Economic dispatch (ED) is one of the most important problems in terms of energy planning, management, and operation in power systems. This study presents a snow ablation optimizer (SAO) algorithm developed with the fuzzy-based fitness–distance balance (FFDB) method for solving ED problems in small-, medium- and large-scale electric power systems and determining the optimal operating values of fossil fuel thermal generation units. The FFDB-based SAO algorithm (FFDBSAO) controls early convergence problems through balancing exploration–exploitation and improves the solving of high-dimensional optimization problems. In the light of extensive experimental studies conducted on CEC2020, CEC2022, and classical benchmark test functions, the FFDBSAO2 algorithm has shown superior performance against its competitors. Wilcoxon and Friedman’s statistical analysis results confirm the performance and efficiency of the algorithm. Moreover, the proposed algorithm significantly reduces total fuel cost by optimizing fossil fuel thermal generation units. According to the results, the scalability and robustness of the algorithm make it a valuable tool for solving large-scale optimization problems in the planning of electric power systems.

The exceptional properties of Permanent Magnet Synchronous Motors (PMSMs), including their small construction, high power-torque density, and high efficiency, make them one of the most popular electrical machines. However, the motor structure needs to be optimized for circumstances like boosting the PMSM’s energy efficiency, optimizing output power, and lowering motor weight and cogging torque. This research aims to identify the optimal values for the parameters essential to achieving the most efficient design of a 15 kW PMSM. For this purpose, a new optimization algorithm is proposed. This proposed algorithm is an application of the fuzzy logic-based fitness distance balance design to the gradient-based optimization algorithm (GBO). The developed algorithm is called fuzzy Fitness Distance Balance Gradient-Based Optimization (fFDBGBO) algorithm. The proposed algorithm and various optimization algorithms with effective results in the literature were tested for the fitness function determined to find the optimal values of Embrace, Offset, Skew Width, Magnet Thickness, and slot bottom width (Bs1) of PMSM. The results indicate that the suggested algorithm achieves better performance than rival algorithms in terms of effectiveness. Compared to the GBO algorithm, the proposed fFDBGBO method achieves a 0.2979% increase in efficiency. Compared to other algorithms, the suggested algorithm’s objective function has the highest slot fill factor (49.9995%), yet it still complies with the specified limit value. Relative to the initial design, the motor efficiency achieved with the fFDBGBO algorithm improved from 91.7788% to 93.0366%, while the magnet weight decreased from 2.14837 to 2.09475, and the total motor weight remained approximately the same as 53.2286 kg and 54.0436 kg.

Meta-Heuristic Search (MHS) algorithms are methods that continue to be popular and continue to be developed day by day in solving complex and high-dimensional global optimization problems. Kepler Optimization Algorithm (KOA) is an up-to-date MHS algorithm created by considering Kepler's laws for determining the position and velocity of planets. In the optimization process of the KOA, the position of each planet indicates a possible solution candidate, while the best solution is expressed as the sun. Obtaining the best solution using MHS algorithms in any optimization problem depends on avoiding the local solution traps in the search area. The equilibrium between exploration and exploitation is crucial for the diversity of solution candidates. In achieving this balance, the success of the search process depends on the reference position of the solution candidates determined by the selection method. Fitness Distance Balance (FDB) is a powerful selection method for determining the reference positions that guide the search process. Using the FDB, the most promising solution candidates for improving the population's search process are determined. In this study, a new FDBKOA is presented using the FDB method to increase the effectiveness of the KOA, avoid local solution traps, and develop the global optimum solution. Then, improved FDBKOA is compared with KOA in solving four challenging benchmark problems such as CEC2014, CEC2017, CEC2020, and CEC2022 for various problem types. When the results obtained are evaluated, it is seen that the FDB method increases the performance of KOA, and the FDBKOA algorithm gives more effective solutions than KOA in experimental studies.

