Using Optimal Geometric Average Technique to Solve Extreme Point Multi- Objective Quadratic Programming Problems

Abstract

In this paper, we suggested a new technique by using optimal geometric average for the value of functions, to solve extreme point multi- objective quadratic programming problem (EPMOQPP), via transforming it to extreme point single-objective quadratic programming problem(EPSOQPP), then solve the problem by Wolfe’s method [1] , and an algorithm is given for its solution, also using cutting plane technique when the optimal value of the objective function is not an extreme point of constraints, the computer application for this algorithm was tested on a number of numerical examples, which are also solved by several techniques (Chandra Sen.'s, mean, median, and optimal arithmetic). After comparing, the results indicate that the new technique is best than others as shown in table (3).

Advanced Transformation Technique to Solve Multi-Objective Optimization Problems

“…The main limitation of MOO is that its computational burden grows in size with the number of objectives. Various types of solution procedure have been already developed for solving MOO problems [2]- [21]. Some of them deal with theory and some of them concern with solution methods and applications.…”

“…Optimal cutting plane procedure [19] and Arithmetic average transformation technique [20] had been used by Sulaiman and Rahim. Optimal average maximum-minimum technique and Optimal geometric average technique had been used by Sulaiman-Nawkhass [6] and by Sulaiman-Abdull [21] gradually to solve multi-objective quadratic programming problem.…”

Statistical Averaging Method and New Statistical Averaging Method for Solving Extreme Point Multi–Objective Linear Programming Problem

“…A new statistical averaging method for MOLPP has been proposed by Nahar and Alim [8]. Geometric average technique to solve Extreme Point Multi-Objective Quadratic Programming Problems (EPMOQPP) has been given by Sulaiman et al [9]. Hossain et al [10] proved an alternative approach for solving extreme point linear fractional programming problem.…”