📚 Welcome to the pymoors Documentation

This is the official documentation for the pymoors project.

What is pymoors?

pymoors is a library of genetic algorithms for solving multi-objective optimization problems. Its main goal is to provide a faster tool than current Python libraries, as it is built purely in Rust.

Genetic Algorithms are exposed to Python via pyo3.

Key Features

• Implemented in Rust for superior performance.
• Accessible in Python through pyo3.
• Specialized in solving multi-objective optimization problems using genetic algorithms.

Introduction to Multi-Objective Optimization

Multi-objective optimization refers to a set of techniques and methods designed to solve problems where multiple objectives must be satisfied simultaneously. These objectives are often conflicting, meaning that improving one may deteriorate another. For instance, one might seek to minimize production costs while maximizing product quality at the same time.

General Formulation

A multi-objective optimization problem can be formulated in a generic mathematical form. If we have \(k\) objective functions to optimize, it can be expressed as:

\[ \begin{aligned} &\min_x \quad (f_1(x), f_2(x), \dots, f_k(x)) \\ &\text{subject to:} \\ &g_i(x) \leq 0, \quad i = 1, \dots, m \\ &h_j(x) = 0, \quad j = 1, \dots, p \end{aligned} \]

Where: - \( x \) represents the set of decision variables. - \( f_i(x) \) are the objective functions. - \( g_i(x) \leq 0 \) and \( h_j(x) = 0 \) represent the constraints of the problem (e.g., resource limits, quality requirements, etc.).

Unlike single-objective optimization, here we seek to optimize all objectives simultaneously. However, in practice, there is no single “best” solution for all objectives. Instead, we look for a set of solutions known as the Pareto front or Pareto set.

The Role of Genetic Algorithms in Multi-Objective Optimization

Genetic algorithms (GAs) are search methods inspired by biological evolution techniques, such as selection, crossover, and mutation. Some of their key characteristics include:

• Heuristic: They do not guarantee finding the global optimum but can often approximate it efficiently for many types of problems.
• Parallel Search: They work with a population of potential solutions, which allows them to explore multiple regions of the search space simultaneously.
• Lightweight: They usually require less information about the problem (e.g., no need for gradients or derivatives), making them suitable for complex or difficult-to-model objective functions.

Advantages for Multi-Objective Optimization

1. Natural Handling of Multiple Objectives: By operating on a population of solutions, GAs can maintain an approximation to the Pareto front during execution.
2. Flexibility: They can be easily adapted to different kinds of problems (discrete, continuous, constrained, etc.).
3. Robustness: They tend to perform well in the presence of noise or uncertainty in the problem, offering acceptable performance under less-than-ideal conditions.

Beauty and Misbehavior Optimization Problem

In this unique optimization problem, there is only one individual who optimizes both beauty and misbehavior at the same time: my little dog Arya!

Arya not only captivates with her beauty, but she also misbehaves in the most adorable way possible. This problem serves as a reminder that sometimes the optimal solution is as heartwarming as it is delightfully mischievous.