The Transient Stability Constrained Optimal Power Flow (TSCOPF) has become an important tool for power systems today. TSCOPF is a nonlinear optimisation problem, making its solution difficult, especially for small power systems. This paper presents a new optimisation method that incorporates Fitness-Distance Balance (FDB) with the Artificial Ecosystem Optimisation (AEO) algorithm to improve the solution quality in multi-dimensional and nonlinear optimisation problems. The proposed method, named the Fitness-Distance Balance Artificial Ecosystem Optimisation (FDBAEO), also has the capacity to solve the TSCOPF problem efficiently. In order to evaluate the proposed algorithm, it was tested on IEEE CEC benchmarks and on an IEEE 30-bus test system for the TSCOPF problem. Simulation results were compared with the basic AEO algorithm and other current meta-heuristic methods reported in the literature. The results showed that the proposed method was more effective in converging at the global optimum point in solving the TSCOPF problem compared to the other algorithms. This situation indicates that the design changes made in the decomposition phase of the AEO were more suitable for simulating the operation of the algorithm in the real world. The FDBAEO has exhibited a promising performance in solving both single-objective optimisation and constrained real-world engineering design problems.

This paper presents a novel optimization algorithm called hyper-heuristic fitness-distance balance success-history-based adaptive differential evolution (HH-FDB-SHADE). The hyper-heuristic algorithms have two main structures: a hyper-selection framework and a low-level heuristic (LLH) pool. In the proposed algorithm, the FDB method is preferred as a high-level selection framework to evaluate the LLH pool algorithms. In addition, a total of 10 different strategies is derived from five mutation operators and two crossover methods for using them as the LLH pool. Balancing the exploration and exploitation capability of FDB is the main reason for being the selection framework of the proposed algorithm. The success of the HH-FDB-SHADE algorithm was tested on CEC-17 and CEC-20 benchmark test suits for different dimensional search spaces, and the obtained solutions from the HH-FDB-SHADE were compared to 10 different LLH pool algorithms. In addition, the HH-FDB-SHADE algorithm has been applied to optimize the control parameters of PID, PIDF, FOPID, and PIDD2 in the optimal automatic voltage regulator (AVR) design problem to reveal the improved algorithm's performance more clearly and prove its success in solving engineering problems. The results obtained from the AVR system are compared with five other effective meta-heuristic search algorithms such as the fitness-distance balance Lévy Flight distribution, differential evolution, Harris–Hawks optimization, Barnacles mating optimizer, and Moth–Flame optimization algorithms in the literature. The results of the statistical analyses indicate that HH-FDB-SHADE is the best-ranked algorithm for solving CEC-17 and CEC-20 benchmark problems and gives better results compared to the LLH pool algorithms. Besides, the proposed algorithm is more effective and robust than five other meta-heuristic algorithms in solving optimal AVR design problems.

The concept of distributed energy, where different energy sources are combined in remote locations, forms the basis of today's power systems overall energy production logic. Furthermore, advancements in power electronic infrastructures have emphasized their increased utilization within power systems. In particular, the transition from current source converters (CSC) technology to voltage source converters (VSC) technology has made it easier to integrate power grids with different characteristics into existing power systems. High voltage direct current (HVDC) transmission applications also play a significant role in this integration. In these increasingly complex power systems with various infrastructures and applications, maintaining a sustainable, secure, economical, and environmentally-friendly balance between supply and demand becomes more challenging using classical approaches. In this study, a metaheuristic algorithm is proposed for solving the power flow problems in hybrid AC/DC power systems that include VSC-based, Multi-Terminal HVDC grids. The proposed algorithm is an enhanced version of the symbiotic organisms search (SOS) algorithm and is named di-SOS (diversity improved SOS with Parazite RFDB) algorithm. To demonstrate the effectiveness of the developed algorithm, comparisons were made with SOS algorithm variants and 15 different metaheuristic algorithms found in the literature using various test functions. Nonparametric Wilcoxon signed-rank tests and Friedman tests were performed the compared algorithms and in the comparison between SOS algorithm variants, the di_1-SOS variant of the di_SOS algorithm performed the best with an algorithm score of 2.245. In the comparison with the other 15 metaheuristic algorithms, the di_1-SOS algorithm ranked first with a ranking score of 4.525, demonstrating its success in solving classical test functions. Finally, the algorithm was employed to address power flow problems concerns within hybrid AC/DC power systems, employing altered instances of the IEEE 14-bus and IEEE 30-bus test networks. The acquired outcomes substantiated the efficacy of the algorithm in strategic formulation of AC/DC power systems and in resolving intricate real-world engineering problems, characterized by nonlinearities and constraints.

