solving numerical examples on the computer then the good results have been often, as compared to the previous method [2]. Keywords: fractional programming problem, Multiobjctive linear programming problem. ‫م‬ ‫حل‬ ‫سألة‬ ‫األهداف‬ ‫متعددة‬ ‫البرمجة‬ ‫الوسط‬ ‫القيمة‬ ‫باستخدام‬ ‫ى‬ ‫و‬ ‫القيمة‬ ‫المتوسطة‬ ‫سليمان‬ ‫الدين‬ ‫نجم‬ ‫جولنار‬ ‫صادق‬ ‫كلي‬ ‫بية‬ ‫التر‬ ‫ة‬ ‫العلوم‬ ‫كلية‬ ‫الدين‬ ‫صالح‬ ‫جامعة‬ ‫االستالم:‬ ‫تاريخ‬ 25 / 04 / 2005 ‫ال‬ ‫تاريخ‬ ‫قبول:‬ 04 / 09 / 2005 ‫الملخص‬

In this paper, we used arithmetic average transform technique for solving the multi-objective quadratic programming problem (MOQPP) to single-objective quadratic programming problem(SOQPP), through a new method using arithmetic average, then solve the problems by Wolfe's method [3,12].The obtain results are compared with that of modified method given in [11] and with the Chandra Sen. method [7].

Problem statement:The Conjugate Gradient (CG) algorithm which usually used for solving nonlinear functions is presented and is combined with the modified Back Propagation (BP) algorithm yielding a new fast training multilayer algorithm. Approach: This study consisted of determination of new search directions by exploiting the information calculated by gradient descent as well as the previous search direction. The proposed algorithm improved the training efficiency of BP algorithm by adaptively modifying the initial search direction. Results: Performance of the proposed algorithm was demonstrated by comparing it with the Neural Network (NN) algorithm for the chosen test functions. Conclusion: The numerical results showed that number of iterations required by the proposed algorithm to converge was less than the both standard CG and NN algorithms. The proposed algorithm improved the training efficiency of BP-NN algorithms by adaptively modifying the initial search direction.

In this paper the Quadratic fractional objective programming problem (QFPP) with linear constraints, has been defined and developed. The special case for this problem was solved by using the Wolfe's method and a modified simplex approach, by suggesting an algorithm for each method to solve the problem. The computer application for algorithms was tested on a number of numerical examples, consequently reliable results have been found.

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