GOBC-PA 1.3
A new unconstrained global optimization method based on clustering and parabolic approximation
Requires Python: >=3.7

## Table of contents
* [General Info](#general-info)
* [Technologies](#technologies)
* [Setup](#setup)
* [How to use](#how-to-use)
* [Example](#Example)
* [Example 2](#Example2)
* [Cite](#Cite)

## General Info
GOBC-PA: A new unconstrained global optimization method based on clustering and parabolic approximation
 (GOBC-PA) is proposed. Although the proposed method is basically similar to other
 evolutionary and stochastic methods, it represents a significant advancement of global optimization
 technology for four important reasons. First, it is orders of magnitude faster than existing optimization
 methods for global optimization of unconstrained problems. Second, it has significantly better repeatability,
 numerical stability, and robustness than current methods in dealing with high dimensionally
 and many local minima functions. Third, it can easily and faster find the local minimums using the
 parabolic approximation instead of gradient descent or crossover operations. Fourth, it can easily
 adapted to any theoretical or industrial systems which are using the heuristic methods as an intelligent
 system. In this study, we assume that the best cluster center gives the
 position of the possible global optimum. The usage of clustering and curve fitting techniques brings
 multi-start and local search properties to the proposed method. The experimental studies show that
 the proposed methodology is simple, faster and, it demonstrates a superior performance
 when compared with some state of the art methods.

Arguments: (input)
* func         - objective function
* rang         - range of search space
* target       - target function value. That value used for measuring error.
* N            - dimension number of objective function
* ite          - Maximum iteration
* pop_size     - population size
 
 
Arguments: (output)
* Best_point   - Global minimum points
* Best_result  - Global minimum value on global minimum points
* perf         - errors list
* broken_epoch - epoch number of code break
* performance  - best points and their objective value on each epoch
	
## Technologies
Project is created with:
* Python 3.7
	
## Setup
To run this project, install it locally using pip:

```
$ pip install GOBC-PA
```

## How to use

```
from GOBC_PA.GOBC_PA import GOBC_PA
Best_point, Best_result, perf, broken_epoch, performance = GOBC_PA(func,rang,target,N,ite,pop_size)
 
```

## Example

```
import numpy as np
from GOBC_PA.GOBC_PA import GOBC_PA
def func(x):   Rastrigin function
    y= x[0]**2+x[1]**2-np.cos(18*x[0])-np.cos(18*x[1])
    return y
# min range values for each dimension are in the first row, max range values for each dimension are in the second row
rang = np.array([[-1,-1],[1, 1]])
target = -2
N,ite,pop_size = 2,1000,60
Best_point, Best_result, perf, broken_epoch, performance = GOBC_PA(func,rang,target,N,ite,pop_size)
 
```

## Example2

You can make an example like below to see how it sorts files in console output.

```
import numpy as np
from GOBC_PA.GOBC_PA import GOBC_PA
def func2(x):  # Goldstein-Price's Function
    y = (1 + ((x[0] + x[1] + 1) ** 2) * (
                19 - 14 * x[0] + 3 * x[0] ** 2 - 14 * x[1] + 6 * x[0] * x[1] + 3 * x[1] ** 2)) * (
                    30 + ((2 * x[0] - 3 * x[1]) ** 2) * (
                        18 - 32 * x[0] + 12 * x[0] ** 2 + 48 * x[1] - 36 * x[0] * x[1] + 27 * x[1] ** 2))
    return y

rang2 = np.array([[-2,-2],[2, 2]])
target2=3
N,ite,pop_size = 2,1000,60
Best_point, Best_result, perf, broken_epoch, performance = GOBC_PA(func2,rang2,target2,N,ite,pop_size)
 
```

## Cite

Pence, I., Cesmeli, M. S., Senel, F. A., & Cetisli, B. (2016). A new unconstrained global optimization method based on clustering and parabolic approximation. Expert Systems with Applications, 55, 493-507.