In this paper, the multi-objective AC-DC optimal power flow (MO/AC-DC OPF) problem in the presence of renewable energy sources (RESs), flexible AC transmission system (FACTS) devices and multi-terminal direct current (MTDC) systems is introduced for the first time. Conflicting objective functions and the high complexity of the objective and constraint spaces are the main challenges in finding optimal solutions for MO/AC-DC OPF. To overcome these challenges, twelve different versions of the dynamic switched crowding-based multi-objective particle swarm optimization (DSC-MOPSO) algorithm are introduced in this paper. Studies on multimodal optimization problems have shown that all DSC-MOPSO versions have better performance metrics than the MOPSO algorithm. Using the developed DSC-MOPSO and its strong competitors, the Pareto-optimal solution sets of the MO/AC-DC OPF problem are investigated. In these investigations, the performances of the algorithms are tested for the minimization of dual and triple objectives such as fuel cost, voltage level deviation, emission and power loss in a modified IEEE 30-bus power grid. According to the simulation results, the proposed DSC-MOPSO achieved an improvement in fuel cost between 0.02 % and 5.05 % and a reduction in active power loss between 0.44 % and 30.74% compared to its competitors. The Hypervolume (HV) performance metric was used to evaluate the Pareto-front coverage performance of DSC-MOPSO and other optimizers. The results from nine case studies of the MO/AC-DC OPF were statistically analyzed by the Friedman test according to the 1/HV metric. According to the Friedman test results, the rankings of DSC-MOPSO and MOMA are 1.984 and 3.079, respectively, ranking first and second among all competitors. Finally, in this study, feasible solutions for MO/AC-DC OPF problem are identified for the first time and the stability of competitive algorithms in finding these solutions is analyzed for the first time. The success rates and search times of DSC-MOPSO and MOMA algorithms in finding feasible solutions for MO/AC-DC OPF are 91.01 % (30.641 s) and 82.01 % (46.038 s), respectively.

Güç sistemlerinde yer alan senkron generatörlerin talep edilen gücün karşılanabilmesi amacıyla maksimum limitlerde çalıştırılması, hat arızaları veya çeşitli mekanik problemlere neden olur. Bu durum, generatörlerin rotor tarafında düşük frekanslı salınımlar meydana gelmesine yol açar. Sistemde oluşan salınımların sönümlenmesi amacıyla sıklıkla kullanılan denetleyici yapılarının başında, güç sistemi kararlı kılıcısı gelmektedir. Bu denetleyicilerin en uygun parametre değerlerinin belirlenmesi, salınımların etkili bir şekilde sönümlenmesi ve sistem kararlılığının sağlanması açısından oldukça önemlidir. Bu çalışmada, güç sistemi kararlı kılıcısı parametrelerinin en uygun değerlerinin belirlenmesi amacıyla uygunluk mesafe dengesi tabanlı parçacık sürü optimizasyonu kullanılmıştır. Önerilen algoritmanın çok makineli bir güç sistemindeki etkisini test edebilmek amacıyla, farklı arıza senaryoları için elde edilen sistem yanıtlarına ve performans indekslerine bağlı olarak karşılaştırmalar yapılmıştır. Sonuçlar, uygunluk mesafesi dengesine dayalı parçacık sürü optimizasyonu ile elde edilen güç sistemi kararlı kılıcısı parametrelerinin, diğer algoritmalarla belirlenen parametrelere göre sistem kararlılığı açısından daha etkili sonuçlar verdiğini göstermektedir.

