Discussing the article: "Dolphin Echolocation Algorithm (DEA)"

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Check out the new article: Dolphin Echolocation Algorithm (DEA).

In this article, we take a closer look at the DEA algorithm, a metaheuristic optimization method inspired by dolphins' unique ability to find prey using echolocation. From mathematical foundations to practical implementation in MQL5, from analysis to comparison with classical algorithms, we will examine in detail why this relatively new method deserves a place in the arsenal of researchers facing optimization problems.

To better understand how the algorithm works, let's imagine the following situation. You and your friends are looking for gold on a large beach, armed with metal detectors. At the beginning of the search, it makes sense to spread out across the entire area — this way you have a better chance of stumbling upon something interesting. But as soon as one of you hears a strong signal, they inform the others, and gradually the whole team begins to concentrate in promising places. By the end of the search, everyone is digging near the strongest signal. This is the essence of the dolphin echolocation algorithm.

In the algorithm, the role of dolphins is played by search agents - points in the solution space. Each such "dolphin" represents a potential solution to the problem. For example, if we are looking for the minimum of a simple function y = x², then one dolphin may be at the point x = -3 (where y = 9), another at the point x = 1 (where y = 1), and the third will randomly end up at the point x = 0 (where y = 0) - this will be our champion.

But how do dolphins exchange information? This is where the concept of effective radius, denoted as "Re", comes into play. Think about how far the light from a flashlight spreads. At Re = 1 we have a narrow beam that illuminates only the immediate area. At Re = 3, the light spreads wider, covering more space. At Re = 5 or above, the search behaves more like a floodlight. In the context of the algorithm, this means that information about a good solution spreads to neighboring areas, and the strength of this influence decreases with distance.

All this information is accumulated in the form of a "prospectivity map", which the algorithm calls the accumulated fitness (AF). Imagine a heat map of a city, where "hot" zones indicate areas of high activity. In our case, "hot" zones are areas where dolphins have found good solutions (prey). The more successful finds in a particular area, the "hotter" it becomes, attracting other dolphins.

Author: Andrey Dik