A. A. ELSAWY a , Z. M. HENDAWY b , M. A. ELSHORBAGY b a Department of Mathematics, Faculty of Science. b Department of Basic Engineering Science, Faculty of Engineering. a Qassim University, b Menoufiya University. a SAUDI ARABIA, b EGYPT. elsawyus@yahoo.com, zhendawy2010@yahoo.com, mohammed_shorbagy@yahoo.com In this paper, a new algorithm is proposed to solve multiobjective optimization problems (MOOPs) through applying the trustregion (TR) method based on local search (LS) techniques; where the MOOP converting to a single objective optimization problem (SOOP) by using reference point method. In the proposed algorithm, some of the points in the search space are generated. For each point the TR algorithm for solving a SOOP is used to obtain a point on the Pareto frontier. LS technique is applied to get all the points on the Pareto frontier. The algorithm is coded in MATLAB 7.2 and the simulations are run on a Pentium 4 CPU 900 MHz with 512 MB memory capacity. The numerical results show that the proposed method is feasible, and illustrate the ability of finding a Pareto optimal set. Multiobjective optimization; trust region methods; local search technique, Pareto optimal solution; single objective optimization problem; reference point method Line search methods and TR methods both generate steps with the help of a quadratic model of the objective function, but they use this model in different ways. TR methods define a region around the current iterate within which they trust the model to be an adequate representation of the objective function, and then choose the step to be approximate minimzer of the model in this region. If a step is not acceptable, they reduce the size of the region and find a new minimize. In general, the direction of the step changes whenever the size of the TR is altered [13,18]. An approximation of the objective function ( ) by a quadratic model ( ) is computed in a neighborhood of the current iterate , which we refer to as the TR. The model ( ) should be constructed so that it is easier to handle than ( ) itself. At each iteration of TR method, to obtain the next iteration, we solve the following TR sub problem ( ) 1 minimize 2 subject to , = +∇ + ≤ (1) where is hessian of ( ) or approximate to it, and 0 > is the TR radius. This subproblem is constrained optimization problem in which the objective function and the constraint are both quadratic. A general TR algorithm for unconstrained optimization can be given as follows [1]. Given 1 , ∈ ℝ 1 0, > 0, ε ≥ 1 × ∈ ℝ symmetric; 3 4 1 0 1 , τ τ τ < < < < 0 2 0 1, τ τ ≤ ≤ < 2 0, τ > :=1. ! If 2 ε ∇ ≤ then stop; solve the subproblem (1) to give . " Compute ( ) ( ) () ( ) 0 − + = − ; (2) 0 1 ; !" τ + ≤ = + (3) Choose 1 + that satisfies [ ] 3 4 2 2 1 1 , , ; !" τ τ τ τ + ≤ ∈ (4) # Update 1 + ; := + 1; go to Step 2. The constants τ #$%&&%’ can be chosen by users. Typical values are 0 0 τ = , 1 2 τ = , Recent Advances in Engineering ISBN: 978-1-61804-137-1 141