Combined heat and power economic dispatch (CHPED) problem is one of the most widely handled, optimization problem by researchers in modern power systems. CHPED problem is a complicated, non-continuous, and non-convex optimization problem due to the constraints. Moreover, considering the valve-point loading effect (VPLE), transmission losses (TLs), and prohibited operating zones (POZs) of power-only units as constraints, the complexity of CHPED problem increases. Therefore, a powerful optimization algorithm needs to be introduced to find global solution that meets all constraints. In this paper, a novel adaptive fitness-distance balance based artificial rabbits optimization (AFDB-ARO) is developed to solve CHPED problems. AFDB-based guiding mechanism was implemented to enhance the exploration capability of ARO and to strengthen exploitation-exploration balance. A comprehensive experimental study was realized to prove the performance of the proposed algorithm on the CHPED and benchmark problems. In experimental study between AFDB-ARO variants and ARO on 40 benchmark problems, according to Wilcoxon analysis results, all AFDB-ARO variants outperformed the base ARO, and the best AFDB-ARO variant won victory in 20 of 40 problem and achieved similar results in other 20 problem. In other experimental study, AFDB-ARO algorithm was implemented on the CHPED systems with 4-, 5-, 7-, 24-, 48-, 96-, and 192-units, and fifteen case studies were considered using these systems, VPLE, TLs, and POZs. One of the important points of this study was that POZs were considered for the first time in 96- and 192-units system. The results show that AFDB-ARO achieved the best optimal solution in ten of fifteen cases, was same in one case, and obtained almost same results in four cases compared to the literature. Moreover, the stability of the AFDB-ARO and base ARO algorithms in solving the CHPED problem were tested by performing stability analysis. While the mean success rate, mean iteration number, and mean search time were obtained 87.62%, 353.63, and 2.91 sec of AFDB-ARO, respectively, ARO managed to find the optimal solution in two cases. Thus, the superior performance of AFDB-ARO algorithm is confirmed by experimental studies and analysis against ARO algorithm. The source codes of the AFDB-ARO algorithm (proposed method) can be accessed at this link: https://www.mathworks.com/matlabcentral/fileexchange/136846-afdb-aro-an-improved-aro-algorithm-for-optimization-problem.

Combined heat and power economic emission dispatch (CHPEED) problem is a highly complex, non-linear, non-convex multi-objective optimization problem due to two conflicting objectives and various operational constraints such as valve-point loading effect, power transmission loss, prohibited operating zone, and the feasible operating region of combined heat and power unit. In order to overcome these challenges, it is necessary to design an algorithm that exhibits a search behavior, which is suitable for the characteristics of objective and constraint space of the CHPEED problem. For these reasons, a dynamic switched crowding based multi-objective symbiotic organism search (DSC-MOSOS) algorithm was designed to meet the requirements and geometric space of the CHPEED problem. By applying the DSC method in the MOSOS algorithm, it was aimed to improve the exploration ability, to strengthen exploitation-exploration balance, and to prevent the catching into local solution traps. A comprehensive experimental study was carried out to prove the performance of the proposed algorithm on IEEE CEC 2020 multi-modal multi-objective problems (MMOPs) and CHPEED problem. In the experimental study conducted among eleven versions of MOSOS variations created with DSC-method and the base MOSOS algorithm on IEEE CEC 2020 MMOPs, according to Friedman scores based on the four performance metrics, the base MOSOS algorithm ranked the last. In other experimental study, the best DSC-MOSOS variant was applied to solve the CHPEED problem, where 5-, 7-, 10- and 14-unit test systems and eight case studies were considered. The important points of this study were that 10-unit and 14-unit test systems were presented to the literature, and the prohibited operating zone was considered in CHPEED problem for the first time. According to the results obtained from eight case studies obtained from the DSC-MOSOS and fourteen competitor algorithms, while the improvement in cost was between 0.2% and 16.55%, the reduction of the emission value was between 0.2 kg and 42.97 kg compared to the competitor algorithms. On the other hand, the stability of the DSC-MOSOS and the base MOSOS was evaluated using stability analysis. While the MOSOS algorithms was not able to perform a success in any case study, the DSC-MOSOS was achieved an average success rate with 91.16%. Thus, the performance of the DSC-MOSOS over the MOSOS was verified by the results of experimental studies and analysis.

