Enhancing the Performance of Active Distribution Grids: A Review Using Metaheuristic Techniques

Abstract

The electrical power system is composed of three essential sectors, generation, transmission, and distribution, with the latter being crucial for the overall efficiency of the system. Enhancing the capabilities of active distribution networks involves integrating various advanced technologies such as distributed generation units, energy storage systems, banks of capacitors, and electric vehicle chargers. This paper provides an in-depth review of the primary strategies for incorporating these technologies into the distribution network to improve its reliability, stability, and efficiency. It also explores the principal metaheuristic techniques employed for the optimal allocation of distributed generation units, banks of capacitors, energy storage systems, electric vehicle chargers, and network reconfiguration. These techniques are essential for effectively integrating these technologies and optimizing the active distribution network by enhancing power quality and voltage level, reducing losses, and ensuring operational indices are maintained at optimal levels.

1. Introduction

Rapid technological advancements in the electrical power sector have transformed traditional electrical distribution networks into ADNs. This evolution is driven by the integration of various advanced technologies, such as DGUs including photovoltaic systems, synchronous machines, and wind systems, along with ESSs, EVCs, and BCs [1]. These integrations present significant challenges in maintaining optimal voltage levels and minimizing power losses across the network. The complexity and dynamic nature of ADNs require sophisticated optimization methods to ensure their efficient operation, as illustrated in Figure 1. MTs have emerged as powerful tools for addressing these challenges due to their ability to handle complex nonlinear optimization problems effectively. Furthermore, in [2] classical optimization methods were compared with MTs in the context of ADN reconfiguration, demonstrating that MTs require less computational effort and provide better solutions for large-scale systems. This paper aims to provide a comprehensive review of current state-of-the-art MTs in the context of electrical ADNs, highlighting their importance and application in optimizing network performance.

By reviewing these techniques, we seek to identify the most effective strategies for integrating new technologies into ADNs, thereby enhancing their reliability, stability, and overall efficiency. A comprehensive understanding of the behavior and performance of ADNs is crucial for ensuring their efficient operation, where the power flow method stands out as the primary approach through which to calculate essential attributes within ADNs, such as power losses, voltage magnitude, current through the branches, and generators’ power outputs, to develop a robust model for an electrical network [3]. The network model serves as the foundation for formulating an optimization problem, leading to the application of MTs to achieve the best configuration of the system [4,5]. In this sense, many studies have employed this methodology for integrating DGUs, ESSs, BCs, EVCs, and achieving the best layout of the an electrical network, which have become crucial in avoiding efficiency issues [6]. Several works have focused on reviewing specific aspects of ADN performance improvement; for instance, in [7], the authors developed a state-of-the-art handbook on ESSs, highlighting their benefits for generation, transmission, and distribution networks, and off-grid micro-grids. They posit that the optimal location for ESSs in either ADNs or transmission networks can significantly boost system performance. The study presents a systematic methodology, including an extensive literature review covering ESS selection, evaluation criteria, modeling, and solution methods. Similarly, in [8], the authors conducted a state-of-the-art review on voltage control algorithms, noting that due to the integration of DGUs, ADNs exhibit more voltage variation than before. In [9], the authors discussed the maximization of hybrid renewable energy systems’ integration into ADNs due to the reduction in fossil fuel use. They also mentioned some MTs used to facilitate this integration. On the other hand, ref. [10] focused on the field of electrical systems, thoroughly summarizing MTs used to optimize ADN performance by increasing nodal voltage, reducing active power losses, balancing loads, and restoring service through feeder reconfiguration. In [11], the authors identified the most used MTs in electrical network optimization, covering renewable energy integration, load forecasting, power flow, micro-grids, smart grids, and power quality. They also analyzed future challenges for MTs in network optimization. Ref. [12] grouped optimization problems into optimal power flow, which includes the dispatch of real and reactive power, scheduling strategies such as demand response and battery management, and planning stages addressing DGUs location and network reconfiguration. Lastly, ref. [13] discussed recent MTs in the EV sector, emphasizing their role in modernizing the transportation system.

Although numerous metaheuristic techniques have been applied to the optimization of ADNs, MTs may differ in terms of apparent complexity or the number of operational stages they include; however, all of them are fundamentally governed by the same core principles: exploration and exploitation of the solution space. The main distinction lies in how each technique implements and balances these two mechanisms. Some techniques emphasize broader exploration of the search space, while others focus on intensive exploitation of the most promising regions. This work aims at addressing a conceptual gap in the literature (the perception that certain techniques are inherently more complex due to their structure or terminology) by highlighting that, regardless of their external complexity, all metaheuristics rely on the same foundational processes. By emphasizing this underlying regularity, this paper seeks to offer readers a unified perspective, making it clear that every metaheuristic technique, no matter how elaborate it may appear, ultimately operates through the same stages of exploration and exploitation. To address the identified research gap, this paper presents the following key contributions:

• This work conducts a comprehensive and critical review of the most widely used metaheuristic techniques for optimizing ADNs, identifying their fundamental operational stages and assessing their effectiveness in the specific context of electrical networks.
• This study provides a systematic analysis of the exploration and exploitation mechanisms inherent in different metaheuristic algorithms, highlighting how these characteristics influence the optimization performance of ADNs.
• This paper proposes a structured methodology for modeling optimization problems in ADNs, clearly defining the types of objective functions (mono-objective and multi-objective), key network indicators, applied constraints, and optimization targets.
• A classification framework is developed based on the primary objectives and network performance indicators addressed by optimization models, facilitating a deeper understanding of the critical factors that enhance ADN performance.
• Finally, a detailed census of the reviewed studies identifies the most influential network indicators, demonstrating that their optimization significantly improves hosting capacity, reliability, and operational efficiency in ADNs, thus providing a strategic reference for future research and technological development in this area.

The methodology adopted for the development of this study is structured into three main phases. First, the fundamental concepts related to mono-objective and multi-objective functions within the general framework of optimization problems are introduced and explained. Once these theoretical foundations are established, their application is contextualized within the electrical power sector, specifically focusing on the integration of emerging technologies such as DGUs, EVCs, ESSs, BCs, and even network reconfiguration techniques in ADNs. Subsequently, a detailed review of the most commonly used metaheuristic techniques for the optimization of such networks is conducted. To support the comparative analysis, summary tables are included to highlight the most frequently used techniques, their recurrence in the literature, and their application in different scenarios. Each column of the table has been carefully designed to provide relevant technical details. The algorithm column indicates the specific metaheuristic method employed in each study. The type column specifies whether the algorithm is implemented in its simple form or as part of a hybrid approach. The function/target column describes the main optimization objective, such as location, sizing, or multi-objective formulations. The network indicator(s) column lists the performance metrics considered, such as power losses, voltage deviation, or economic costs. The constraints column identifies the operational and technical constraints applied in each case. The test system column provides details about the network used for validation, indicating whether the study was conducted on a real or test network and specifying the number of buses. Finally, the paper no. column links the summarized information to the corresponding reference in the literature. The final phase represents the core methodological contribution of this work: a systematic census of the analyzed articles is performed to identify the most relevant performance indicators which, when optimized (i.e., either minimized or maximized), significantly contribute to enhancing network efficiency, reliability, and hosting capacity. This approach provides a practical reference for future research by offering a solid foundation on the critical parameters that should be considered when designing optimization strategies for ADNs.

Finally, the article is structured as follows: Section 2 introduces a general classification of metaheuristic techniques, highlighting their fundamental principles and categorization, regardless of the specific application domain. Section 3 discusses the distinctions between multi-objective and mono-objective functions in the context of optimization. Section 4, Section 5, Section 6, Section 7 and Section 8 provide an in-depth analysis of the application of metaheuristic techniques for the optimal integration of specific technologies into ADNs. Specifically, Section 4 addresses DGUs, Section 5 focuses on ESSs, Section 6 covers BCs, Section 7 examines EVs, and Section 8 explores the MTs in the network reconfiguration. Section 9 presents the main findings of the review, while Section 10 outlines the overall conclusions, and Section 11 discusses potential future research directions in this field.

