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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. [ABSTRACT FROM AUTHOR]

• A new formulation comprising energy exchange between off-peak and peak load hours. • MOGOA comprising an additional stopping criteria. • Reduced Pareto solution space due to cost analysis at peak load hours. • Better performance than the other heuristic optimization algorithms. • Real load and DG data with site-specific constraints and incentives of Turkey. The penetration of small-scale generators (DGs) and battery energy storage systems (BESSs) into the distribution grid is growing rapidly and reaching a high percentage of installed generation capacity. These units can play a significant role in achieving various objectives if installed at suitable locations with appropriate sizes. In this paper, we present a new multi-objective optimization model to improve voltage profiles, minimize DG and BESS costs, and maximize energy transfer between off-peak and peak hours. We allocate and size DG and BESS units to achieve the first two objectives, while optimizing the operation strategy of BESS units for the last objective. The Multi-Objective Grasshopper Optimization Algorithm (MOGOA) is used to solve the formulated constrained optimization problem. The proposed formulation and solution algorithm are tested on 33-bus and 69-bus radial distribution networks. The advantages of the Pareto solutions are discussed from various aspects, and the Pareto solutions are subjected to cost analysis to identify the best solutions in the context of the worst voltage profiles at peak load times. Finally, the performance of the MOGOA algorithm is compared with the other heuristic optimization algorithms using two Pareto optimality indices. [ABSTRACT FROM AUTHOR]