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In the previous articles of the series Revisiting geometry and Smart neural network optimization, I shared my observations and experiments with neural networks. Besides, I carried out the optimization of the resulting EAs and provided some explanations of their work. Despite all this, I barely touched the subject of the practical application of the obtained results. In this article, I will fix this unfortunate omission.

I will show the practical application of the obtained results and highlight a new algorithm allowing us to expand the capabilities of our EAs. As always, I will use only MetaTrader 5 tools without any third-party software. The article will most likely be similar to a step-by-step instruction. I will try to explain everything in the most accessible and simple way.

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The Bacterial Foraging Optimization (BFO) algorithm is a fascinating optimization technique that can be used to find approximate solutions to extremely complex or impossible numerical function maximization/minimization problems.
The algorithm is widely recognized as a global optimization algorithm for distributed optimization and control.

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In the previous article, we saw how category theory can be potent in complex systems via its concepts of products, coproducts, and the universal property, examples of applications of which in finance and algorithmic trading were shared. Here, we will delve deeper into spans, experiments, and compositions.

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Mathematical expectation in trading is one of the indicators used to evaluate a trading strategy efficiency. In 1738, Daniel Bernoulli published his work "Specimen theoriae novae de mensura sortis" (Exposition of a New Theory on the Measurement of Risk). In this work, he derived the moral expectation equation. The main difference between moral expectation and mathematical expectation is that moral expectation depends on the player's capital and implicitly takes into account the risk of the game.

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Among all the considered models, CNN-LSTM models have generated the best results during the experiments. In this article, we will consider how to create such a model to forecast financial timeseries and how to use the created ONNX model in an MQL5 Expert Advisor.

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In our previous article, we discussed how equalizers in category theory can be employed to estimate volatility changes using sampled data. In this follow-up article, we will delve into composition and cones in category theory by exploring the significance of various cone setups on the end results of analysis.

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By using special data types 'matrix' and 'vector', it is possible to create the code which is very close to mathematical notation while avoiding the need to create nested loops or to mind correct indexing of arrays in calculations. In this article, we will see how to create, initialize, and use matrix and vector objects in MQL5.

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For stable trading, it is usually recommended to diversify both the traded instruments and the trading strategies. The same refers to machine learning models: it is easier to create several simpler models that one complex one. But it can be difficult to assemble these models into one ONNX model. In this article, we will consider one of the ensembles called the voting classifier. We will show you how easy it is to implement such an ensemble.

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The Harmony Search (HS) method is an emerging metaheuristic optimization algorithm that has been used to solve numerous complex problems over the past decade. The Harmony Search algorithm (HS) was first proposed in 2001 by Z. W. Geem. The HS method is inspired by the founding principles of musical improvisation and the search for musical harmony. The combinations of perfect harmony of sounds are matched with the global extremum in the multidimensional optimization problem, while the musical improvisation process is matched with a search for the extremum.

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Monkey Algorithm (MA) is a metaheuristic search algorithm. This article will describe the main components of the algorithm and present solutions for the ascent (upward movement), local jump and global jump. The algorithm was proposed by R. Zhao and W. Tang in 2007. The algorithm simulates the behavior of monkeys as they move and jump over mountains in search of food. It is assumed that the monkeys come from the fact that the higher the mountain, the more food on its top.

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