2. Classification of Metaheuristic Techniques

Metaheuristic techniques can be classified into three general groups—metaphored, non-metaphored, and their variants—as illustrated in Figure 2. These categories are defined according to the procedure used to find the solution, based on the emulation of natural behaviors, physical phenomena, social behaviors, or mathematical functions, as well as the type of problem to be solved, e.g., whether it is a multi-objective, discrete, or continuous problem. Metaphored metaheuristic techniques imitate these natural behaviors, e.g., genetic algorithms, differential evolution algorithms, and particle swarm optimization. On the other hand, non-metaphored techniques follow their own rules to find the optimal solution. An example of these is the tabu algorithm, which explores a specific solution and adds the previous solutions to a list to avoid reconsidering them. The latest classification includes upgrading metaheuristic techniques, such as adaptive ones, where the size of the random step or the search range is automatically adjusted to avoid premature convergence. Examples of these techniques are the adaptive swarm optimization algorithm, the whale optimization algorithm, and the improved harmony search. There are also chaotic techniques, which use greater randomness and a high convergence rate, such as chaotic particle swarm optimization and chaotic genetic algorithm. Additionally, there are acclimated techniques, focused on multi-objective and the discrete approaches, adapting to combinatorial problems (the non-dominated sorting genetic algorithm and multi-objective particle swarm optimization with crowding distance), binary problems (binary particle swarm optimization, binary cat swarm optimization, and binary black holes algorithm), and integer values. Continuous metaheuristic techniques handle floating-point numbers in problems with non-discrete variables, such as temperature. Finally, there are hybrid techniques which combine the advantages of different algorithms. Hybridization can be performed at a low or high level, depending on the degree of interaction between the components of the algorithms. High-level hybridization indicates low interference in the internal functioning of the combined algorithms, while low-level hybridization implies that only one metaheuristic function is incorporated into another [14].

3. Multi-Objective Function and Mono-Objective Function

Any optimization approach has at least four main components: (a) variables, (b) parameters, (c) constraints, and (d) objective function. Variables correspond to values to be determined when the optimization problem is solved. Parameters are the known data that are used to obtain a solution for the optimization problem. Constraints are the relationships between parameters and variables, which can be inequality and equality constraints. The objective function represents a mathematical function to be maximized or minimized, defining an interest variable to be evaluated subject to several constraints. Optimization problems can be classified as MO and MTO based on the number of objective functions. In MTO optimization problems, it is desirable to have a trade-off between objectives. This trade-off can be defined as a compromise between objectives, where if the value of objective A is improved, the value of another objective B is worsened. It is important to note that if there is no compromise between objectives, then the number of objective functions can be reduced. For example, in an MTO optimization problem of electrical networks with two objective functions, if improving one objective function also improves the other, the problem can be reduced to an MO optimization problem considering only one of the two objective functions [15], e.g, optimizing both voltage levels and power losses in electrical networks. While these two objectives are often interrelated, since improving voltage levels can reduce losses, this relationship is not always straightforward. If distributed generation or capacitors significantly raise the voltage at a particular bus, the current flow to the next node may increase, leading to higher losses. Therefore, it is crucial to carefully balance these objectives in an MO approach to avoid unintended consequences. In this context, Figure 3 depicts an MO study where the optimal deployment of DGUs into ADNs can enhance the voltage; at the same time, the power losses are minimized considering an MO approach. The point A indicates the maximum voltage level in the network and the minimal power losses, which indicate better performance of the ADN. However, the point B illustrates worse performance of the ADN due to minimal voltage and maximum power losses within the system.

A representation of MO and MTO approaches is depicted in Figure 4. The MO optimization approach corresponds to an objective function to be maximized or minimized subject to equality and inequality constraints, where the variables can be represented as a vector for continuous or discrete variables in a determined universe. It should be noted that all constraints should be fulfilled to consider that a solution is feasible. In contrast, MTO approaches contemplate two or more objective functions instead of one, which are subject to several constraints [15].

Solving an MTO problem corresponds to finding values for continuous and discrete variables in which all constraints are satisfied and optimum values for objective functions are obtained. Nevertheless, obtaining optimal values for all objective functions could be very difficult or even impossible because, as mentioned before, an MTO optimization problem is preferable to a trade-off between objectives. For this reason, the solving strategy for MTO problems needs to consider several ways to include various objectives simultaneously. For this reason, most of the solving strategies consider reformulating the optimization models in MO optimization problems. These strategies could be resolved by MO problems based on a main objective function considering other objective functions as restrictions [16]. Moreover, a new objective function could be proposed based on a weighted sum for original objective functions from the MTO problem [17].

4. Metaheuristic Techniques for Optimal Integration of DGUs into an ADN

Behind the integration of DGUs, the primary objectives are reducing both CO₂ emissions and electrical billing costs, aligning with international standards and fostering sustainable development. Furthermore, it is imperative to acknowledge the diverse array of technologies that a DGU can encompass, facilitating the injection of both real and reactive powers into the system. Figure 5 illustrates a typical aerial distribution network commonly found in rural or peri-urban areas, characterized by the use of utility poles and pole-mounted transformers. It also shows the different types of DGUs that can be integrated into an ADN, such as solar modules, wind turbines, and synchronous machines, highlighting the bidirectional nature of power flow in the system.

Moreover, this evolution has brought about greater regulatory flexibility and more efficient dispatch strategies, ultimately leading to an overall improvement in system performance. Among the notable improvements is the mitigation of issues previously encountered in traditional networks, such as power losses and voltage fluctuations [18]. In this regard, DGUs play an essential role not only in enhancing key metrics of ADNs but also in generating a cascade of complications, including energy wastage, overloaded branches, strained transformers, and burdened generators [19]. Therefore, the strategic placement of DGUs in the network can yield substantial benefits, offering better voltage regulation and reducing power losses across the entire system. To minimize these complications and properly optimize the integration of DGUs into distribution networks, a growing number of investigations have turned to metaheuristic techniques (MTs). Essentially, a defining characteristic of MTs is their ability to navigate and explore large solution spaces to identify the most optimal outcome, which is suitable for finding the best way to deploy DGUs in a large-scale electrical distribution network [20].

In this context, the authors of [21] have developed an integral MTO function encapsulated as follows. The first objective function refers to a reduction in total energy expenditure, encompassing both the reduction of purchased energy costs and the costs of unsupplied energy; in addition, it considers the installation expenses of the DGUs. The second objective function aims to address power losses, and this entails a comparison between power losses within systems without DGUs and those with DGUs installed. The third objective function is designed to minimize voltage drops in the buses within the system. The solution for the MTO function is obtained using the MT known as the ant lion algorithm. In this algorithm, both the ant lions and the ants are randomly defined. Each ant lion and ant represent a possible solution to the optimization problem. Ant lions create funnel-shaped traps in the sand, which are modeled by modifying the positions of the ants that represent potential solutions to the problem. However, the movements of the ants are influenced by the position of the ant lions, which represent the best current solutions. All these behaviors are simulated within the algorithm through mathematical equations. Once an ant falls into an ant lion’s trap, the position of the ant lion corresponds to a solution and is updated to obtain the closer ant, which is a better solution. It is worth mentioning that, during the optimization process, ant lions can modify their traps, reflecting the adaptation of solutions over time. At the end of each iteration, the quality of the solutions found by the ant lions is compared, and the best solution is preserved and used in subsequent iterations [21,22]. Similarly, in [23], the formulation of an MTO function is presented to determine the optimal locations of DGU and BC within an ADN. The MTO function encompasses key evaluation metrics such as power losses within the system and voltage deviation. To solve this problem, the MMGSA-EE has been implemented, based on the gravitational search algorithm, in which each potential solution to the problem may be considered a particle in space, to which a mass related to its fitness for the adjustment function is assigned. Particles attract each other with a force that is proportional to their masses and inversely proportional to the distance between them, meaning the fittest particles possess a greater attraction force. Thus, particles move in the search space under the influence of these gravitational forces, allowing the algorithm to explore the search space [24]. Similarly, an MO function can be formulated for an optimization problem, which has a lower complexity than an MTO function (see Figure 4). In studies [6,25,26,27,28], the authors formulate an optimization problem where the objective function is an MO, aiming to find both the best position and generation capacity of DGU within an ADN based on minimizing power losses within the system. These formulations include constraints such as voltage levels, balance of reactive and real powers, upper and lower limits for the capacity of DGUs, and limited capacity in the ADN’s elements to ensure optimal performance. In this way, as shown in refs. [6,25], the authors employed a WOA, where the number of whales is the initial population, representing potential solutions to the optimization problem, with the best current solution in any iteration considered the target prey. The algorithm alternates between mathematical equations that mimic the random search for prey and the movement toward a selected whale, allowing for effective exploration of the solution space. Moreover, the position of the other whales is used to simulate a random search, further enhancing the exploration of the algorithm. A particular feature of the whale algorithm is its spiral bubble method, represented by a mathematical equation within the algorithm (to simulate the way humpback whales trap their prey) to increase the exploitation of this algorithm. It is worth mentioning that the WOA randomly decides whether to employ the direct approach or spiral movement to simulate the hunting behavior of whales. After each search and hunting session of the whales, the algorithm adjusts the best solution found so far, repeating until the number of either iteration is met or a specific error is reached [29].

