Numerical optimization principles and analysis of the Whale Optimization Algorithm (WOA)

The Whale Optimization Algorithm (WOA) is a nature-inspired metaheuristic optimization algorithm that simulates the hunting behavior of humpback whales and is used for the optimization of numerical problems.

The Whale Optimization Algorithm (WOA) starts with a set of random solutions and optimizes based on a randomly selected search agent or the best solution so far through position updates of the search agent in each iteration.

Inspiration for whale optimization algorithm

The whale optimization algorithm is inspired by the hunting behavior of humpback whales. Humpback whales prefer food found near the surface, such as krill and schools of fish. Therefore, humpback whales gather food together to form a bubble network by blowing bubbles in a bottom-up spiral when hunting.

In the "upward spiral" maneuver, the humpback whale dives about 12 m, then begins to form a spiral bubble around its prey and swims upward toward the surface.

Whale optimization algorithm logic

The whale optimization algorithm is a group-based random optimization algorithm that is simple and robust. This algorithm has the ability to avoid falling into local optimal solutions and find global optimal solutions, so it performs well when solving optimization problems under different or unconstrained conditions. The whale optimization algorithm is an optimal algorithm.

1. Surround prey

Humpback whales can identify the location of prey and surround it. In the whale algorithm, the best search agent is considered to be the target prey or a location close to the optimal point, and other search agents will strive to move closer to the best search agent.

The whale algorithm assumes that the current best candidate solution is the target prey or close to the optimal solution. Other search agents will try to update their position to the best search agent.

2. Bubble Net Hunting

In the Whale Optimization Algorithm (WOA), the spiral bubble net is mathematically modeled and optimized; the hunting behavior is simulated using random or best search agents to chase prey; use spirals to simulate the humpback whale's bubble net attack mechanism.

3. Searching for prey

The same method based on variation of the {\displaystyle{\thing{A}}} vector can be used to search for prey (exploration). In fact, humpback whales search randomly based on each other's location.

Update the search agent's position during the exploration phase based on a randomly selected search agent instead of the best search agent.

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