5. Firefly Algorithm (FA)

The Firefly algorithm is developed from the characteristic relationship between line intensity and fireflies [138]. Different authors proposed a FA that can track the global peak of PV systems under partial shading. Two variables, namely *γ*, the light absorption coefficient, and *α*, the random coefficient, are used to randomize the first position of the firefly. A modified version of FA called simplified firefly algorithm (SFA) is proposed in [139,140], where the initial position of the firefly is selected between zero and one. The optimization equation of SFA is represented as:

$$X\_{l}^{t+1} = X\_{l}^{t} + \beta (X\_{\bar{l}} - X\_{l}) \tag{21}$$

where


*β* is the firefly attractiveness factor.

The objective function of SFA is to generate the maximum available photovoltaic output power, and the firefly position represents the duty cycle *d*.

6. Ant Colony Optimization (ACO)

ACO is an optimization technique based on the food-searching behavior of ants. ACO is an efficient and robust MPPT tracking the global peak of PV systems during partial shading conditions [141]. Different researchers evaluated the technique under varying irradiance and different shading patterns. The algorithm has a fast tracking speed of around one-tenth of the conventional MPPT methods for partial shading conditions [142,143].

7. Artificial Bee Colony (ABC)

Similar to ACO, ABC algorithms are an optimization technique based on the foodsearching behavior of bees. The advantage of this algorithm is that it uses few parameters, and the convergence criteria are not dependent on the initial condition of the system [74]. The disadvantage of this method is that it is complex for practical implementation, and the tracking speed is slow compared to other MPPT methods used for partial shading conditions. The algorithm sometimes settles at the local peak rather than tracking the global peak [144]. The algorithm classifies the artificial bees into three categories: employed bees, onlooker bees, and the last scouts. Figure 11 depicts the flow chart of ABC, where the algorithm has four phases. The first phase initializes the algorithm by setting the different parameters. The second phase activates the employed bees searching for food, and the third phase activates the onlooker bees waiting in the hive to decide. The fourth phase is the scouting phase, where the bees search for random food sources. All three groups communicate and coordinate to obtain the optimal solution quickly. In the algorithm, the food source is the maximum power, and the duty cycle of the DC–DC converter is the food position. For implementing ABC in MPPT for PV system, the duty cycle for the DC–DC converter is calculated as follows:

$$\begin{array}{l}d = d\_{\text{min}} + rand[0, 1](d\_{\text{max}} - d\_{\text{min}})\\new d = d + \wp\_{\varepsilon}(d - d\_{p})\end{array} \tag{22}$$

where

*d* is the current duty cycle, *dmin* is the minimum value of the duty cycle, *dmax* is the maximum value of the duty cycle), *φ<sup>e</sup>* is a constant between [−1, 1], and *dp* is the previous duty cycle.

**Figure 11.** Flow chart of artificial bee colony optimization [145].

8. Cuckoo Search (CS)

The CS method is another optimization technique based on the levy flight mechanism of cuckoo birds [146,147]. The levy flight mechanism algorithm represents the cuckoos' search for a nest. The algorithm is a modified form of PSO with robust performance, high convergence speed, and efficiency. CS needs less tuning variables compared to PSO [148].

9. Jaya Algorithm (JA)

R.V. Rao introduced JA, whichis based on animal activities [149]. The algorithm is based on the distinct feature of animals or humans from the population. Naturally, humans or animals try to mimic the elite members of society and want to distance themselves from the lazy group. Figure 12 presents the flow chart of the JA. The candidate solution moves towards the best solution and tries to move away from the worst solution. The algorithm's

simplicity and fast convergence make it the primary choice by different researchers to solve various engineering problems [150,151].

**Figure 12.** Flow chart of Jaya algorithm [152].

4.1.3. Hybrid MPPT Techniques

1. Hybrid GWO and P&O MPPT Algorithm

The authors in [84] combined P&O and GWO to enhance the performance of the MPPT control of the PV system under partial shading. The method works in two phases. In the first phase, GWO is implemented, and P&O is activated in the second phase to enhance the tracking speed. The computational burden and search space have been reduced by hybridizing the two techniques. This hybrid algorithm of GWO and P&O has several advantages, including fast-tracking speed, high efficiency, and high-tracking capability. Figure 13 presents the flow chart of the hybrid method where GWO is executed in the first phase and P&O in the second phase.

**Figure 13.** Flowchart of hybrid GWO and P&O algorithm [153].