Table 1. Metaheuristic algorithms employed in the integration of DGUs into ADNs.

Algorithm	Type	Function/Target	Network Indicator (s)	Constraints	Test System	Paper No.
Ant lion	Simple	Multi-objective	Purchased energy cost	Voltage index	33-Buses	[21]
optimization		Location + sizing	DGU cost	Power loss index	69-Buses
			Power losses	Cost of energy
				Voltage deviation
Whale	Simple	Mono-objective	Power losses	Power balance	15-Buses	[6]
optimization		Location		Power loss index	33-Buses
					69-Buses
					85-Buses
					118-Buses
Chimpanzees	Simple	Mono-objective	Power losses	Power flow	33-Buses	[26]
optimization		Location		Nodal voltage	69-Buses
				Branch current	119-Buses
MOPSO	Simple	Multi-objective	Power losses	DGUs’ total power	33-Buses	[30]
		Location + sizing	Nodal voltage	Generator rating	69-Buses
			Voltage index	Nodal voltage
				Branches current
MMGSA-EE	Simple	Multi-objective	Power losses	Nodal voltage	33-Buses	[23]
		Location	Voltage deviation	Branch current	69-Buses
				DGUs’ capacity	119-Buses
Improved wild	Simple	Mono-objective	Power losses	Power balance	33-Buses	[27]
horse		Location		Nodal voltage	69-Buses
				Branch current	119-Buses
				DGU size
Multi-objective	Simple	Multi-objective	Power losses	Nodal voltage	33-Buses	[25]
Whale optimization		Location	Economic losses	Power balance	69-Buses
				Branch currents
				DGUs capacity
Improved salp	Simple	Multi-objective	Power loss cost	Power balance	33-Buses	[19]
swam		Location	Reliability cost	Nodal voltage	69-Buses
				DGU power
				Branch currents
Adaptive	Simple	Multi-objective	Power losses	Nodal voltage	69-Buses	[28]
genetic		Location	Voltage deviation	Branch currents	52-Buses
				DGUs capacity
				Max.Min.Tap setting
Krill herd	Simple	Mono-objective	Power losses	Power balance	33-Buses	[31]
		Location + sizing		Nodal voltage	69-Buses
				Branch current	118-Buses
				Real power
				Reactive power
Knitro solver	Simple	Mono-objective	Power losses	Power balance	33-Buses	[32]
MINLP		Location + sizing		Nodal voltage	69-Buses
				Substation capacity
				DGUs capacity
				Amount of DGUs
				DGUs power factor
				Power flow
Intelligent	Simple	Mono-objective	Power losses	Power balance	10-Buses	[33]
Water drop		Location + sizing		Nodal voltage	33-Buses
				Branch current	69-Buses
Backtracking search	Simple	Multi-objective	Power losses	Power balance	33-Buses	[34]
Optimization		Location	Voltage deviation	Nodal voltage	94-Buses
				DGU sizing
				Power flow
				DGU penetration
				Power losses (DGUs)
				Network short circuit
Ant colony	Hybrid	Multi-objective	Power losses	Power balance	33-Buses	[35]
optimization		Location + sizing	Voltage deviation	Nodal voltage	69-Buses
With artificial			Emissions CO2	DGU generation
Bee colony			Energy cost
Quasi-oppositional	Simple	Multi-objective	Power losses	Power balance	33-Buses	[36]
Chaotic symbiotic		Location + sizing	Nodal voltage	Nodal voltage	69-Buses
Organism search				Branch current	118-Buses
				DGU capacity
				DGU power factor
				DGU penetration
COLAHA	Simple	Multi-objective	Power loss index	Power balance	69-Buses IEEE	[37]
Centroid-based oppositional learning		Reconfig. and optimal placement of	Voltage profile index	Voltage limits	118-Buses IEEE
Artificial hummingbird algorithm		DGs, SCs, and EVCs	Power factor index	DG size
			DG penetration index	SC size
		EVCs power loss index	Radiality constraint
Competitive search optimization	Hybrid	Multi-objective	Power losses	Voltage	69-Buses IEEE	[38]
With fuzzy and chaos theory		Optimal placement and sizing of	Voltage profile	DG capacity
		DGs, SCs, and EVCs	Power factor	Branch current
			Voltage stability index	Capacitor capacity
			Power loss index	EVCs’ power profile
			DG penetration index	Radiality
Multi-objective	Simple	Multi-objective	Power loss	Bus voltage	33-Buses IEEE	[25]
Whale optimization		Siting and sizing of DGs	Annual economic loss	DG capacity	69-Buses IEEE
(MOWOA)			Voltage profile	Power balance
			Cost savings index

lists each paper that aims at the sitting and sizing of DGUs, focusing on the main elements for modeling an optimization problem, by considering the size of the test system for understanding the robustness of the MT employed.

5. Metaheuristic Algorithms for Optimal Integration of ESSs into an ADN

Numerous electrical markets have embraced the integration of ESSs equipped with renewable technologies like wind and photovoltaic systems. This shift aims to reduce the reliance on non-renewable resources as the primary source of electrical energy for consumers while concurrently curbing CO₂ emissions within the electrical sector [39]. In this context, the use of ESSs will be essential to deal with variations of renewable energy sources, by identifying several types of ESSs as is documented in [40], where it is highlighted that batteries are the most common storage elements within ESSs.

On the other hand, the integration of ESSs within an ADN facilitates the implementation of different demand-side response methodologies aimed at smoothing peak demand during specified time frames. For instance, consumers can store energy during off-peak periods for subsequent sales during peak hours. Alternatively, they can utilize stored energy to reduce their demand during peak periods bringing lower electricity bills, as discussed in [41]. Hence, as ESS injects power into an ADN, the proper sizing and placement become imperative for enhancing the grid performance. Therefore, it is essential to evaluate the optimal location and sizing of a ESS in an ADN, because they can significantly influence the performance indices of the grid such as voltage profiles and power losses, similar to the considerations for DGUs. To effectively allocate the ESSs within an ADN, MTs are employed to determine the most suitable position of ESSs for the aforementioned specific objectives, while adhering to a set of constraints: energy not supplied, state of charge, energy cost, life cycle cost, and ESS power limit.

The proper location and sizing of ESSs are key characteristics considered to maximize the performance of an ADN. Studies such as [42,43,44] have modeled MTO and MO problems to obtain the appropriate location and capacity for ESSs to maximize the performance of the ADNs, starting from minimizing active power losses and voltage drops across the system. Similarly, MTO functions have been modeled to optimize the operational costs of ESS and DGU in ADNs. In [45,46,47], optimization models were developed to determine the optimal location, capacity, and operation of BESSs with PVs by using an MTO function that minimizes the energy not supplied, reduces load losses, decreases load costs, decreases fossil fuel emission costs, and alleviates voltage drops within the network. Moreover, the MTO functions are subject to various constraints, including BESS capacity, PV power capacity, BESS power limits during charging and discharging, BESS state of charge, power balance between reactive and real power, apparent power flow through lines, and voltage levels at buses. To address these optimization problems, authors have employed various MTs to find the best solution for each problem. Such is the case in [42], where the authors used a PSO algorithm with an MTO approach due to the complexity of the problem, aiming to optimize the values of active power losses and voltage drops. The strength of PSO is that particles, which represent solutions, are evaluated with respect to the particle with the best fit for the objective function. Each particle in the space is evaluated within an objective function to determine how good the solution that each particle represents is. It is important to mention that each particle adjusts its position in the search space based on the best position found by itself and the best position found by any particle in the swarm. Additionally, the algorithm uses coefficients to weigh the influence of the best personal position and the best global position. On the other hand, in [44], a hybridization of the SCA and the AOA is used to significantly enhance the exploration and exploitation phases of the algorithm. Firstly, the AOA algorithm uses multiplication and division operators to explore the search space to find promising areas and employs subtraction and addition operators to exploit the promising area identified during the exploration phase to find the best solution. Meanwhile, the sine and cosine algorithms initialize a set of search agents randomly within the limits of the search space to calculate the fitness function for all agents and store the best solution found so far. Once the possible solutions are determined, the algorithm’s own parameters are updated, and then the position of the agents is adjusted using equations that include the sine and cosine functions to guide the agent toward the next position region, thus helping to balance the search for a better solution in new areas and refine solutions near the best found. It must be mentioned that the algorithm randomly uses the sine and cosine functions to add diversity to the movement of the agents [48].

