• Energy Research

In this article, an improved variant of the grey wolf optimizer (GWO) named gaze cues learning-based grey wolf optimizer (GGWO) is proposed. The main intentions are to reduce the existing high selective pressure and low diversification of the GWO algorithm, which results in premature convergence, local optima trapping, and stagnation problems. The GGWO algorithm benefits from two new search strategies: neighbor gaze cues learning (NGCL) and random gaze cues learning (RGCL) inspired by the gaze cueing behavior in wolves. The NGCL strategy enhances the exploitation ability and local optima avoidance. The RGCL, however, boosts the population diversity and balance between exploration and exploitation. The cooperation among three search strategies GWO, NGCL, and RGCL, improves diversification, exploration, and exploitation. The GGWO algorithm performance was evaluated by conducting CEC'18 test functions. Furthermore, the results of GGWO were compared with nine metaheuristic algorithms KH, iwPSO, WOA, GWO, GWO-EPD, HGWOSCA, EEGWO, BOA, and VAGWO. Moreover, the experimental results were statistically analyzed by the Wilcoxon signed-rank and Friedman tests. Additionally, four real engineering design problems and two problems of optimal power flow (OPF) for the IEEE 30-bus and IEEE 118-bus are optimized to verify the applicability of the GGWO in practice. The results show that the GGWO algorithm has been able to provide competitive and superior results to the compared algorithms, and it is capable of solving engineering problems. ; No Full Text

In this article, an improved variant of the grey wolf optimizer (GWO) named gaze cues learning-based grey wolf optimizer (GGWO) is proposed. The main intentions are to reduce the existing high selective pressure and low diversification of the GWO algorithm, which results in premature convergence, local optima trapping, and stagnation problems. The GGWO algorithm benefits from two new search strategies: neighbor gaze cues learning (NGCL) and random gaze cues learning (RGCL) inspired by the gaze cueing behavior in wolves. The NGCL strategy enhances the exploitation ability and local optima avoidance. The RGCL, however, boosts the population diversity and balance between exploration and exploitation. The cooperation among three search strategies GWO, NGCL, and RGCL, improves diversification, exploration, and exploitation. The GGWO algorithm performance was evaluated by conducting CEC'18 test functions. Furthermore, the results of GGWO were compared with nine metaheuristic algorithms KH, iwPSO, WOA, GWO, GWO-EPD, HGWOSCA, EEGWO, BOA, and VAGWO. Moreover, the experimental results were statistically analyzed by the Wilcoxon signed-rank and Friedman tests. Additionally, four real engineering design problems and two problems of optimal power flow (OPF) for the IEEE 30-bus and IEEE 118-bus are optimized to verify the applicability of the GGWO in practice. The results show that the GGWO algorithm has been able to provide competitive and superior results to the compared algorithms, and it is capable of solving engineering problems. ; No Full Text

Abstract The grey wolf optimizer (GWO) is a well-known nature-inspired algorithm, which shows a sufficient performance for solving various optimization problems. However, it suffers from low exploration and population diversity because its optimization process is only based on the best three wolves greedily, and the information of other wolves does not consider. In this paper, a representative-based grey wolf optimizer (R-GWO) is proposed to tackle with these weaknesses of the GWO. The R-GWO introduces a search strategy named representative-based hunting (RH) a combination of three effective trial vectors inspired by alpha wolves’ behaviors to improve the exploration and diversity of the population. The RH search strategy utilizes a representative archive to reduces the greediness and enhance the diversity of solutions, and it can also strike balance between the exploration and exploitation using a non-linear control parameter. The performance and applicability of the proposed R-GWO were evaluated on CEC 2018 benchmark functions and six engineering design problems. The results were compared by eight state-of-the-art metaheuristic algorithms: PSO, KH, GWO, WOA, EEGWO, BOA, HHO, and HGSO. Moreover, the results were statistically analyzed by three test Wilcoxon rank-sum, Friedman and mean absolute error (MAE). The performance results show that on all 29 functions with dimensions 30, 50, and 100, the R-GWO is superior to the competitor algorithms except on function 27 on all dimensions and function 22 on dimension 30. The proposed R-GWO is the most effective algorithm compared with competitor algorithms, with an overall effectiveness of 95.4%. The experimental and statistical results show that the R-GWO is competitive and superior to compared algorithms and can solve engineering design problems better than competitor algorithms.

Abstract The grey wolf optimizer (GWO) is a well-known nature-inspired algorithm, which shows a sufficient performance for solving various optimization problems. However, it suffers from low exploration and population diversity because its optimization process is only based on the best three wolves greedily, and the information of other wolves does not consider. In this paper, a representative-based grey wolf optimizer (R-GWO) is proposed to tackle with these weaknesses of the GWO. The R-GWO introduces a search strategy named representative-based hunting (RH) a combination of three effective trial vectors inspired by alpha wolves’ behaviors to improve the exploration and diversity of the population. The RH search strategy utilizes a representative archive to reduces the greediness and enhance the diversity of solutions, and it can also strike balance between the exploration and exploitation using a non-linear control parameter. The performance and applicability of the proposed R-GWO were evaluated on CEC 2018 benchmark functions and six engineering design problems. The results were compared by eight state-of-the-art metaheuristic algorithms: PSO, KH, GWO, WOA, EEGWO, BOA, HHO, and HGSO. Moreover, the results were statistically analyzed by three test Wilcoxon rank-sum, Friedman and mean absolute error (MAE). The performance results show that on all 29 functions with dimensions 30, 50, and 100, the R-GWO is superior to the competitor algorithms except on function 27 on all dimensions and function 22 on dimension 30. The proposed R-GWO is the most effective algorithm compared with competitor algorithms, with an overall effectiveness of 95.4%. The experimental and statistical results show that the R-GWO is competitive and superior to compared algorithms and can solve engineering design problems better than competitor algorithms.