Günümüzde talep edilen ve tüketilen enerji miktarında çok yoğun artışların olması ile birlikte, yenilenebilir enerji kaynaklarından enerji üretiminde artışlar olmaktadır. Bir elektrik şebekesinde yenilenebilir enerji kaynaklarının dahil edilerek kullanılması ile birlikte ağın ekonomik ve verimli çalışabilmesi için en uygun şeklide planlanması problemini de ortaya çıkarmaktadır. Bu tez çalışmasında, yenilenebilir enerji kaynaklarından olan rüzgâr ve gücü entegreli güç sistemleri problemlerinden olan optimal güç akışı problemi ele alınmıştır. Optimal güç akışı problemi doğrusal olmayan yapıya ve çeşitli kısıtlamalara sahip olan, kontrol parametrelerin en uygun değerlerinin belirlendiği bir optimizasyon problemidir. Ayrıca, güneş ve rüzgar enerjisinin doğasını birleştirmek problemin karmaşıklığını artırmaktadır. Bu tür problemlerin çözümünde yapay zeka tekniklerinden olan sezgisel arama algoritmaları tercih edilmektedir. Bu tez çalışmasında optimal güç akışı probleminin çözümü için Üçgenleme topolojisi toplama iyileştiricisi (ÜTTİ) algoritmasının öncelikle mesafe uygunluk dengesi tabanlı geliştirilmesi gerçekleştirilmiştir. Geliştirilen algoritma rüzgar ve güneş enerji kaynaklarının dahil edildiği optimal güç akışı probleminde uygulanmış olup, literatürdeki farklı algoritmaların sonuçları ile karşılaştırılmıştır. Elde edile sonuçlar, önerilen algoritmanın bu güç sistemi probleminde etkili olduğunu açık bir şekilde göstermektedir.

Nowadays, with the use of various energy technologies, interest in integrated energy systems is increasing, where the energy hub(EH) is the most attractive in them. EH optimization problems are the complex and high-dimensional due to the combining the different energy sources and the generation of different demands at the output. For this reason, the meta-heuristic search algorithms needs to be used to solve the EH problems. In this study, a novel LSHADE with semi-parameter adaptation hybrid with CMA-ES including fitness-distance balance(FDB-LSHADESPACMA) was developed to solve EH optimization problems. Using the five input energy carriers and four output energy sources, different EH structures were created and three test systems were presented to the literature for the first time. Besides, two objective functions were used which are minimization of total cost and total loss. To validate the performance of FDB-LSHADESPACMA, it was applied on benchmark and EH optimization problems. In experimental study about EH optimization problems, six case studies were considered. Accordingly, the FDB-LSHADESPACMA was obtained 3292.2784mu, 1.6753pu, 5052.0203mu, 2.1126pu, 5217.2151mu, and 2.7051pu for Case-1, Case-2, Case-3, Case-4, Case-5, and Case-6, respectively. The simulation results demonstrated that FDB-LSHADESPACMA achieved successful performance for solving both EH optimization and benchmark problems.

