الفهرس 
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Abstract
In recent years, water resources management has become a major issue due to the increasing needs for more and better-quality water. It has also become a complicated problem because of the more sophisticated way the water is used, the antagonistic water uses, and the needs to sustainability. So, we introduce a way of managing underground water aquifers, the confined steady flow problems where the transmissivities at nodes inside the zone are represented by a fuzzy number. This problem is a fuzzy maltiobjective nonlinear programming problem. This problem optimizes the sum of the water heads at each well, the total water pumping, and the capital and installation cost. There are many different types of algorithms to solve the underground water confined steady flow problem in three dimensions under fuzziness.
Nowadays, new algorithms have been developed by the inspiration from nature. In this thesis, we describe with details four of meta-heuristic approaches are Genetic algorithm (GA), Particle swarm optimization (PSO) Firefly algorithm (FA) and Water Cycle Algorithm (WCA) and two novel hybrid algorithms, firstly, using water cycle algorithm WCA and Particle swarm optimization PSO, secondly, using Firefly algorithm FA and Particle swarm optimization PSO. The two novel hybrid algorithms and pure algorithms are applied to solve 10 benchmark problems. The simulation results of the hybrid approaches and comparison with classical PSO, FA and WCA algorithms confirm the effectiveness of the proposed algorithms in solving various benchmark optimization problems. Finally, we introduce a comparison study among original algorithms and two hybrid approaches to solve fuzzy underground water confined flow problem in three dimensions. And this application is solved with different membership functions. The experimental results, analysis and statistical tests prove that the hybrid algorithm WCA-PSO overcomes the other algorithms.