### Install pypop7 from GitHub

Source: https://pypop.readthedocs.io/en/latest/_sources/installation.rst.txt

Install the latest cutting-edge version of pypop7 directly from its GitHub repository for development purposes. This involves cloning the repository and performing an editable installation.

```bash
git clone https://github.com/Evolutionary-Intelligence/pypop.git
cd pypop
pip install -e .
```

--------------------------------

### Install PyPop7 using Pip

Source: https://pypop.readthedocs.io/en/latest/index.html

Use pip to automatically install pypop7 via PyPI. This is the recommended method for most users.

```bash
$ pip install pypop7

```

--------------------------------

### Install PyPop7 using pip

Source: https://pypop.readthedocs.io/en/latest/_sources/index.rst.txt

Use pip to automatically install pypop7 via PyPI. Refer to the online documentation for alternative installation methods.

```bash
$ pip install pypop7
```

--------------------------------

### DS Initialize Starting Point

Source: https://pypop.readthedocs.io/en/latest/_modules/pypop7/optimizers/ds/ds.html

Initializes or retrieves the starting point 'x' for the Direct Search optimizer. If restarting or if 'x' was not provided, it generates a random point within the initial boundaries. Otherwise, it uses the provided 'x'.

```python
def _initialize_x(self, is_restart=False):
        if is_restart or (self.x is None):
            x = self.rng_initialization.uniform(self.initial_lower_boundary, self.initial_upper_boundary)
        else:
            x = np.copy(self.x)
        assert x.shape == (self.ndim_problem,)
        return x
```

--------------------------------

### CLPSO Initialization and Optimization Example

Source: https://pypop.readthedocs.io/en/latest/_modules/pypop7/optimizers/pso/clpso.html

Demonstrates how to initialize and run the CLPSO optimizer to minimize the Rosenbrock function. Ensure problem and option dictionaries are correctly defined.

```python
import numpy
from pypop7.benchmarks.base_functions import rosenbrock  # function to be minimized
from pypop7.optimizers.pso.clpso import CLPSO
problem = {'fitness_function': rosenbrock,  # define problem arguments
           'ndim_problem': 2,
           'lower_boundary': -5*numpy.ones((2,)),
           'upper_boundary': 5*numpy.ones((2,))}
options = {'max_function_evaluations': 5000,  # set optimizer options
           'seed_rng': 2022}
clpso = CLPSO(problem, options)  # initialize the optimizer class
results = clpso.optimize()  # run the optimization process
# return the number of function evaluations and best-so-far fitness
print(f"CLPSO: {results['n_function_evaluations']}, {results['best_so_far_y']}")
```

--------------------------------

### Benchmark Optimizers with COCO Platform

Source: https://pypop.readthedocs.io/en/latest/tutorials/tutorials.html

This snippet demonstrates benchmarking optimizers using the COCO platform with PyPop7. Ensure COCO is installed and follow the installation guide carefully. This code generates data for post-processing with cocopp.

```python
"""Demo for `COCO` benchmarking using only `PyPop7` here:
   https://github.com/numbbo/coco

   To install `COCO` successfully, please read the above open link carefully.
"""
import os
import webbrowser  # for post-processing in the browser

import numpy as np
import cocoex  # experimentation module of `COCO`
import cocopp  # post-processing module of `COCO`

from pypop7.optimizers.es.maes import MAES


if __name__ == '__main__':
    suite, output = 'bbob', 'COCO-PyPop7-MAES'
    budget_multiplier = 1e3  # or 1e4, 1e5, ...
    observer = cocoex.Observer(suite, 'result_folder: ' + output)
    minimal_print = cocoex.utilities.MiniPrint()
    for function in cocoex.Suite(suite, '', ''):
        function.observe_with(observer)  # to generate data for `cocopp` post-processing
        sigma = np.min(function.upper_bounds - function.lower_bounds) / 3.0
        problem = {'fitness_function': function,
                   'ndim_problem': function.dimension,
                   'lower_boundary': function.lower_bounds,
                   'upper_boundary': function.upper_bounds}
        options = {'max_function_evaluations': function.dimension * budget_multiplier,
                   'seed_rng': 2022,
                   'x': function.initial_solution,
                   'sigma': sigma}
        solver = MAES(problem, options)
        print(solver.optimize())
    cocopp.main(observer.result_folder)
    webbrowser.open('file://' + os.getcwd() + '/ppdata/index.html')

```

--------------------------------

### Initialize and Optimize with Nelder-Mead

Source: https://pypop.readthedocs.io/en/latest/_modules/pypop7/optimizers/ds/nm.html

