Due to the complex mathematical structures of the models in engineering, heuristic methods which do not require derivative are developed. This paper improves recently developed Grey Wolf Optimization Algorithm by extending it with three new features: namely presenting a new formulation for evaluating the positions of search agents, applying mirroring distance to the variables violating the limits, and proposing a dynamic decision approach for each agent either in exploration or exploitation phases. The performance of Advanced Grey Wolf Optimization (AGWO) method is tested using several optimization test functions and compared to several heuristic algorithms. Moreover, a planning problem in smart grids is solved by considering different objective functions using 33 and 141 bus distribution test systems. From the numerical simulation results, we observe that, AGWO is able to find the best results compared to other methods from 10 and 9 out of 13 test functions for 30 and 60 variables, respectively. Similar to this, it finds best function values for 5 out of 10 fixed number of variable test functions. Also, the result of the CEC-C06 2019 benchmark functions shows that AGWO outperforms 8 for optimization problems from 10. In power distribution system planning problem, better objective function values were determined by using AGWO, resulting a better voltage profile, less losses, and less emission costs compared to solutions obtained by Grey Wolf Optimization (GWO) and Particle Swarm Optimization (PSO) algorithms.