الفهرس 
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Abstract
One of the most important issues in science and engineering is the system of nonlinear equations (SNLEs), and there are still a lot of unanswered concerns in this field. The SNLE can be solved using one of two approaches: conventional or advanced. The necessity for accurate initial estimations, function continuity, differentiability, and many calculations are only a few of the drawbacks of traditional approaches. Furthermore, sophisticated algorithms
borrow their methods from the ways that animals behave in groups, such as fish schools, bird flocks, and insect swarms. They are also thought of as computer simulations of swarm systems found in nature. These algorithms gained a lot of popularity due to their avoidance of
local solutions, gradient-free mechanism, and flexibility. They provide us ideal various alternatives and are simpler and more effective than traditional approaches. The heap-based optimizer algorithm (HBO) is a relatively new optimization method that
has been used for a range of optimization problems, including image processing, machine learning, engineering design, wireless networking, and electricity energy. It uses a
mathematical model to determine the best course of action. A new hybrid intelligent algorithm is presented in this research to solve SNLEs. It is a
composite of the heap based optimizer (HBO) and chaotic search technique (CST). The proposed methodology is named chaotic heap based optimizer (CHBO). CHBO is designed as an optimization process, whereby feasible and infeasible solutions are updated to move closer to the optimum value. The use of this hybrid intelligent methodology aims to improve performance, increase solution versatility, avoid the local optima trap, speed up convergence and optimize the search process. Firstly, SNLEs are transformed into an optimization problem. Secondly, CHBO is used to solve this optimization problem: HBO is used to update the feasible solutions, whereas the infeasible solutions are updated by CST. One of the most
significant advantages of the suggested technique is that it does not ignore infeasible solutions that are updated, because these solutions are often extremely near to the optimal solution, resulting in increased search effectiveness and effective exploration and exploitation. Finally, the proposed approach (CHBO and THBO) is assessed with several benchmark problems, Constrained optimization problems and other engineering applications in realworld. Simulation results show that the proposed CHBO is competitive and better in comparison to others, which illustrates the effectiveness of the proposed algorithm. The results have high precision and show good agreement in comparison with similar methods,
and they further proved the ability of THBO to solve real-world applications.
This thesis consists of five main chapters. These chapters can be described in the following
manner: CHAPTER 1: In this chapter a survey on related topics of optimization. Mathematical model of optimization problems is introduced. Then, a classification of optimization
problems is introduced. Also, we show in these chapter optimization techniques for solving system of non-linear equations. CHAPTER 2: This chapter aims to introduce the working principles of heap based optimizer algorithm and explain how the heap based optimizer is applied for solving optimization
problems. Also, we introduce in this chapter the heap based optimizer parameters and the advantages and disadvantages of using heap based optimizer for optimization problems.
CHAPTER 3: In this chapter, a new algorithm is proposed to solve system of non-linear equations. A new algorithm is a combination between one of optimization techniques (heap
based optimizer algorithm) and chaos theory (CHBO) to enhance the performance and reaching to the optimal solution. It is a new algorithm that combines heap based optimizer algorithm searching features and chaos searching features for solving system of non-linear
equations. Various kinds of benchmark problems have been tested to illustrate the successful result in finding optimal solution. CHAPTER 4: This chapter intends to implement our new approach (THBO) for solving constrained optimization problems and explained it in detail. The experimental results for
applications that have been tested are discussed. The results are compared with another approach to show the reliability of our approach and its ability for solving load flow problem. CHAPTER 5: This chapter describes some concluding remarks, recommendations and some points for further researches.