Demonstrates how to initialize the NM optimizer with problem and option settings, and then run the optimization process. It shows how to define the problem, set optimizer parameters like maximum function evaluations and initial guess, and print the optimization results.

```python
import numpy
from pypop7.benchmarks.base_functions import rosenbrock  # function to be minimized
from pypop7.optimizers.ds.nm import NM
problem = {'fitness_function': rosenbrock,  # define problem arguments
           'ndim_problem': 2,
           'lower_boundary': -5*numpy.ones((2,)),
           'upper_boundary': 5*numpy.ones((2,))}
options = {'max_function_evaluations': 5000,  # set optimizer options
           'seed_rng': 2022,
           'x': 3*numpy.ones((2,)),
           'sigma': 0.1,
           'verbose': 500}
nm = NM(problem, options)  # initialize the optimizer class
results = nm.optimize()  # run the optimization process
# return the number of function evaluations and best-so-far fitness
print(f"NM: {results['n_function_evaluations']}, {results['best_so_far_y']}")
```

--------------------------------

### Initialize and Optimize with SRS

Source: https://pypop.readthedocs.io/en/latest/rs/srs.html

Demonstrates how to initialize the SRS optimizer with problem and option configurations and run the optimization process. The output shows the number of function evaluations and the best fitness found.

```python
1>>> import numpy
2>>> from pypop7.benchmarks.base_functions import rosenbrock  # function to be minimized
3>>> from pypop7.optimizers.rs.srs import SRS
4>>> problem = {'fitness_function': rosenbrock,  # define problem arguments
5...            'ndim_problem': 2,
6...            'lower_boundary': -5*numpy.ones((2,)),
7...            'upper_boundary': 5*numpy.ones((2,))}
8>>> options = {'max_function_evaluations': 5000,  # set optimizer options
9...            'seed_rng': 2022,
10...            'x': 3*numpy.ones((2,)),
11...            'sigma': 0.1}
12>>> srs = SRS(problem, options)  # initialize the optimizer class
13>>> results = srs.optimize()  # run the optimization process
14>>> # return the number of used function evaluations and found best-so-far fitness
15>>> print(f"SRS: {results['n_function_evaluations']}, {results['best_so_far_y']}")
16SRS: 5000, 0.0017821578376762473
```

--------------------------------

### Define a Rosenbrock objective function

Source: https://pypop.readthedocs.io/en/latest/_sources/index.rst.txt

Define a custom objective (cost or fitness) function to be minimized. This example uses the notorious Rosenbrock function and sets up the problem dictionary including the fitness function, dimension, and boundaries. This is a common setup for black-box optimization problems.

```python
import numpy as np  # for numerical computation (PyPop7's computing engine)
def rosenbrock(x):  # one notorious function in the optimization community
    return 100.0*np.sum(np.square(x[1:] - np.square(x[:-1]))) + np.sum(np.square(x[:-1] - 1.0))
ndim_problem = 1000  # problem dimension
problem = {'fitness_function': rosenbrock,  # fitness function to be minimized
           'ndim_problem': ndim_problem,  # problem dimension
           'lower_boundary': -5.0*np.ones((ndim_problem,)),  # lower search boundary
           'upper_boundary': 5.0*np.ones((ndim_problem,))}
```

--------------------------------

### Initialize and Optimize with MAES

Source: https://pypop.readthedocs.io/en/latest/_sources/user-guide.rst.txt

Demonstrates initializing the MAES optimizer with a defined problem and options, then running the optimization process. Ensure all necessary imports are present.

```python
>>> problem = {'fitness_function': rosenbrock,  # cost function to be minimized
...            'ndim_problem': ndim_problem,  # dimension of cost function
...            'lower_boundary': -5.0*np.ones((ndim_problem,)),  # lower search boundary
...            'upper_boundary': 5.0*np.ones((ndim_problem,))}  # upper search boundary
>>> from pypop7.optimizers.es.maes import MAES  # replaced by any other BBO in this library
>>> options = {'fitness_threshold': 1e-10,  # to terminate when the best-so-far fitness is lower than 1e-10
...            'max_function_evaluations': ndim_problem*10000,  # maximum of function evaluations
...            'seed_rng': 0,  # seed of random number generation (which should be set for repeatability)
...            'sigma': 3.0,  # initial global step-size of Gaussian search distribution
...            'verbose': 500}  # to print verbose information every 500 generations
>>> maes = MAES(problem, options)  # to initialize the black-box optimizer
>>> results = maes.optimize(args=100.0)  # args as input arguments of fitness function
>>> print(results['best_so_far_y'], results['n_function_evaluations'])
7.57e-11 15537
```