Table 2. Metaheuristic algorithms employed in the integration of ESSs into an ADN.

Algorithm	Type	Function/Target	Network Indicator (s)	Constraints	Test System	No. Paper
Particle swarm	Simple	Multi-objective	Energy not supplied	Power flow	30-Buses	[42]
optimization		Location + sizing		Nodal voltage
Multi-objective evolutionary	Hybrid	Mono-objective	Reliability network	Branch current	30-Buses	[45]
algorithm based on		Reliability network		DGUs power	69-Buses
decomposition		DGUs + BESS		Power losses
				Charg./dischar. of BESS
				Charg./dischar decisions
				Nodal voltage
				Network reliability
Equilibrium	Simple	Multi-objective	Energy not supply cost	Nodal voltage	30-Buses	[46]
optimization		Location + sizing	Life cycle cost	Apparent power flow	69-Buses
		BESS + PV	Energy loss cost	Power balance
			CO2 emission costs	BESS state of charge
				BESS power
				PV power
				BESS capacity
Artificial ecosystem	Simple	Mono-objective	Energy cost	Power balance	18-Buses	[43]
optimization		Location + sizing		Nodal voltage	33-Buses
				Branch current	69-Buses
				BESS power
				BESS capacity
Crow search	Hybrid	Multi-objective	ESSs cost	Nodal voltage	33-Buses	[47]
with differential		Location + sizing	Power losses cost	Flicker level
operator		WTs + ESS	Flicker emission cost
			Voltage deviation cost
Arithmetic optimization	Hybrid	Multi-objective	Power losses	Power balance	30-Buses	[44]
with sine–cosine		Location + sizing		Nodal voltage	69-Buses
				Branches currents
Self-learning	Simple	Multi-objective	Voltage deviation	Nodal voltage	33-Buses	[49]
particle swarm		SOC management	SOC deviation	BESS power
optimization				SOC
Chu and Beasley	Hybrid	Mono-objective	Energy losses	Power balance	69-Buses	[50]
genetic algorithm		Location		Nodal voltage
		BESS + CB		Location
				ESS power output
				Battery operative state
				SOC
				Batteries installed
				Amount of ESS.
CPLEX	Simple	Multi-objective	Life cycle cost	BESS power capacities	9-Buses	[51]
solver		Location + sizing	Generation cost	BESS.
				Charging/discharging
				BESS’s energy
				Power flow balance
Henry gas solubility	Hybrid	Mono-objective	Active power losses	System voltage limits	9-Buses	[52]
optimization with		Location		DGU sizing
Simulated annealing		BESS + PV		Battery sizing
				Branch currents
				Power balance
Particle swarm	Simple	Multi-objective	BESS power	BESS power capacity	17-Buses	[53]
optimization		Sizing	Capital cost	BESS energy capacity
			Operating cost	Nominal frequency
			Maintenance cost	BESS cost
				O&M cost
Multi-objective	Simple	Multi-objective	ENS cost	BESS capacity	30-Buses	[54]
equilibrium optimization		Location	PVS and BESS life cost	Amount of PV installed	69-Buses
		BESS + PVS	Energy loss cost	BESS power rating
			CO2 emission cost	Charged and discharged BESS
				SOC
				Nodal voltage
				Power flow
Artificial bee	Simple	Multi-objective	Voltage deviation	Power balance	33-Buses	[55]
colony		Location	Power losses	Nodal voltage
			Line loading	Branch current
				ESS location
				ESS power
				SOC
Genetic	Simple	Mono-objective	Voltage deviation	BESS location	8500-Buses	[56]
algorithm		Location + sizing		BESS capacity
				Initial SOC
				SOC limit
				Maximum discharge rate
				Minimum charge rate

encompasses the most used MTs employed for integrating ESSs technology into ADNs, considering the main parameters in optimization problems, such as type of function, target, network indicators, constraints, and test system size.

6. Metaheuristic Algorithms for Optimal Integration of BCs into an ADN

The use of BCs allows the performance of the ADN to be increased, reducing power losses by up to 13% [57,58]. Therefore, BCs enable the supply of the necessary reactive power to maintain the voltage level within established limits and reduce power losses [59,60]. To minimize power losses in an ADN successfully through the use of BCs, two phases are necessary; the first one involves determining the appropriate bus for installing BCs, and the second one sizing the BCs correctly [61]. It is important to note that there are two types of BCs in an ADN; fixed BCs and switchable BCs [58]. Figure 6 depicts a typical pole-mounted installation of a capacitor bank on an aerial distribution network, commonly found in rural or peri-urban areas. The diagram highlights the main structural components, such as the utility pole, ceramic insulators, PT200 crossarm structure, fuse cutout, and the three-phase distribution wires, which are essential for integrating BCs into the network infrastructure.

To determine the optimal location and size of the BCs, many authors have developed studies where they have modeled optimization problems aimed at increasing the voltage level, reducing power losses, and maximizing the economic benefits of the ADNs through the use of BCs, which are solved by metaheuristic techniques as in [62,63]. In studies such as [64,65,66,67], the problems of the optimal placement and sizing of BCs in the ADNs are addressed. Consequently, the authors propose maximizing voltage stability, minimizing power losses, and achieving annual net savings. Thus, both MTO and MO functions are formulated, focusing on reducing the cost of power losses and the installation cost of capacitors; ensuring the balance between reactive and active power; and reducing loss cost, capacitor installation cost, the reactive cost of capacitors per kVA, and the operational cost of the capacitor to maximize the performance of the ADNs. Similarly, these formulations are subject to both equality and inequality constraints due to the characteristics of the ADNs, such as voltage limits, substation power factor, capacitor size, total compensation, real power limit, reactive power limit, network power factor, and maximum network line capacity. To solve the aforementioned problems, authors have implemented various MTs to find the best location and size for BCs. In [66], the sunflower algorithm is used, which determines the movement of each sunflower based on its orientation and a defined displacement constant and establishes another pollination probability constant that affects this movement, representing the probability of finding better solutions in the search space. Additionally, this algorithm allows for the elimination of the worst sunflowers, which represent the worst solutions in the population, and new sunflowers are created randomly within the problem limits [68]. However, in [66], an improved sunflower algorithm is developed, consisting of improvements in terms of adaptability and exploration of the search space. The modifications therein focus on making the algorithm less sensitive to the parameters of pollination rate and mortality rate and on improving the ability of individual sunflowers to significantly increase the search space and find the global optimum of the problem. Moreover, in [67], hybridization of the SSA and the SCA is used to increase exploitation and exploration in the search for the best solution to the optimization problem. In the SSA, once the population is adjusted, the position of the leader salp and its followers are updated using the algorithm’s own equations to increase the exploration and exploitation of the algorithm. It is important to note that each follower’s position is updated based on its current position and that of the follower ahead of it by using the equation defined for this stage, creating a chain-following effect, where each follower adjusts its position relative to the follower ahead of it [69]. However, the sine–cosine algorithm initializes a set of search agents randomly within the search space limits to calculate the fitness function for all agents and store the best solution found so far. Once the possible solutions are determined, the algorithm’s own parameters are updated, and then the position of the agents is adjusted using equations that include the sine and cosine functions to guide the agent toward the next position region, helping to balance the search for a better solution in new areas and refine solutions near the best found. Therefore, the hybridization consists of updating the leader salp position in SSA by using the SCA exploration technique.

Table 3. Metaheuristic algorithms employed in the integration of BCs into an ADN.

