###### Abstract  
This paper presents a new optimization technique based on the hybridization of two meta-heuristic methods, Jellyfish Search (JS) and Moth Flame Optimizer (MFO), to solve the Optimal Power Flow (OPF) problem. The JS algorithm offers good exploration capacity but lacks performance in its exploitation mechanism. To improve its efficiency, we combined it with the Moth Flame Optimizer, which has proven its ability to exploit good solutions in the search area. This hybrid algorithm combines the advantages of both algorithms. The performance and precision of the hybrid optimization approach (JS-MFO) were investigated by minimizing well-known mathematical benchmark functions and by solving the complex OPF problem. The OPF problem was solved by optimizing non-convex objective functions such as total fuel cost, total active transmission losses, total gas emission, total voltage deviation, and the voltage stability index. Two test systems, the IEEE 30-bus network and the Mauritanian RIM 27-bus transmission network, were considered for implementing the JS-MFO approach. Experimental tests of the JS, MFO, and JS-MFO algorithms on eight well-known benchmark functions, the IEEE 30-bus, and the Mauritanian RIM 27-bus system were conducted. For the IEEE 30-bus test system, the proposed hybrid approach provides a percent cost saving of 11.4028%, a percent gas emission reduction of 14.38%, and a percent loss saving of 50.60% with respect to the base case. For the RIM 27-bus system, JS-MFO achieved a loss percent saving of 50.67% and percent voltage reduction of 62.44% with reference to the base case. The simulation results using JS-MFO and obtained with the MATLAB 2009b software were compared with those of JS, MFO, and other well-known meta-heuristics cited in the literature. The comparison report proves the superiority of the JS-MFO method over JS, MFO, and other competing meta-heuristics in solving difficult OPF problems. optimization; hybrid JS-MFO; power flow; hybrid method; grid +
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0000-0001-9999-4000-9999-4000-9999-4000-9999-40000-9999-4000-9999-40000-99999-40000-99999-40000-99999-40000-9999-40000-99999-40000-99999-40000-99999-40000-99999-400000-99999-40000-99999-40000-99999-40000-99999-4 thermal generating units based on fossil fuel burning. In this case, the environmental dispatch problem is evoked by considering the complex function of gas emission [4]. One of the OPF problems cited previously requires the optimal adjustment of power system control variables, including active power from generating units, the voltage magnitude of the generating buses, the tap ratio of regulating transformers, and the generated reactive powers from VAR compensators. The active power and voltage magnitude of generating buses are continuous variables, while the tap settings of transformers and reactive power from VAR compensators are discrete control variables, which yield to a Mixed-Integer Nonlinear Programming (MINLP) optimization problem. Various classical optimization methods have been applied in the literature to solve OPF problems, such as the gradient-based method [5], linear programming, the [PERSON] method, and the interior point method [6], among others. These methods based on gradient concepts present some drawbacks in dealing with MINLP and highly dimensional OPF problems, particularly their convergence to a local minimum failing in achieving the global optimal solution with highly nonlinear constraints and discontinuous objective functions.