الفهرس 
CHAPTER 1: Survey on Multiobjective Optimization ProblemsOnly 14 pages are availabe for public view
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Abstract
Multi-Objective optimization problem (MOOP) is a very important research topic for both scientists and engineers and there are still many open questions in this area. Numerical optimization techniques are single objective optimization methods that optimize only one objective function. When these methods are applied to a MOOP, the problem is transformed to a single objective optimization problem by combining multiple objectives into a single objective. Trust region (TR) method is a term used in numerical optimization to denote the subset of the region of the objective function to be optimized that is approximated using a model function (often a quadratic). If an adequate model of the objective function is found within the TR then the region is expanded; conversely, if the approximation is poor then the region is contracted. TR methods are also known as restricted step methods. Evolutionary algorithms (EAs), on the other hand, are particularly suited for MOOPs. EAs are use mechanisms inspired by biological evolution, such as reproduction, mutation, recombination, and selection. Evolutionary algorithms often perform well approximating solutions to all types of problems because they ideally do not make any assumption about the underlying fitness landscape; this generality is shown by successes in fields as diverse as engineering, art, biology, economics, marketing, genetics, operations research, robotics, social sciences, physics, politics and chemistry.
In this thesis, we attempt to apply these techniques in solving MOOPs for the advantages of these methods and thus the possibility of applying them to solve some engineering problems. So, a new algorithm is introduced to solve MOOPs through applying the TR method based on local search techniques. Also, a hybrid algorithm that combines both of the TR Algorithm (Numerical optimization technique) and particle swarm optimization (PSO) (Evolutionary algorithms technique) to solve MOOPs is presented. This thesis consists of seven main chapters. These chapters can be described in the following manner:
CHAPTER 1: The most important aim of this chapter is to introduce the classification of optimization problems, Mathematical Programming Techniques for multiobjective optimization problems, Evolutionary Algorithms, Methods for solving nonlinear optimization problem, and clarify the difference between line search and trust region VAbstract.
CHAPTER 2: In this chapter a survey on two optimization techniques; trust region algorithm and particle swarm optimization is introduced. First, we explain the trust region globalization strategy for the unconstrained optimization problem and equality constrained optimization problem. Also we show that trust region concept can be extended to the general nonlinear programming problem, and multiobjective optimization problems. Next, particle swarm optimization and several of its variants and applications are presented.
CHAPTER 3: A new algorithm is proposed to solve multi-objective optimization problems through applying the trust-region algorithm based on local search techniques. The MOOP is handled by Reference Point Interactive Approach. Various kinds of multiobjective benchmark problems have been tested and the numerical results show that the proposed method is feasible, and illustrate the ability of finding a Pareto optimal set.
CHAPTER 4: In this chapter, a hybrid approach (RP based on TR-PSO) for solving the multiobjective optimization problems is presented. It combines two optimization techniques trust region and particle swarm optimization. It is a new algorithm that performs random searching and deterministic searching for solving multiobjective optimization problems. Various kinds of multiobjective benchmark problems have been tested to illustrate the successful result in finding a Pareto optimal set.
CHAPTER 5: This chapter intends to implement our approach (RP based on TR-PSO), which is a combination between numerical optimization method and one of the evolutionary algorithms, in solving multi-objective engineering component design problems and present an optimal design of these Problems. The results are compared with another approaches (which solving these design problems) to show the reliability of our approach and its ability for solving this kind of problems.
CHAPTER 6: The purpose of this chapter is to apply RP Based on TR-PSO to the environmental economic dispatch (EED) problem to demonstrate the superiority of our approach and confirms its potential to solve complex engineering applications. Simulation results are presented for the standard IEEE 30-bus system.
CHAPTER 7: This chapter describes some concluding remarks, recommendations and some points for further researches.