In this study, firstly, the balance between the exploration and exploitation capabilities of the weighted mean of vectors (INFO) algorithm was developed using the fitness–distance balance (FDB) method. Then, the FDB-INFO algorithm was developed with a hyper-heuristic method to create the beginning optimal population by using Linear Population Reduction Success History-based Adaptive Differential Evolution (LSHADE) and a novel Hyper-FDB-INFO algorithm was presented. Finally, the developed Hyper-FDB-INFO algorithm was applied to solve the optimal placement and sizing of FACTS devices for the optimal power flow (OPF) problem incorporating wind energy sources. Moreover, determining the placement and sizing of FACTS devices is an additional problem to minimize the total cost of generation and reducing the power losses of the power system. The experimental results showed that the Hyper-FDB-INFO algorithm is a more effective solver than the SHADE-SF, INFO, FDB-INFO and Hyper-INFO algorithms for wind power and FACTS devices integrating the OPF problem.

Bu çalışmada, yapay sinir ağı (YSA) ve uyarlamalı ağ tabanlı bulanık çıkarım sistemi (ANFIS) ile pomza ve diyatomit içerikli çimento harçlarının basınç dayanımlarının tahmini yapılmıştır. YSA için kademeli ileri geri yayılım algoritması, ANFIS için ise Gauss üyelik fonksiyonu tercih edilmiştir. Modellerin oluşturulmasında toplam 7 tip çimento ile üretilen harçların 2., 7., 28. ve 90. hidratasyon günlerinde belirlenen basınç dayanım sonuçları kullanılmıştır. Modellerin eğitim ve test süreçlerinde; 5 giriş (hidratasyon günü, Portland çimento, pomza, diatomit, su) ve 1 çıkış (basınç dayanımı) parametresi kullanılmıştır. Deney sonuçlarıyla modelden elde edilen sonuçların karşılaştırılması R2, MAPE ve RMSE gibi istatistiksel yöntemlerle gerçekleştirilmiştir. Elde edilen veriler, YSA modeli ile elde edilen sonuçların tüm hidratasyon günleri için hemen hemen gerçek değerlere ulaşıldığını ve bu modelin başarılı bir tahmin modeli olduğunu göstermektedir.

This article presents the single objective optimal power flow (OPF) formulation incorporating both renewable energy sources, and voltage source converter-based multiterminal direct current transmission lines, simultaneously. To solve the formulated OPF problem, powerful metaheuristic optimization algorithms including adaptive guided differential evolution, marine predators algorithm, atom search optimization, stochastic fractal search (SFS), and fitness-distance balance-based SFS (FDB-SFS) are employed. The performance of the algorithms is tested for the minimization of fuel cost, pollutant emissions of thermal generators, voltage deviation, and active power loss in a modified IEEE 30-bus power network. The simulation results give that FDB-SFS achieved the best results on the fuel cost (786.5361 $/h), the fuel cost with valve point effect (815.6644 $/h), and the fuel cost with emission-carbon tax (820.5991 $/h). In addition, FDB-SFS reduced voltage deviation and active power loss values by 14.2587% and 6.7438% compared to SFS. The nonparametric Wilcoxon and Friedman statistical test results confirmed that FDB-SFS is an effective and robust algorithm that can be used in the optimization of the introduced OPF problem.

In this study, a novel hybridization approach, which is called CMASFS and is based on the covariance matrix adaptation evolution strategy (CMA-ES) and the stochastic fractal search (SFS) algorithms. To make the proposed algorithm dynamic, Gaussian walk equations involved in the diffusion process of SFS have been updated and the algorithm decide to use which the Gaussian walk equations. The effectiveness of the proposed algorithm is tested using CEC2017 benchmark functions having unimodal, multimodal, hybrid, and composition functions in 10, 30, 50, and 100 dimensions. The performance of the CMASFS algorithm is compared with 17 metaheuristic algorithms given in the literature over the CEC2017 benchmark functions. According to the results, it is seen that CMASFS is generally obtained better mean error values. Moreover, to show the superiority of the proposed algorithm, Friedman analysis and the Wilcoxon rank-sum test are applied to the test results of the algorithms. The results of the Wilcoxon signed-rank test show that the improvement with the CMASFS algorithm is statistically significant on the majority of the CEC2017. The results of Friedman test verify that the CMASFS is obtained the best rank compared to both the original SFS and other compared algorithms.

