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Optimization algorithms are proposed to tackle different complex problems in different areas. In this paper, we firstly put forward a new memetic evolutionary algorithm, named Monkey King Evolutionary (MKE) Algorithm, for global optimization. Then we make a deep analysis of three update schemes for the proposed algorithm. Finally we give an application of this algorithm to solve least gasoline consumption optimization (find the least gasoline consumption path) for vehicle navigation. Although there are many simple and applicable optimization algorithms, such as particle swarm optimization variants (including the canonical PSO, Inertia Weighted PSO, Constriction Coefficients PSO, Fully Informed Particle Swarm, Comprehensive Learning Particle Swarm Optimization, Dynamic Neighborhood Learning Particle Swarm). These algorithms are less powerful than the proposed algorithm in this paper. 28 benchmark functions from BBOB2009 and CEC2013 are used for the validation of robustness and accuracy. Comparison results show that our algorithm outperforms particle swarm optimizer variants not only on robustness and optimization accuracy, but also on convergence speed. Benchmark functions of CEC2008 for large scale optimization are also used to test the large scale optimization characteristic of the proposed algorithm, and it also outperforms others. Finally, we use this algorithm to find the least gasoline consumption path in vehicle navigation, and conducted experiments show that the proposed algorithm outperforms A* algorithm and Dijkstra algorithm as well. [ABSTRACT FROM AUTHOR]