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Multi-Dimensional Optimal Power Flow (MDOPF) is a fundamental task in power systems engineering aimed at optimizing the operation of electrical networks while considering various constraints such as power generation, transmission, and distribution. The mathematical model of MDOPF involves formulating it as a non-linear, non-convex optimization problem aimed at minimizing specific objective functions while adhering to equality and inequality constraints. The objective function typically includes terms representing the Fuel Cost (FC), Entire Network Losses (ENL), and Entire Emissions (EE), while the constraints encompass power balance equations, generator operating limits, and network constraints, such as line flow limits and voltage limits. This paper presents an innovative Improved Kepler Optimization Technique (IKOT) for solving MDOPF problems. The IKOT builds upon the traditional KOT and incorporates enhanced local escaping mechanisms to overcome local optima traps and improve convergence speed. The mathematical model of the IKOT algorithm involves defining a population of candidate solutions (individuals) represented as vectors in a high-dimensional search space. Each individual corresponds to a potential solution to the MDOPF problem, and the algorithm iteratively refines these solutions to converge towards the optimal solution. The key innovation of the IKOT lies in its enhanced local escaping mechanisms, which enable it to explore the search space more effectively and avoid premature convergence to suboptimal solutions. Experimental results on standard IEEE test systems demonstrate the effectiveness of the proposed IKOT in solving MDOPF problems. The proposed IKOT obtained the FC, EE, and ENL of USD 41,666.963/h, 1.039 Ton/h, and 9.087 MW, respectively, in comparison with the KOT, which achieved USD 41,677.349/h, 1.048 Ton/h, 11.277 MW, respectively. In comparison to the base scenario, the IKOT achieved a reduction percentage of 18.85%, 58.89%, and 64.13%, respectively, for the three scenarios. The IKOT consistently outperformed the original KOT and other state-of-the-art metaheuristic optimization algorithms in terms of solution quality, convergence speed, and robustness. [ABSTRACT FROM AUTHOR]

This article proposes an enhanced quasi-reflection jellyfish optimization (QRJFO) algorithm for solving the optimal power flow (OPF) problem. The multi-dimension objective functions are the fuel costs, transmission losses and pollutant emissions. Despite the simple structure of the jellyfish optimization algorithm, it requires significant exploitation and exploration control characteristics to support its capability. In the proposed QRJFO, a cluster is chosen randomly for every jellyfish from the population to reflect the social group that shares information in it. It varies from one to the next. The exploration phase is supported by introducing quasi-opposition-based learning. The performance of the proposed QRJFO algorithm is evaluated on the IEEE 57-bus, practical West Delta Region system and large-scale IEEE 118 bus. The simulation results demonstrate the quality of the solution and resilience of QRJFO. It is very significant for operating power systems from economic, technical and environmental perspectives. [ABSTRACT FROM AUTHOR]

This paper proposes an improved marine predators' optimization algorithm (IMPOA) for solving the combined heat and power (CHP) economic dispatch problem. This problem provides optimal scheduling of heat and power generation supplies and pursues to minimize the overall fuel cost (OFC) supply of cogeneration units considering their operational constraints. Four test systems are considered to check the performance of both the MPOA and the proposed IMPOA. The first test system is small sized which involve 5-unit, whereas the second system is medium sized which contains 48-unit system. The third and fourth test systems are large sized systems. The third test system includes 84-unit, which are divided into 40 power-only units, 20 heat only units, and 24 CHP units. The fourth test system includes 96-unit, which are divided into 52 power-only units, 20 heat-only units, and 24 CHP units. The obtained results clearly show the capability, efficiency, and feasibility of the IMPOA with respect to other relevant optimization techniques for optimal solutions of small, medium and large-scale systems. Additionally, the convergence characteristics of the proposed IMPOA are stable and the arrival of the optimal solution is faster than the conventional MPOA. [ABSTRACT FROM AUTHOR]