Algorithm	Type	Function/Target	Network Indicator (s)	Constraints	Test System	Paper No.
Particle swarm optimization	Simple	Mono-objective	Power losses	Nodal voltage	34-Buses	[64]
electromagnetic-like		Location + sizing		Branch current	85-Buses
				Power factor
				Capacitor size
				Reactive power
Salp swarm with	Hybrid	Mono-objective	Power losses	Loss-sensitive factor	15-Buses	[67]
sine–cosine		Location	Energy cost		30-Buses
					69-Buses
					85-Buses
Remora optimization	Simple	Multi-objective	Loss cost	Power flow	33-Buses	[65]
		Location + sizing	Capacitor cost	Nodal voltage	69-Buses
			Operation cost	Reactive power
				Power factor
				Branch current
				Capacitors size
Non-dominated	Simple	Multi-objective	Voltage index	Power balance	33-Buses	[58]
sorting genetic		Location + sizing	Net savings	Nodal voltage	94-Buses
algorithm II				Branch current
				Capacitor size
				Reactive power
Improved sunflower	Simple	Mono-objective	Operational cost	Voltage quality	33-Buses	[66]
optimization algorithm		Location		Power flow balance	84-Buses
				Reactive power	118-Buses
				Amount of capacitors
				Capacitor size
Whale optimization	Simple	Multi-objective	Operational cost	Nodal voltage	34-Buses	[70]
		Location	Power losses	Reactive power	85-Buses
Genetic	Simple	Mono-objective	Power losses	Unbalance voltage	14-Buses	[71]
algorithm		Location + sizing		Active power	30-Buses
				Reactive power	33-Buses
				Power angle
Fire hawk	Hybrid	Mono-objective	Power losses	Power balance	Not mentioned	[72]
spiking neural		Location	Voltage deviation	Transformer capacity
network algorithm		CB + EVCs		EV charging power
The chaotic bat	Simple	Mono and multi-objective	Power losses	Load balance	34-Buses	[73]
		Location	Voltage deviation	Nodal voltage	118-Buses
		CB + DGUs	Voltage-sensitive index	Branch current
				Number of DGUs
				DGU size
				Number of capacitors
				Capacitor size
				Power flow balance
Quantum-behaved	Hybrid	Multi-objective	Nodal voltage	EVs power	34-Buses	[74]
Gaussian mutational		Location	Power losses	Branch power
Dragonfly		CB + EVCs		Power EVs
Improved harmony	Simple	Mono-objective	Total cost	Load flow	85-Buses	[75]
		Location + sizing		Nodal voltage	118-Buses
				Reactive power
				Power factor
				Branch current
				Capacitor rating
Genetic	Simple	Multi-objective	Power losses	Power balance	78-Buses	[76]
algorithm		Location	Installation cost	Branch current	96-Buses
		CB + DGUs		Nodal voltage
Golden jackal	Simple	Mono and multi-objective	Active power losses	Power balance	118-Buses	[77]
optimization		Location	Voltage deviation	Nodal voltage
		CB + DGUs	Voltage stability index	DG capacity
				DG operation
				DG location
Genetic	Simple	Mono-objective	Capacitor cost	Nodal voltage	34-Buses	[78]
algorithm		Location	Nodal voltage	Branch current
				Harmonic distortion
				Capacitor sizes
				Amount of capacitors
Improved harmony	Simple	Mono-objective	Total cost	Load flow	15-Buses	[79]
algorithm		Location + sizing		Nodal voltage	69-Buses
				Reactive power	118-Buses
				Power factor
				Branch current
				Capacitor rating
Particle swarm	Simple	Multi-objective	Energy loss cost	Power flow balance	85-Buses	[80]
optimization		Location	Power losses cost	Capacitor capacity	59-Buses
			Substation capacity release cost
			Capacitor placement chargers
COLAHA	Simple	Multi-objective	Power loss index	Power balance	69-Buses IEEE	[37]
Centroid-based oppositional learning		Reconfig. and optimal placement of	Voltage profile index	Voltage limits	118-Buses IEEE
Artificial hummingbird algorithm		DGs, SCs, and EVCs	Power factor index	DG size
			DG penetration index	SC size
			EVC power loss index	Radiality constraint
GO + H3PEM	Hybrid	Multi-objective	Power losses	Power balance	69-Buses IEEE	[81]
(Growth Optimizer with Hong 3-Point		Reconfig. and optimal placement of BEV/CSs,	Voltage index	Voltage limits	85-Buses IEEE
Estimate method)		RESs, and capacitors	BEV hosting capacity	Current on branches	94-Node Portuguese network
				DG output
				Capacitor reactive power
				Charging station size
				Radiality
Parallel search real coded	Simple	Multi-objective	Energy loss reduction	Power balance	33-Buses IEEE	[82]
Genetic algorithm		Sitting and sizing of CSs, V2G, and capacitors	Voltage stability index	Voltage limits	69-Buses IEEE
(PSRCGA)			Voltage deviation index	Branch current
			Capacitor installation cost	Capacitor bank capacity
			V2G energy cost	V2G injection
				Radiality
Competitive search optimization	Hybrid	Multi-objective	Power losses	Voltage	69-Buses IEEE	[38]
with fuzzy and chaos theory		Optimal placement and sizing of	Voltage profile	DG capacity
		DGs, SCs, and EVCs	Power factor	Branch current
			Voltage stability index	Capacitor capacity
			Power loss index	EV demand and charger power profile
			DG penetration index	Radiality

depicts the main MTs, network indicators, constraints, and objective functions employed in the optimization problem for the integration of BCs into ADNs.

7. Metaheuristic Algorithms for Optimal Integration of EVs into an ADN

Recently, the transportation sector has generated a significant increase in CO₂ emissions. In Europe, studies have shown that approximately 30 percent of CO₂ emissions are generated by the vehicular sector [83]. Consequently, various governments have promoted laws to limit and reduce CO₂ emissions to enhance quality of life in the coming years [84], allowing for the modernization of vehicular technology. Currently, EVs are classified into three different groups: fully electric vehicles that have an electric motor and a battery bank, which can be recharged by connecting to an external electric power source; hybrid electric vehicles composed of an electric motor and a combustion engine, which cannot be connected to an external power system and whose charging process is carried out through another process such as vehicle braking; finally, plug-in hybrid electric vehicles that have both an electric motor and a combustion engine that can be connected to an external electric power source [85]. However, a station charger for electric vehicles is an element indispensable for the modernization of the transportation sector. Figure 7 shows a conventional electric vehicle charger and its main elements.

Furthermore, it is worth noting that recharging the batteries of electric vehicles can minimize the performance of ADNs due to their high power demand, potentially saturating the capacity of system components such as transformers and feeders [86]. Therefore, the deployment and charging time of EVs within an ADN is crucial. For this reason, MTs play a pivotal role in integrating electric vehicles into the ADNs without diminishing their performance.

In this regard, studies conducted in [87,88] produced optimization via the rapid integration of electric vehicle charging stations with PV systems into ADNs, posing a challenge, as they can lead to excessive power losses and voltage drops beyond the permissible limits. Thus, in [87], an MTO function has been formulated, focusing on minimizing both active and reactive power losses, the minimization of the average voltage deviation index, and maximizing the voltage stability index throughout the system. This MTO function is subject to both equality and inequality constraints for real and reactive power balance, voltage level at each bus, current limit in branches, and charging power. The optimization problem in [87] is solved using the hybridization of two MTs, a BFOA, and a PSO algorithm. To start, an initial population is first generated using the BFOA method, which allows for diverse and extensive exploration of the search space; at this point, strategies such as chemotaxis, swarming, reproduction, elimination, and dispersion inherent in BFOA are applied, each being mathematical equations that model bacterial behavior in the algorithm, to improve and adapt solutions, meaning better exploration of the algorithm within the search space to find the best solution. After the potential solutions are adjusted by the fitness function, a transition to the PSO algorithm is made. In this phase, the particles move towards the best solutions found, adjusting their velocities and positions based on their individual experiences and those of the best in the swarm, representing the exploitation phase of the algorithm. This is repeated until a certain criterion is reached, such as a maximum number of iterations or convergence towards an optimal solution. In summary, the hybrid BFOA-PSO algorithm combines the exploratory capabilities of BFOA with the exploitation efficiency of PSO, offering a robust and balanced approach for optimization in a wide variety of complex optimization problems. Therefore, several MTs may be employed for solving optimization problems in ADNs; however, each MT has a different approach due to the objectives in each situation.

Table 4. Metaheuristic algorithms employed in the integration of EVs into an ADN.

