Neuroevolution-based system that simulates investments in the stock market based on the BOVESPA index. Final project of the course SSC0713 - Evolutionary systems applied to robotics. Link to a video in Portuguese summarizing the project: https://youtu.be/SU2fhCUOZ4M.
First, make sure you have a recent version of Python 3. To install the dependencies, open a command shell in the project's root directory and execute the following:
- pip install -r requirements.txt
To run the program, use the command:
- python3 main.py
To improve itself, the system uses concepts of evolutionary computing. Specifically, a genetic algorithm, metaheuristic inspired by the process of natural selection, is used. The evolution process used by the program can be summarized in the following steps:
- Generate a population of n individuals; each individual represents an investor.
- Repeat e times, where e is the number of epochs considered:
- For each investor present in the population, do:
- Simulate the investor's actions (buying and selling shares) in the stock exchange over a predefined period of time.
- Calculate and save the investor's fitness, defined as the percentage of profit it made during the simulation.
- Generate a new population of n individuals, following the steps:
- Add the individual with the highest fitness (investor with the best profit) to the new population.
- Repeat n - 1 times:
- Consider a probabilistic distribution in which individuals with higher fitness are more likely to be selected.
- Select one individual i1 of the old population (without removing it).
- Create a new individual i2 similar to i1, but with small, random differences (mutation).
- Add i2 to the new population.
- Randomly select an individual (except for the one with the highest fitness) from the new population and kill it.
- Randomly generate a new individual and add it to the new population.
- Discard the old population and restart the loop considering the new population.
- For each investor present in the population, do:
During the investment simulations, the investors are provided, for each trading day of the considered period, with historic data of the BOVESPA Index (or IBOVESPA), benchmark index of about 60 stocks that are traded on the B3 (Brasil Bolsa Balcão), which account for the majority of trading and market capitalization in the Brazilian stock market. The database, obtained at https://br.investing.com/, contains the opening and closing number of points the IBOVESPA had in each trading session from December 27 of 2000 to June 15 of 2020.
For the purposes of our simulations, the IBOVESPA is treated as an exchange-traded fund (ETF), i.e., an investment fund traded on stock exchanges, much like stocks. The price of each "IBOVESPA share" in a given instant is equal to the IBOVESPA divided by 1000.
In each trading session, the investor (an individual of the population), represented by the class Investor, can decide to take one of the following actions:
- buy IBOVESPA shares;
- do nothing;
- sell IBOVESPA shares.
The investor can take only one action in each trading day, during its end. In order to make a decision, the investor is provided, in each trading session, with the following informations:
- the current amount of cash he has;
- the number of shares he has;
- the average price paid by the investor for his shares;
- the closing price of the "IBOVESPA shares" for the past d days, where d is a predefined number.
The main component of each investor is his "brain". We give that name to the Artificial Neural Network (ANN) responsible for making decisions for the investor. The ANN takes, as input, a vector with the information above. It outputs a real number h. The program rounds h to the nearest integer and interprets it as follows:
- h > 0: action to buy h shares of IBOVESPA;
- h = 0: no action;
- h < 0: action to sell |h| shares of IBOVESPA.
As we've seen, the reproduction step occurs after each generation. The individuals with the best fitness are selected from the old population and used to generate individuals for a new population (the next generation). In the context of this project, this means that during the reproduction step the neural networks of the best investors of the past generation are selected and used to generate the neural networks of the new generation. The new neural networks have the same topology of their ancestors, but slightly different weights.
Our goal, by changing the weights of the ANNs in the population, is to achieve, after each generation, individuals with a higher fitness. The process of generating neural networks with evolutionary algorithms (a genetic algorithm, in our case) is called neuroevolution (hence the name of the project).
Two different reproduction techniques were tested in this project: elitism and reward-based selection. The elitist approach selects the individual with the best fitness and mates him with all the other individuals in the population. The result of the mating of two individuals is a new neural network whose weights are the sum of its parents' weights divided by 2 and multiplied by a mutation rate.
In the reward-based approach, on the other hand, the probability of selecting an individual is proportional to its fitness. Given a sorted zero-indexed list with n individuals, where the worst-fitness individual occupies the index 0 and the best-fitness individual occupies the index n - 1, the chance of the individual in the index i to be picked is given by 2i divided by the sum of the whole distribution. When selected, the weights of the individual's neural network are multiplied by a mutation rate and used to generate a new ANN, that will belong to an individual of the new generation.
The reward-based reproduction was the one that yielded the best results. In both cases, the best individual was preserved between generations. In addition, after the reproduction stage, one individual of the new population was randomly killed and replaced by a new randomly generated individual. This strategy, called predation (Simões & Barrone, 2002), was used to avoid local optimums, adding new "genetic material" to the population.
The mutation rate used was mutable itself. It's inversely proportional to the increase of the population fitness in the last generations. This means that when the population's fitness hasn't increased much (or has decreased) over a given number of generations, the mutation rate is increased, forcing the population to change more quickly. On the other hand, when the population fitness has been increasing rapidly and steadily, the mutation rate is lowered, in order to keep the evolution process in the "current tracks".
A population of 20 investors was considered. Each investor started with R$1000 of cash available to buy stocks. In each trading session, the investors had access to the past 30 days of closing prices of the "IBOVESPA shares". The population was "trained" with data from December 27 of 2000 to March 05 of 2015 (total of 3500 trading sessions). The evaluation was performed with data from March 06 of 2015 to June 12 of 2020 (total of 1345 trading sessions).
The performance of the top 3 investors of the population, with the evaluation data (previously unknown to the individuals), is plotted below, along with the IBOVESPA's performance during the same period. The red investor, specifically, handled crises and crashes exceptionaly well.