• An economic environmental operation in hybrid AC-MTDC power systems is introduced. • An Improved Artificial Hummingbird Optimizer (IAHO) is developed to minimize fuel costs, environmental pollution, and losses in AC-MTDC systems. • The proposed IAHO includes a variety of territorial foraging tactics and a linear control process that improve both local and universal searching capabilities. • The simulation findings declare high economic, environmental, and technical benefits via the proposed IAHO with significant outperformance over several reported algorithms. Innovative technologies of multi-terminal high voltage direct current (HVDC), often known as "MTDC," represent additional features for better active and reactive power control when hybridized with traditional AC power systems. In this sequence, optimal operation in hybrid AC and MTDC power systems becomes highly economically and environmentally necessary. This paper presents an Improved Artificial Hummingbird Optimizer (IAHO) technique for reducing total generation fuel costs, environmental pollution, and whole power losses in AC-MTDC power systems. The proposed IAHO includes a variety of territorial foraging tactics (TFTs) and a Linear Control Process (LCP) which improve both local and universal searching capabilities. The proposed IAHO and AHO are performed on modified IEEE 57-bus and 30-bus hybrid AC and multi-terminal HVDC power systems. The simulation findings declare high economic, environmental, and technical benefits based on the proposed IAHO. A significant reduction in fuel costs, emissions, and losses with 22%, 59.51%, and 71.83% compared to the initial case for the IEEE 57-bus hybrid AC-MTDC power system. Also, the IEEE 30-bus hybrid AC-MTDC power system significantly reduced fuel costs, emissions, and losses by 17.01%, 16.04%, and 28.49% compared to the initial case. Moreover, the significant outperformance of the proposed IAHO is demonstrated over several reported algorithms. [ABSTRACT FROM AUTHOR]

The optimal power flow is considered as a crucial tool in the power systems' operation and planning. To demonstrate, it aims at minimizing the operational costs of energy production and transmission by adjusting control variables with maintaining economic, operational, and environmental constraints. This article proposes and scrutinizes an Improved Heap-based Optimization Algorithm as a novel technique that successfully enhances the performance of a recently algorithm, namely Heap-based Optimization algorithm to address the optimal power flow problem. In the improved optimizer, an effective exploitation feature is emerged with the conventional version to improve its performance by enhancing the searching around the leader position. This enhancement can avoid being trapped in a local optimum and increase its global search capabilities. For the sake of practicality, the optimizers are developed with diverse objectives of the optimal power flow problem with minimization of fuel cost, emission amount, and transmission power losses with additional restrictions in real power systems that include valve-point effect and security constraints. A proposed multi-objective, improved heap optimization algorithm is investigated to solve multiobjective cases studied. The proposed multi-objective is developed based on the Pareto concept. Three standard systems: IEEE 57-bus system, a large scale 118-bus system, and a practical System are utilized to reveal the suitability and performance of the proposed technique in solving the optimal power flow problem. To illustrate the effectiveness of the proposed optimizer in handling non-convex and diverse scale optimization problems, a comparative analysis has been illustrated with those in the literature. • An Improved Heap-based Optimization Algorithm addresses the OPF problem. • A proposed multi-objective improved heap optimization algorithm is investigated. • Three standard systems are utilized to reveal the suitability and performance of the proposed. • The effectiveness of the proposed optimizer has been illustrated compared with others. • Significant reductions, in the technical economic point of views for single and multiobjective frameworks. [ABSTRACT FROM AUTHOR]

An enhanced multi-objective Quasi-Reflected Jellyfish Search Optimizer (MOQRJFS) is presented in this article for solving multi-dimensional Optimal Power Flow (MDOPF) issue with diverse objectives which display the minimization of economic fuel cost, total emissions, and the active power loss with satisfying operational constraints. Despite the simple structure of JFS with control of exploitation and exploration, searching capability of the JFS requires more support. Hence, two modifications are performed on the standard JFS algorithm. The first modification is that a cluster with a random size has been proposed which illustrates the social community that can share the data in the cluster and are dissimilar from one to another. The second modification is that a quasi-opposition-based learning is emerged in JFS to support the exploration phase. As selection criteria for the best solutions, a fuzzy decision-making strategy is joint into MOQRJFS optimizer. Additionally, the Pareto optimality concept is added to extract the non-dominated solutions. The superiority of the MOQRJFS is proved throughout application on IEEE 30-bus system, IEEE 57-bus system, the West Delta Region System of 52 bus (WDRS-52) in Egypt, and a large scale 118-bus system. Thirteen cases with economic, environmental, and technical objectives of MDOPF are included in this study. The outcomes of the proposed MOQRJFS have been compared with the conventional MOJFS and the reported techniques in the literature. It is clearly observed that the MOQRJFS give the minimum values compared with these techniques which reveals its robustness, effectiveness, and superiority when handling MDOPF among other techniques. • An enhanced multi-objective Quasi-Reflected Jellyfish Search Optimizer is presented. • Two modifications are performed on the standard JFS algorithm. • The superiority is proved on four test systems. • Thirteen cases with economic, environmental, and technical objectives are considered. • The outcomes of the proposed optimizer have been compared with others. [ABSTRACT FROM AUTHOR]