Babai

The library has not been released yet and is under development. contributions are welcomed.

C++ Optimization Library (Version 0.1)

Babai(means sheep) is a C++ Optimization library based on Eigen and GSL.

Features

• Solving Unconstrained Optimization Problems
• [to do] Multi-Objective Optimization Problems
• [to do] Constrained Optimization Problems
• [to do] Stochastic Optimization Problems ## How to use Babai Babai requirements:
• C++ compiler that support C++17 (GCC, ...)
• CMake
• GNU Scientific Library
  

to use Babai, you only need to include the include/Babai/babai.hpp. It will include all problem types and optimizers. to build your program, don't forget to link the gsl and gslcblas.also you can use -O3 -march=native flags to increase the performance. this is an example using CMake: cmake cmake_minimum_required(VERSION 3.0) project(BabaiTest) set(CMAKE_CXX_STANDARD 17) set(CMAKE_CXX_FLAGS "-O3 -march=native") include_directories(include) add_executable(app source.cpp) target_link_libraries(app gsl gslcblas)

Gradient-Free Solvers

Adaptive Particle Swarm Optimization

The APSO solver was implemented based on this paper: - Zhan, Z. H., Zhang, J., Li, Y., & Chung, H. S. H. (2009). Adaptive particle swarm optimization. IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics), 39(6), 1362-1381.

Parameters Adaption and Elitist Learning are implemented.

Examples

minimizing the function:

```cpp

include

// include main Babai header

include "Babai/babai.hpp"

int main(){ // create an optimization problem auto p = new babai::problem();

// set number of objective function variables p->dimension(100);

// set lower bound and upper bounds for variables // if the bounds are not same for all variables you can pass a vector // for example : p->lowerbound(v) where v is an Eigen::RowVectorXd p->lowerbound(-10.0)->upper_bound(10.0);

// define the objective using either minimize or maximize method // the objective function could be a lambda function // type of the input is a reference to Eigen::RowVectorXd // you can use all Eigen vector operations or simply access the elements and define your own operation p->minimize( { return v.norm(); });

// create an instance of Adaptive Particle Swarm optimizer auto pso = new babai::PSO();

// set number of particles and problem pso->npop(20)->problem(p);

// trace and control iterations // this function runs in every iteration // type of the input is same as the pso variable (i.e a pointer to the optimizer) pso->iterate( { // using the trace, you can access all parameters of the solver std::cout << "step :" << trace->step() << " | " << "loss :" << trace->best() << " | " << "objective evaluations :" << trace->nfe() << std::endl;

// continue until convergence
if (trace->best() < 0.01)
  trace->stop(); // stop iterations

}); // print the best found position std::cout << "best found position : " << std::endl; std::cout << pso->best_position() << std::endl; return 0; }

```

Parameters

The parameters and methods which are accessible inside the trace function are as follow: - stop() stops optimizer iterations
- step() returns number of performed iterations - best() returns best objective function value - nfe() returns number of the objective function evaluations - npop() returns number of particles
- best_position() returns best found position as a vector - best_local_positions() returns best local position for all particles as a matrix - positions() returns the positions of all particles as a matrix - velocity() returns the velocity of all particles as a matrix
to see explanation for the parameters listed below, refer to the APSO paper - inertia_weight(), returns the inertia weight - self_cognition() returns the Self Cognition - ‍social_influence() returns the Social Influence - evolutionary_factor(), returns the Evolutionary Factor - elitist_learning_rate() returns the Elitist Learning Rate

Gradient-Based Solvers

[to do]

Developers

• Amirabbas Asadi, (amir137825@gmail.com) ## References
• Zhan, Z. H., Zhang, J., Li, Y., & Chung, H. S. H. (2009). Adaptive particle swarm optimization. IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics), 39(6), 1362-1381.