Algorithm	Type	Function/Target	Network Indicator (s)	Constraints	Test System	No. Paper
Improved particle	Hybrid	Multi-objective	Power losses	Power balance	10-Buses	[88]
swarm optimization		EV charging time	Tap position	Transformer capacity
			Load deviation	EV’s power
			Degree of satisfaction	Nodal voltage
				Branch power
				Battery status
Particle swarm optimization	Hybrid	Multi-objective	Load variance	Charge power	10-Buses	[89]
and gravitational		EV charging time	Customer savings	Discharging power
search				User travel demand
				Feeder capacity
				Schedulable time
				EV battery capacity
Archimedes	Simple	Multi-objective	Power losses	Real power	10-Buses	[90]
optimization		Location	Voltage deviation	Reactive power	33-Buses
			Voltage stability index	Nodal voltage	69-Buses
Arithmetic	Simple	Mono-objective	Power losses	Nodal voltage	33-Buses	[91]
optimization		Location		DGU power
		EVCs + DGU		Battery SOC
				Power flow
Improved whale	Simple	Multi-objective	Construction costs	Users per CS	45-Buses	[92]
optimization		Location + sizing	O&M cost	Charging station capacity
			Charging station cost	Charging demand
				Amount of charging stations
Particle swarm	Simple	Multi-objective	Operation cost	Power balance	33-Buses	[93]
optimization algorithm		Charging and discharging time	Environmental pollution	Nodal voltage
			Peak valley difference of load	Power flow
			Nodal voltage offset rate
			Power losses
			Lower charge cost
Chicken swarm optimization	Hybrid	Mono-objective	Direct costs	Amount of charging stations	33-Buses	[94]
teaching learning		Location	Indirect costs	Reactive power
-based optimization				Maximum load
				Power balance
Artificial bee colony	Hybrid	Multi-objective	Energy loss cost	Power balance	33-Buses	[95]
and firefly		Location	Energy imported cost	Grid energy cost
-based optimization			Energy supplied cost	Store capacity
			Cost of energy supplied by parking lots	Rate of charge
				Rate of discharge
				Power balance
				Rate of charge
				Nodal voltage
				Branch current
				Generation capacity
Tabu search and	Hybrid	Mono-objective	Energy supplied cost	Power balance	449-Buses	[96]
-greedy randomized		Charging coordination	Charge of PEVs	Nodal voltage
Adaptive search procedure			Voltage violation cost	Branch current
				DGU capacity
				Energy balance
				PEV power
Particle swarm optimization	Hybrid	Multi-objective	Costs	Power balance	Allahabad	[97]
and genetic algorithm		Location + sizing	Power balance	Nodal voltage	Distribution
			Real power loss index	Real power generation	system
			Reactive power loss index	Reactive power generation
			Voltage profile index
Genetic algorithm	Simple	Multi-objective	Charging station costs	Charging location	15-Buses	[98]
		Location	Desired traveler convenience	Charging condition
				Amount of EVs
Quantum binary lightning	Simple	Multi-objective	Thermal line loading effect	Branch current	37-Buses	[99]
search algorithm		Location	Voltage deviation	Nodal voltage
COLAHA	Simple	Multi-objective	Power loss index	Power balance	69-Bus IEEE	[37]
Centroid-based oppositional learning		Reconfig. and optimal placement of	Voltage profile index	Voltage limits	118-Buses IEEE
Artificial hummingbird algorithm		DGs, SCs, and EVCs	Power factor index	DG size
			DG penetration index	SC size
			EVCs power loss index	Radiality constraint
Hiking optimization algorithm	Simple	Multi-objective	Energy losses	Energy balance	33-Bus IEEE	[100]
(HOA)		EV integration and RES management	Procurement cost	Voltage limits
			Voltage deviation	Storage operation limits
			Operational cost	Charging/discharging limits for EVs
				DGs operational
				Load shedding
				Renewable energy operational
				Power flow
				Radiality
GO + H3PEM	Hybrid	Multi-objective	Power losses	Power balance	69-Bus IEEE	[81]
(Growth Optimizer with Hong 3-Point		Reconfig. and optimal placement of BEV/CSs,	Voltage index	Voltage limits	85-Buses IEEE
estimate method)		RESs, and capacitors	BEV hosting capacity	Current on branches	94-Node Portuguese network
				DG output
				Capacitor reactive power
				Charging station size
				Radiality
Parallel search real coded	Hybrid	Multi-objective	Energy loss reduction	Power balance	33-Bus IEEE	[82]
genetic algorithm		Sitting and sizing of CSs, V2G, and capacitors	Voltage stability index	Voltage limits	69-Bus IEEE
(PSRCGA)			Voltage deviation index	Branch current
			Capacitor installation cost	Capacitor bank capacity
			V2G energy cost	V2G injection
				Radiality
Competitive search optimization	Hybrid	Multi-objective	Power losses	Voltage	69-Bus IEEE	[38]
with fuzzy and chaos theory		Optimal placement and sizing of	Voltage Profile	DG capacity
		DGs, SCs, and EVCs	Power factor	Branch current
			Voltage stability index	Capacitor capacity
			Power loss index	EV demand and charger power profile
			DG penetration index	Radiality
Modified symbiotic organism	Simple	Multi-objective	Power losses	Bus voltage	Tanzania 79-Node system	[101]
search (MSOS)		Optimal placement of EVCS and PVs	Voltage deviation	PV output
			Voltage profile	Power balance
			Active load index	Line loading
			Voltage stability index	Radiality
				PV capacity
Galaxy gravity	Simple	Multi-objective	Power loss	Voltage deviation index	69-Bus IEEE	[102]
optmization (GGO)		Optimal siting of EVCS	Reliability indices	Charging station capacity	25-Node road + 69-Bus IEEE
			(SAIDI, SAIFI, AENS, CAIDI)	EV load probability distributions
			Location deviation from centroid	Travel distance of users
			Investment cost	Bus voltage
				Branch current

depicts the main MTs employed for the best deployment of EVCs into ADNs, considering the most important details of each paper analyzed and previously mentioned.

8. Metaheuristic Algorithms for an Optimal Reconfiguration of an ADN

An ADN can change its topology configuration by opening and closing its switches to modify the power flow with the purpose of maximizing network performance [103]. Network reconfiguration allows for reducing power losses that lead to an increase in the voltage level profile. Moreover, in ADNs, there are load variations over a time interval, for which a technique called dynamic reconfiguration has been implemented as a solution [103]. This technique helps to reduce the likelihood of ampacity limit violations in the transmission or distribution feeders, transformers, and the permitted voltage level within the system immediately [104]. However, the reconfiguration must ensure that no node is isolated from the system in order to maintain operational continuity. Figure 8 illustrates the IEEE 33-bus radial distribution system, which has been widely adopted in numerous optimization studies due to its representative structure and moderate complexity. This system includes 37 distribution lines, of which 5 (highlighted in orange) are normally open tie-lines that allow reconfiguration opportunities. The presence of these tie-lines enables topological changes while maintaining radiality, which is essential for enhancing operational performance in distribution networks.

Therefore, network reconfiguration helps to reduce the variability to meet the system’s optimal levels [105]. So, the objectives of network reconfiguration can be grouped as follows: reduction of power losses, improvement of the voltage profile, load balancing, and service restoration [10]. Consequently, to carry out a successful reconfiguration of an ADN, various authors have used MTs to find the best layout for the network.

In [106], the authors formulated an MTO function to find the best reconfiguration for an ADN with several DGUs. Each element in the MTO function is weighted, resulting in a sum of four objective functions aimed at minimizing power losses, enhancing network voltage stability, reducing voltage oscillation, and ensuring network reliability, viewed as the energy not supplied to the end user. Similarly, in [107], the focus is on establishing a reconfiguration optimization model for an ADN using an MTO function, which aims to minimize economic cost, reduce active power losses, and minimize voltage deviation. In [108], the distribution network reconfiguration is based on minimizing total power losses to ensure an improved voltage profile in the network. An MO function is established to decrease power losses across all branches of the system, considering the state of switches, and consequently to maximize the voltage level. Moreover, a reconfiguration approach considering DGUs is addressed in [109], where the authors have defined an MTO function focused on minimizing all power losses, load balance indices, and maximizing the penetration level of DGU in the system. The primary constraints for all these objective functions include the capacity of DGU, maximum permitted distributed generation capacity, network voltage limits, thermal limits of feeders, power balance, current limit in the branch, the number of groups for parallel capacitor bank/SVC switching, the number of open/closed switches in the entire system, the thermal capacity of branches and transformers, and network topology to maintain a radial configuration. To find the best configuration network in each case, the authors implemented various MTs. In [107], the sparrow algorithm is used, where the sparrow population is divided into discoverers and joiners, controlled by the population scale factor. Additionally, a third class called explorers allows for broader exploration of the best solution within the search space. After the sparrows’ behavior is adjusted by the fitness function, the position of a discoverer sparrow is updated considering a random condition using a formula that incorporates a normal distribution and random numbers. For the same approach, ref. [108] utilizes the hawk algorithm, where the initial number of hawks in the population is a fixed parameter, and their specific characteristics (open/closed switch) are randomly determined. During the exploration phase, solutions represented by hawks use two perching strategies for finding potential new solutions. The algorithm improves exploitation to converge on the best solution, updating hawk positions based on the chosen attack strategy. Lastly,

Table 5. Metaheuristic algorithms employed for reconfiguration of an ADN.

