3.3.3. EV Charging Based on Shuffled Frog Leaping Algorithm (SFLA)

The SFLA is a meta-heuristic or, precisely, a memetic approach motivated from frog jumping. This algorithm considers a frog group's observed behavior while finding a location with a maximum amount of food. A population of frogs is randomly assigned in the search space. The memeplexes are generated by dividing the population into several groups. The memeplexes are evolved separately in different directions within the search space. In every memeplex, the frogs are influenced by each other. This influence makes the frogs experience a memetic evolution. Hence, the memetic evolution helps the memeplexes enhance every frog's performance to achieve the goal. During the evolution, an individual frog can change the direction based on the best frog's information in a memeplex or from the population's best frog. After an individual frog has improved its position, the frog's information can be enhanced further. The memeplexes are shuffled with each other after a particular number of memetic evolution, and then the new memeplexes are generated. This improves the ability of the frogs to find the best solution within the search space.

The position of the worst frog is updated, following the expressions given in Equations (15)–(17).

$$\mathcal{S}\_{l} = r \times (X\_b - X\_w^{new}) \tag{15}$$

$$X\_w^{new} = X\_w^{current} + \mathcal{S}\_i \tag{16}$$

so that;

$$
\dot{S}i\_{\rm min} < \dot{S}i < \dot{S}i\_{\rm max} \tag{17}
$$

where the variation of the frog's location in a single jump is *Si*. *r* is a random uniformly distributed number ranging between 0 and 1. The most and least permissible variation of the frog's location is *Si*min and *Si*max. The number of memeplexes is 10, the number of frogs in a memeplex is 10, the number of frogs in a sub memeplex is 10, and the population size is 100. *Si*min and *Si*max vary from 0.9 to 0.4, the tolerance is 0.1, and the random value ranges from 0 to 1. The step by step procedure of implementing the SFLA is given as follows:

