“…3 , which include 2D views of the functions, search history, average fitness history, and convergence curves. The qualitative analysis depicts the exploration/exploitation balance of the optimization algorithm, through various metrics, especially the fluctuation of solutions diversity [ 39 , 40 ], over the course of the optimization process. Fig.…”
Section: Simulations Results and Discussionmentioning
This paper proposes an enhanced version of Equilibrium Optimizer (EO) called (EEO) for solving global optimization and the optimal power flow (OPF) problems. The proposed EEO algorithm includes a new performance reinforcement strategy with the Lévy Flight mechanism. The algorithm addresses the shortcomings of the original Equilibrium Optimizer (EO) and aims to provide better solutions (than those provided by EO) to global optimization problems, especially OPF problems. The proposed EEO efficiency was confirmed by comparing its results on the ten functions of the CEC’20 test suite, to those of other algorithms, including high-performance algorithms, i.e., CMA-ES, IMODE, AGSK and LSHADE_cnEpSin. Moreover, the statistical significance of these results was validated by the Wilcoxon’s rank-sum test. After that, the proposed EEO was applied to solve the the OPF problem. The OPF is formulated as a nonlinear optimization problem with conflicting objectives and subjected to both equality and inequality constraints. The performance of this technique is deliberated and evaluated on the standard IEEE 30-bus test system for different objectives. The obtained results of the proposed EEO algorithm is compared to the original EO algorithm and those obtained using other techniques mentioned in the literature. These Simulation results revealed that the proposed algorithm provides better optimized solutions than 20 published methods and results as well as the original EO algorithm. The EEO superiority was demonstrated through six different cases, that involved the minimization of different objectives: fuel cost, fuel cost with valve-point loading effect, emission, total active power losses, voltage deviation, and voltage instability. Also, the comparison results indicate that EEO algorithm can provide a robust, high-quality feasible solutions for different OPF problems.
“…3 , which include 2D views of the functions, search history, average fitness history, and convergence curves. The qualitative analysis depicts the exploration/exploitation balance of the optimization algorithm, through various metrics, especially the fluctuation of solutions diversity [ 39 , 40 ], over the course of the optimization process. Fig.…”
Section: Simulations Results and Discussionmentioning
This paper proposes an enhanced version of Equilibrium Optimizer (EO) called (EEO) for solving global optimization and the optimal power flow (OPF) problems. The proposed EEO algorithm includes a new performance reinforcement strategy with the Lévy Flight mechanism. The algorithm addresses the shortcomings of the original Equilibrium Optimizer (EO) and aims to provide better solutions (than those provided by EO) to global optimization problems, especially OPF problems. The proposed EEO efficiency was confirmed by comparing its results on the ten functions of the CEC’20 test suite, to those of other algorithms, including high-performance algorithms, i.e., CMA-ES, IMODE, AGSK and LSHADE_cnEpSin. Moreover, the statistical significance of these results was validated by the Wilcoxon’s rank-sum test. After that, the proposed EEO was applied to solve the the OPF problem. The OPF is formulated as a nonlinear optimization problem with conflicting objectives and subjected to both equality and inequality constraints. The performance of this technique is deliberated and evaluated on the standard IEEE 30-bus test system for different objectives. The obtained results of the proposed EEO algorithm is compared to the original EO algorithm and those obtained using other techniques mentioned in the literature. These Simulation results revealed that the proposed algorithm provides better optimized solutions than 20 published methods and results as well as the original EO algorithm. The EEO superiority was demonstrated through six different cases, that involved the minimization of different objectives: fuel cost, fuel cost with valve-point loading effect, emission, total active power losses, voltage deviation, and voltage instability. Also, the comparison results indicate that EEO algorithm can provide a robust, high-quality feasible solutions for different OPF problems.
“…The TRADE obtained lowest average rank; however, the bar graphs presented in Figure 5a shows that the IDEBW, TRADE, DEGOS, and SHADE are considered as significantly equal, while the CJADE and IMODE are significantly worse with these algorithms. In this section, the performance of the IDEBW is compared with that of 5 other meta-heuristics algorithms such as TDSD [63], EJaya [64], AGBSO [65], HMRFO [66],and disGSA [67]. The HMRFO, disGSA, AGBSO, and EJaya methods are recently developed variants of meta-heuristics such as MRFO, GSA, BSO, and Jaya algorithms, respectively, whereas the TDSD is a hybrid variant of three search dynamics such as spherical search, hypercube search, and chaotic local search.…”
The exploration of premium and new locations is regarded as a fundamental function of every evolutionary algorithm. This is achieved using the crossover and mutation stages of the differential evolution (DE) method. A best-and-worst position-guided novel exploration approach for the DE algorithm is provided in this study. The proposed version, known as “Improved DE with Best and Worst positions (IDEBW)”, offers a more advantageous alternative for exploring new locations, either proceeding directly towards the best location or evacuating the worst location. The performance of the proposed IDEBW is investigated and compared with other DE variants and meta-heuristics algorithms based on 42 benchmark functions, including 13 classical and 29 non-traditional IEEE CEC-2017 test functions and 3 real-life applications of the IEEE CEC-2011 test suite. The results prove that the proposed approach successfully completes its task and makes the DE algorithm more efficient.
“…A moderate level of population variety is usually beneficial to the performance of evolutionary algorithms. High population diversity promotes algorithm exploration, whereas low population diversity promotes algorithm exploitation [36]. The population diversity is considered and calculated as follows:…”
Section: Analysis Of Population Diversitymentioning
The equilibrium optimizer (EO) is a novel physics-based meta-heuristic optimization algorithm that is inspired by estimating dynamics and equilibrium states in controlled volume mass balance models. As a stochastic optimization algorithm, EO inevitably produces duplicated solutions, which is wasteful of valuable evaluation opportunities. In addition, an excessive number of duplicated solutions can increase the risk of the algorithm getting trapped in local optima. In this paper, an improved EO algorithm with a bis-population-based non-revisiting (BNR) mechanism is proposed, namely BEO. It aims to eliminate duplicate solutions generated by the population during iterations, thus avoiding wasted evaluation opportunities. Furthermore, when a revisited solution is detected, the BNR mechanism activates its unique archive population learning mechanism to assist the algorithm in generating a high-quality solution using the excellent genes in the historical information, which not only improves the algorithm's population diversity but also helps the algorithm get out of the local optimum dilemma. Experimental findings with the IEEE CEC2017 benchmark demonstrate that the proposed BEO algorithm outperforms other seven representative meta-heuristic optimization techniques, including the original EO algorithm.
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