The Whale Optimization Algorithm
The article titled, “The Whale Optimization Algorithm” by Seyedali Mirjalili and Andrew Lewis highlights an advancement in engineering software that proposes the use of meta-heuristic optimization algorithm. The algorithm relies on simple concepts and thus is easy to implement, it does not require gradient information, it can bypass local optima and can also be utilized on a wide array of problems from different disciplines (Mirjalili & Lewis, 2016). This approach highlights three main categories that include an evolution-based, a physics-based, and a swarm-based method.
The whale optimization algorithm is applied in solving optimization problems and includes three operators; one that simulates the search for prey, the other that encircles prey while the other uses the bubble-net foraging behavior of humpback whales. The bubble-net feeding is a foraging behavior that whales use during hunting (Mirjalili & Lewis, 2016). They create a circle of distinctive bubbles that offers a path they can use to hunt down krill or small fish that move in herds mainly because they can recognize the location of their prey encircling them.
Thus, with the encircling prey algorithm, it is assumed that the current best candidate solution is the target prey that is close to the optimum and, as such, makes use of the formulas.

Where;

Further, there is the bubble-net attacking method that makes use of this formula.

Therefore;

Then there is the search for prey algorithm that utilizes the formula below in mimicking how humpback whales search randomly according to the position of each other.

Consequently, these formulas can be applied in solving the economic dispatch problem, in breast cancer diagnosis, optimal power flow problems, as well as in solving multi-objective optimal vehicle fuel consumption among other areas.

References
Mirjalili, S., & Lewis, A. (2016). The whale optimization algorithm. Advances in engineering software, 95, 51-67.