Algorithm	Type	Function/Target	Network Indicator (s)	Constraints	Test System	No. Paper
Lévy flight	Hybrid	Multi-objective	Active power losses	Power flow	33-Buses	[110]
and chaos disturbed beetle		Reconfiguration	Load balancing index	Nodal voltage	118-Buses
antennae search			Voltage deviation index	Branch current
				Network topology
				Configuration structure
Ant colony	Simple	Multi-objective	Power losses	Power flow balance	33-Buses	[109]
optimization		Reconfiguration	Load balancing	Transformers’ temperature
			DG penetration level	Branch current
				Nodal voltage
Moth-flame	Simple	Multi-objective	Power losses	DGUs capacity	33-Buses	[106]
		Reconfiguration	Voltage stability index	Nodal voltage
		with DGUs	Voltage variation	Feeders temperature
			ENS cost
Sparrow search	Simple	Multi-objective	Economic cost	Power balance	33-Buses	[107]
		Dynamic reconfiguration	Active power losses	Nodal voltage
			Nodal voltage deviation	Branch current
				Shunt capacitor switching
Harris–Hawk	Simple	Multi-objective	Active power losses	Nodal voltage	85-Buses	[108]
		Reconfiguration	Nodal voltage	Branch currents	295-Buses
				Opened/closed switches
Parallel slime	Simple	Multi-objective	Active power losses	Power flow	33-Bus IEEE	[111]
mould		Reconfiguration	Number-switching operation	Nodal voltage
		Considering DGUs	Voltage stability index	Branch currents
			Load balance index	Branch power
				DGUs active power
				DGUs reactive power
				Radial topology
Simple mixed particle	Simple	Mono-objective	Power losses	Real power balance	33-Buses	[112]
swarm optimization		Reconfiguration		Nodal voltage	69-Buses
		Location + sizing DGUs		Branch currents
				Branch power
				DGUs capacity
				DGUs location
Enhanced genetic	Simple	Mono-objective	Power losses	Radial network	33-Buses	[113]
algorithm		Reconfiguration	System reliability	Nodal voltage	69-Buses
				Branch currents	136-Buses
				Kirchhoff’s laws
JAYA and improved	Simple	Multi-objective	Active power losses	DGUs positions	33-Buses	[114]
elitist-Jaya		Reconfiguration +	Loadability enhancement	Nodal voltage	69-Buses
		Location and sizing DGUs		DGUs capacity
				Radial configuration
				Isolation
Improved sine—cosine	Simple	Multi-objective	Active power loss	Power balance	33-Buses	[115]
		Reconfiguration +	Overall voltage stability	DGUs position	69-Buses
		Location + sizing DGUs		DGUs capacity
				DGUs penetration
				Nodal voltage
				Voltage stability index
				Radial configuration
				Isolation
Genetic algorithm with	Hybrid	Mono-objective	Power losses	Power flow	32-Buses	[116]
varying population size		Reconfiguration			Nodal voltage
				Branch currents
Runner-root	Simple	Multi-objective	Real power loss	Power flow	32-Buses	[117]
		Reconfiguration	Load balancing among branches	Nodal voltage	70-Buses
			Load balancing	Radial configuration
			Number of switching operation
			Voltage deviation

shows the MTs more employed for meeting the best topology’s ADN, highlighting the main parameters and indicators employed in each optimization case.

9. Findings

MTs have demonstrated a strong capacity to address complex problems in distribution networks, thanks to their robustness and flexibility. Unlike conventional heuristic methods, which may often converge prematurely to suboptimal solutions, MTs incorporate mechanisms that enable more comprehensive exploration of the solution space. Their key distinguishing features include broad applicability, adaptability, and potential for hybridization. The following attributes summarize their advantages [118]:

• MTs can be applied across a wide range of optimization problems.
• MTs are suitable for real-world applications.
• MTs can be hybridized with other techniques to enhance their performance.
• MTs can be parallelized to reduce execution time.
• MTs possess self-adaptive capabilities during the search process.

To better understand how MTs operate in practice, it is important to examine the general structure of these algorithms. Despite the diversity of MTs, most share four core stages: initialization, fitness evaluation, exploitation, and exploration. These stages are executed iteratively to drive the search toward optimal solutions.

• Initialization stage: A population of candidate solutions is generated based on the programmer’s design. The population size is a key parameter, as it influences the convergence rate and helps prevent premature convergence.
• Fitness stage: Each individual in the population is evaluated using an objective function to assess its performance. This function may be referred to by various names depending on the field: fitness function, cost function, utility function, profit function, etc.
• Exploitation stage: The most promising individuals are used to intensify the search in their vicinity, with the aim of refining the solutions. However, this stage must be balanced with exploration to avoid stagnation in local optima [119].
• Exploration stage: This stage expands the search to broader regions of the solution space to avoid premature convergence. Many MTs implement hybridization strategies at this stage to combine strengths of different algorithms and enhance global search performance [119].

Figure 9 summarizes the full MT process, which continues looping through these stages until specific stopping conditions are met, such as the number of iterations, runtime limits, or convergence thresholds. In addition to analyzing the algorithms themselves, the reviewed studies also shed light on the network performance indicators commonly used to evaluate ADN configurations. These include voltage deviation, power losses, energy not supplied, and load variation. Figure 10 presents a word cloud generated using NVivo 14 software (Lumivero, Denver, CO, USA), which visualizes the frequency of appearance of these indicators. In particular, voltage deviation and power losses are the most frequently targeted indicators for minimization or maximization, especially when integrating DGUs, ESSs, BCs, and EVCs. These metrics play a pivotal role in the evaluation of the efficiency and effectiveness of new configurations in distribution systems.

Beyond performance indicators, another critical dimension that is increasingly being addressed in recent studies is the consideration of uncertainty within the mathematical formulation of optimization problems in distribution networks. Incorporating uncertainty is crucial to ensure robust and realistic solutions in dynamic and stochastic environments. In this review, several approaches were identified to model uncertainties in key parameters such as renewable generation, electricity demand, and user charging behavior. For instance, ref. [35] addressed uncertainty in wind generation and demand through probabilistic power flow using the point estimation method (PEM), providing an efficient alternative to computationally intensive techniques like Monte Carlo simulation. Similarly, ref. [45] recognizes the uncertainty in the load profiles and incorporates a stochastic operational model within their MOEA/D algorithm for the joint planning of DG and BESS units in 30- and 69-bus networks. Ref. [89] considers uncertainty in electric vehicle user behavior by constructing a probabilistic model of charging start times, which is integrated into an optimized charging/discharging schedule via a hybrid PSO-GSA algorithm. Finally, ref. [110] explicitly incorporates stochastic fluctuations from DG sources and EV loads into a multi-objective dynamic reconfiguration model, highlighting the role of uncertainty in network stability and supply quality. These studies demonstrate that uncertainty treatment can be achieved through methods such as point estimation, stochastic programming, scenario generation, and behavioral probabilistic modeling, thereby enhancing the practical applicability of MT-based optimization in highly variable environments.

On the other hand, based on the analysis of Table 1, Table 2, Table 3, Table 4 and Table 5, the use and variants of MTs to solve optimization problems in ADNs were examined. A prevailing trend identified in these studies is the frequent hybridization of two or more MTs to enhance the ability to reach optimal solutions. Among the techniques reviewed, PSO is the second most commonly used, followed by GA and the WOA. Figure 11 presents the frequency with which each MT was found in the reviewed literature. This prevalence of PSO in recent studies is due not only to its simplicity and effectiveness but also to its flexibility when combined with other algorithms. A direct comparison between studies employing the PSO algorithm highlights the advantages of hybridizing it with techniques of different nature. For instance, ref. [88] proposed an enhanced electric vehicle charging strategy based on PSO, incorporating elements from GA and simulated annealing. This hybridization aims to prevent premature convergence by introducing random perturbations and allowing the acceptance of suboptimal solutions with a decreasing probability. As a result, a 6% reduction in the objective function is achieved compared to standard PSO, along with improvements in load distribution and the system’s voltage profile. Similarly, ref. [89] introduces a hybrid technique combining PSO with the gravitational search algorithm, named IGSAPSO, specifically designed for the optimal scheduling of electric vehicle charging and discharging within a multi-objective optimization framework. This approach not only integrates the global memory mechanisms of PSO with the local exploitation capabilities of GSA but also implements adaptive inertia factors, asymmetric learning, and elite strategies. When evaluated using the CEC-2005 benchmark functions, IGSAPSO achieves a mean error of 0.0 in several unimodal functions, outperforming the classical PSO, whose mean error ranges from 1.43 to 313.0. Moreover, in practical applications for vehicle charging systems, the proposed algorithm significantly reduces the total charging cost and the load variance of the power network. These quantitative results reinforce the evidence that hybridizing PSO with non-metaheuristic techniques can yield substantial improvements in complex energy planning problems, both in terms of accuracy and operational stability.

Finally, one of the most significant applications of MTs in ADN optimization lies in maximizing the hosting capacity for the integration of cutting-edge technologies to take advantage of renewable energy sources. Figure 12 illustrates three scenarios of network performance with increasing levels of optimization. The red curve represents a baseline system without MT intervention, where network saturation is reached at lower hosting levels. In the second scenario (blue curve), DGUs are optimally placed and sized using MTs, which reduces power congestion and allows more renewable energy to be hosted. This improvement is achieved by stabilizing the nodal voltages across the network, since the current flowing through a distribution line is directly related to the voltage difference between the nodes and the line impedance. By reducing voltage differences through appropriate DGU placement, line currents are decreased, thus postponing the saturation state. Furthermore, the third scenario (green curve) demonstrates the additional benefit of incorporating a BESS, whose location and capacity are also optimized using MTs, improving network flexibility and increasing the hosting capacity level without exceeding operational limits. In more advanced optimization approaches, the simultaneous sizing and allocation of DGUs, BESSs, and other resources such as capacitor banks and reconfiguration of the feeder topology can be performed. Each of these measures contributes to reducing line loading, balancing voltage profiles, and avoiding critical congestion points, thereby shifting the network further from saturation [120].

10. Discussion

In this analysis, three studies stand out due to their use of real distribution networks as case studies, offering a valuable practical perspective from which to improve the optimization of distribution systems through the optimal integration of EVCs. The first study [81], validated on a real 94-node network in Portugal, demonstrated that the GO algorithm achieved significant improvements, reducing power losses by 93.6% and enhancing the voltage profile by 31.52%, outperforming other methods such as COA, GWO, and PSO. Specifically, GO improved the voltage stability index by 24.568% compared to COA, 24.778% compared to GWO, and 23.514% compared to PSO. In addition to these technical advances, the study robustly addressed uncertainty modeling using the Hong’s three-point estimation method, considering stochastic variations in load ratio, renewable generation, and battery electric vehicle power consumption. However, despite the methodological rigor, the study did not incorporate an economic cost analysis of investment, operation, or maintenance costs, and environmental criteria such as CO₂ emission reduction were also not explicitly addressed. The second study [97], validated on the real distribution system of Allahabad, India, achieved a 6.72% reduction in active power losses, decreasing from 18.992 MW with GA to 18.532 MW with GAIPSO and 18.724 MW with PSO. Additionally, the charging capacity increased to 412 EV chargers with GAIPSO, compared to 200 with GA and 333 with PSO. Although the location and sizing of the stations were optimized and the objective function included detailed economic components such as land, equipment, and installation costs, sensitivity analysis and uncertainty conditions were not formally addressed, and environmental criteria were also omitted. Lastly, the third study [101], validated on a 79-node real distribution network in Tanzania, employed a modified SOS algorithm with penalty mechanisms to optimize the simultaneous placement of EVCs and PV systems. The results demonstrated that the SOS algorithm consistently outperformed PSO and GWO across different scenarios. For instance, when placing three EVCS and one PV system, SOS achieved a power loss of 4.28 kW and a voltage deviation of 0.02899 V, compared to 4.66 kW and 0.02902 V with PSO and 4.60 kW and 0.03277 V with GWO. In all configurations, the SOS algorithm maintained distinct EVCs locations, complying with the optimization constraints, while the other algorithms failed to do it. Although the study did not incorporate installation or operational costs into the optimization model, it briefly mentioned them as potential factors to be considered in future research. Additionally, it did not explicitly address environmental criteria such as CO₂ emissions, nor did it explore sensitivity analysis or uncertainty conditions in depth. However, based on our analysis, we observed that most studies in this field rely on standard IEEE test systems, particularly the 33-bus and 69-bus networks, due to their well-defined characteristics. These systems allow results to be more consistent and comparable across different studies, facilitating the objective evaluation of proposed methodologies. Moreover, we recommend conducting more detailed sensitivity analysis to address uncertainty related to electric vehicle demand, renewable generation variability, and other elements such as energy storage systems and capacitor banks, which would enhance the robustness of optimization models under dynamic conditions. Furthermore, it is essential for future studies to explicitly incorporate environmental criteria, such as CO₂ emission reductions, into optimization models to improve the sustainability of power distribution infrastructures. The use of standardized case studies, such as IEEE benchmark systems, is also encouraged to facilitate more objective comparisons between different methodologies and ensure clearer assessments of their efficiency. However, to enhance the representativeness and realism of these test systems, future research should consider incorporating uncertainty modeling approaches. Scenario analysis, for instance, provides a practical and accessible tool to examine various operational states of the network; robust optimization can ensure feasible solutions under extreme conditions; and probabilistic methods, although more computationally demanding, can capture the stochastic behavior of key variables such as electric vehicle demand, renewable generation, and energy storage availability. Combining these methods would improve the reliability and adaptability of the proposed strategies, even when applied to standardized test systems such as the IEEE networks, thereby strengthening their validity under dynamic and variable conditions in the electrical environment. Looking ahead, it would be valuable to extend research efforts toward larger-scale networks and more complex scenarios involving network reconfiguration, energy storage integration, and dynamic load distribution, which would help to validate the applicability of the proposed approaches in real-world large-scale systems.

11. Conclusions

The findings of this research highlight the relevance and potential of metaheuristic MTs for optimizing the performance of ADNs. These techniques enable the resolution of complex problems through the integration of advanced technologies such as DGUs, ESSs, BCs, and EVCs as well as through network reconfiguration strategies. Their application enhances voltage levels and reduces power losses, both of which are key indicators for assessing whether a distribution network is operating optimally. A fundamental aspect identified in this study is the common structure underlying all MTs, which follows four essential stages: initialization, fitness evaluation, exploration, and exploitation. The effectiveness of a given technique depends on its ability to balance the latter two stages, as this directly influences its capacity to avoid premature convergence and reach global optima. In this context, the proper definition of the initial population, the design of the exploration and exploitation mechanisms, and the formulation of the objective function are critical to the success of the optimization process. Within the analysis conducted, the hybridization of metaheuristic techniques emerges as an effective strategy through which to enhance performance. By combining two or more algorithms, the strengths of both exploratory and exploitative capabilities are reinforced, thereby overcoming the limitations of individual methods. This hybrid approach increases the robustness of solutions, particularly in complex scenarios, by avoiding entrapment in local optima. Certain algorithms, such as PSO and GA, along with their variants, were also observed to be widely employed in network optimization. Their versatility has been demonstrated in both standard implementations and in hybrid, multi-objective, and adaptive schemes, confirming their effectiveness in addressing a wide range of problems in distribution systems. With respect to network performance indicators such as voltage deviation and power losses, these parameters were confirmed as fundamental for improving operational efficiency. Optimizing these indicators allows for the integration of renewable technologies without compromising network stability, since improvements in voltage profiles also lead to reduced losses, positively impacting overall system performance. Notably, the analysis revealed that MTs contribute significantly to increasing the hosting capacity of renewable energy resources. The optimal sizing and placement of technologies such as DGUs and ESSs allow for greater penetration of renewable energy without overloading lines or transformers, which is an essential factor in advancing toward a more sustainable and resilient grid.