The optimal power flow of the hybrid AC/DC power grids including voltage source converter (VSC) based multi-terminal high voltage direct current (MTHVDC) links is a popular real-world engineering problem which optimal solution has been investigated. Due to the constraint and objective functions of this power system planning problem, the high geometric complexity of the search space in which it is defined makes it difficult to find the global optimum solution for this problem. This requires the development of an efficient meta-heuristic search algorithm for optimizing the optimal power flow problem involving hybrid AC/DC electrical networks. In order to solve the proposed problem, a comprehensive study has been conducted on the recently developed phasor particle swarm optimization (PPSO) algorithm, which has strong features. For this purpose, the search capabilities of PPSO were analyzed based on the problem and according to the results of the analysis, PPSO’s search operators were redesigned to meet the requirements in the search space of the power system planning problem. In this process, fitness-distance balance (FDB) method was used for the selection of solution candidates that guided the search process in PPSO, and two FDB-based PPSO variations were developed. The performances of the developed variations were tested, and the most effective ones were determined. The proposed FDBPPSO algorithm has been applied to the solution of the optimal power flow problem in hybrid AC/DC power systems as well as unimodal, multi-modal, hybrid and composition type problems in the CEC 2020 test suite. According to the results obtained from the experimental studies, determining the positions of the particles using the FDB-based guide mechanism improved the exploration and balanced search capabilities of the PPSO. Thanks to this improvement, effective solutions were found for the proposed power system planning problem and presented to the literature for the first time.

Optimal reactive power flow (ORPF) is of great importance for the electrical reliability and economic operation of modern power systems. The integration of distributed generations (DGs) and two-terminal high voltage direct current (HVDC) systems into electrical networks has further complicated the ORPF problem. Due to the high computational complexity of the ORPF problem, a powerful and robust optimization algorithm is required to solve it. This paper proposes a powerful metaheuristic algorithm namely fitness-distance balance-based adaptive gaining-sharing knowledge (FDBAGSK). In the performance evaluation, 39 IEEE CEC benchmark functions are used to compare FDBAGSK with the original AGSK algorithm. Moreover, the proposed algorithm is applied to perform the ORPF task in modified IEEE 30- and IEEE 57-bus test systems. The effectiveness of the FDBAGSK method was tested for the optimization of three non-convex objectives: active power loss, voltage deviation and voltage stability index. The ORPF results obtained from the FDBAGSK algorithm are compared with other optimization algorithms in the literature. Given that all results are together, it has been observed that FDBAGSK is an effective method that can be used in solving global optimization and constrained real-world engineering problems.

In the power industry, the design of an efficient optimal power flow (OPF) model is one of the important research challenges. This study presents the formulation and solution of the OPF problem in the presence of RESs, VSC-MTDC transmission lines, and FACTS devices, simultaneously. Fuel cost, voltage deviation, and power loss were selected as OPF objectives and optimized with state-of-the-art metaheuristic algorithms such as MFO, BSA, COA, MRFO, TLABC, and FDB-TLABC. Based on the optimization results, FDB-TLABC has obtained the best fuel cost results of 785.5850 $/h, 815.1251 $/h, and 820.3022 $/h on the IEEE 30-bus power network. Besides, the algorithm reduced voltage deviation and active power loss by 11.76% and 0.52% compared to TLABC which second most successful algorithm, respectively. The experimental results are statistically analyzed using Wilcoxon signed-rank test. The analysis results show that the FDB-TLABC is a robust and powerful method to solve the introduced OPF problem.