The optimal power flow (OPF) is a practical problem in a power system with complex characteristics such as a large number of control parameters and also multi-modal and non-convex objective functions with inequality and nonlinear constraints. Thus, tackling the OPF problem is becoming a major priority for power engineers and researchers. Many metaheuristic algorithms with different search strategies have been developed to solve the OPF problem. Although, the majority of them suffer from stagnation, premature convergence, and local optima trapping during the optimization process, which results in producing low solution qualities, especially for real-world problems. This study is devoted to proposing an effective hybridizing of whale optimization algorithm (WOA) and a modified moth-flame optimization algorithm (MFO) named WMFO to solve the OPF problem. In the proposed WMFO, the WOA and the modified MFO cooperate to effectively discover the promising areas and provide high-quality solutions. A randomized boundary handling is used to return the solutions that have violated the permissible boundaries of search space. Moreover, a greedy selection operator is defined to assess the acceptance criteria of new solutions. Ultimately, the performance of the WMFO is scrutinized on single and multi-objective cases of different OPF problems including standard IEEE 14-bus, IEEE 30-bus, IEEE 39-bus, IEEE 57-bus, and IEEE118-bus test systems. The obtained results corroborate that the proposed algorithm outperforms the contender algorithms for solving the OPF problem.

The optimal power flow (OPF) is a practical problem in a power system with complex characteristics such as a large number of control parameters and also multi-modal and non-convex objective functions with inequality and nonlinear constraints. Thus, tackling the OPF problem is becoming a major priority for power engineers and researchers. Many metaheuristic algorithms with different search strategies have been developed to solve the OPF problem. Although, the majority of them suffer from stagnation, premature convergence, and local optima trapping during the optimization process, which results in producing low solution qualities, especially for real-world problems. This study is devoted to proposing an effective hybridizing of whale optimization algorithm (WOA) and a modified moth-flame optimization algorithm (MFO) named WMFO to solve the OPF problem. In the proposed WMFO, the WOA and the modified MFO cooperate to effectively discover the promising areas and provide high-quality solutions. A randomized boundary handling is used to return the solutions that have violated the permissible boundaries of search space. Moreover, a greedy selection operator is defined to assess the acceptance criteria of new solutions. Ultimately, the performance of the WMFO is scrutinized on single and multi-objective cases of different OPF problems including standard IEEE 14-bus, IEEE 30-bus, IEEE 39-bus, IEEE 57-bus, and IEEE118-bus test systems. The obtained results corroborate that the proposed algorithm outperforms the contender algorithms for solving the OPF problem.

Abstract In this article, an Improved Grey Wolf Optimizer (I-GWO) is proposed for solving global optimization and engineering design problems. This improvement is proposed to alleviate the lack of population diversity, the imbalance between the exploitation and exploration, and premature convergence of the GWO algorithm. The I-GWO algorithm benefits from a new movement strategy named dimension learning-based hunting (DLH) search strategy inherited from the individual hunting behavior of wolves in nature. DLH uses a different approach to construct a neighborhood for each wolf in which the neighboring information can be shared between wolves. This dimension learning used in the DLH search strategy enhances the balance between local and global search and maintains diversity. The performance of the proposed I-GWO algorithm is evaluated on the CEC 2018 benchmark suite and four engineering problems. In all experiments, I-GWO is compared with six other state-of-the-art metaheuristics. The results are also analyzed by Friedman and MAE statistical tests. The experimental results and statistical tests demonstrate that the I-GWO algorithm is very competitive and often superior compared to the algorithms used in the experiments. The results of the proposed algorithm on the engineering design problems demonstrate its efficiency and applicability.

Abstract In this article, an Improved Grey Wolf Optimizer (I-GWO) is proposed for solving global optimization and engineering design problems. This improvement is proposed to alleviate the lack of population diversity, the imbalance between the exploitation and exploration, and premature convergence of the GWO algorithm. The I-GWO algorithm benefits from a new movement strategy named dimension learning-based hunting (DLH) search strategy inherited from the individual hunting behavior of wolves in nature. DLH uses a different approach to construct a neighborhood for each wolf in which the neighboring information can be shared between wolves. This dimension learning used in the DLH search strategy enhances the balance between local and global search and maintains diversity. The performance of the proposed I-GWO algorithm is evaluated on the CEC 2018 benchmark suite and four engineering problems. In all experiments, I-GWO is compared with six other state-of-the-art metaheuristics. The results are also analyzed by Friedman and MAE statistical tests. The experimental results and statistical tests demonstrate that the I-GWO algorithm is very competitive and often superior compared to the algorithms used in the experiments. The results of the proposed algorithm on the engineering design problems demonstrate its efficiency and applicability.