--------------------------------

### Visualize Fitness Convergence with (1+1)-ES

Source: https://pypop.readthedocs.io/en/latest/user-guide.html

This example visualizes the fitness convergence of Rechenberg’s (1+1)-Evolution Strategy on the sphere function. It demonstrates how to set up the problem and optimizer options, run the optimization, and plot the fitness over function evaluations. Ensure seaborn and matplotlib are installed for plotting.

```python
import numpy as np
import seaborn as sns
import matplotlib.pyplot as plt
from pypop7.benchmarks.base_functions import sphere
from pypop7.optimizers.es.res import RES
sns.set_theme(style='darkgrid')
plt.figure()
for i in range(3):
    problem = {'fitness_function': sphere,
               'ndim_problem': 10}
    options = {'max_function_evaluations': 1500,
               'seed_rng': i,
               'saving_fitness': 1,
               'x': np.ones((10,)),
               'sigma': 1e-9,
               'lr_sigma': 1.0/(1.0 + 10.0/3.0),
               'is_restart': False}
    res = RES(problem, options)
    fitness = res.optimize()['fitness']
    plt.plot(fitness[:, 0], np.sqrt(fitness[:, 1]), 'b')  # sqrt for distance
    plt.xticks([0, 500, 1000, 1500])
    plt.xlim([0, 1500])
    plt.yticks([1e-9, 1e-6, 1e-3, 1e0])
    plt.yscale('log')
plt.show()
```

--------------------------------

### Initialize and Optimize with SCEM

Source: https://pypop.readthedocs.io/en/latest/_sources/user-guide.rst.txt

Shows how to initialize the SCEM optimizer with specific problem and hyper-parameter options, including custom mean and sigma values for the search distribution. Requires importing necessary components from pypop7.

```python
>>> import numpy as np
>>> from pypop7.benchmarks.base_functions import rosenbrock  # function to be minimized
>>> from pypop7.optimizers.cem.scem import SCEM
>>> problem = {'fitness_function': rosenbrock,  # define problem arguments
...            'ndim_problem': 10,
...            'lower_boundary': -5.0*np.ones((10,)),
...            'upper_boundary': 5.0*np.ones((10,))}
>>> options = {'max_function_evaluations': 1000000,  # set optimizer options
...            'seed_rng': 2022,
...            'mean': 4.0*np.ones((10,)),  # initial mean of Gaussian search distribution
...            'sigma': 3.0}  # initial std (aka global step-size) of Gaussian search distribution
>>> scem = SCEM(problem, options)  # initialize the optimizer class
```

--------------------------------

### Initialize and Run NSA Optimizer

Source: https://pypop.readthedocs.io/en/latest/_modules/pypop7/optimizers/sa/nsa.html

Example demonstrating how to initialize and run the NSA optimizer to minimize the Rosenbrock function. Ensure all required problem and option parameters are correctly set.

```python
import numpy  # engine for numerical computing
from pypop7.benchmarks.base_functions import rosenbrock  # function to be minimized
from pypop7.optimizers.sa.nsa import NSA
problem = {'fitness_function': rosenbrock,  # define problem arguments
           'ndim_problem': 2,
           'lower_boundary': -5*numpy.ones((2,)),
           'upper_boundary': 5*numpy.ones((2,))}
options = {'max_function_evaluations': 5000,  # set optimizer options
           'seed_rng': 2022,
           'x': 3*numpy.ones((2,)),
           'sigma': 1.0,
           'temperature': 100.0}
nsa = NSA(problem, options)  # initialize the optimizer class
results = nsa.optimize()  # run the optimization process
# return the number of function evaluations and best-so-far fitness
print(f"NSA: {results['n_function_evaluations']}, {results['best_so_far_y']}")
```

--------------------------------

### Install PyPop7 using Pip

Source: https://pypop.readthedocs.io/en/latest/installation.html

Use this command to install the PyPop7 package from the Python Package Index (PyPI).

```shell
pip install pypop7

```

--------------------------------

### Initialize and Optimize with SGES

Source: https://pypop.readthedocs.io/en/latest/nes/sges.html

Demonstrates how to initialize the SGES optimizer with problem and option configurations and run the optimization process. Ensure 'fitness_function' is set to a function to be minimized.

```python
1>>> import numpy
2>>> from pypop7.benchmarks.base_functions import rosenbrock  # function to be minimized
3>>> from pypop7.optimizers.nes.sges import SGES
4>>> problem = {'fitness_function': rosenbrock,  # to define problem arguments
5...            'ndim_problem': 2,
6...            'lower_boundary': -5.0*numpy.ones((2,)),
7...            'upper_boundary': 5.0*numpy.ones((2,))}
8>>> options = {'max_function_evaluations': 5000,  # to set optimizer options
9...            'seed_rng': 2022,
10...            'mean': 3.0*numpy.ones((2,))}
11>>> sges = SGES(problem, options)  # to initialize the optimizer class
12>>> results = sges.optimize()  # to run the optimization process
13>>> print(f"SGES: {results['n_function_evaluations']}, {results['best_so_far_y']}")
14SGES: 5000, 0.0190
```

--------------------------------

### IPSO Class Initialization and Optimization

Source: https://pypop.readthedocs.io/en/latest/pso/ipso.html

Demonstrates how to initialize the IPSO optimizer with problem and options, and then run the optimization process.

```APIDOC
## IPSO Class

### Description
Initializes the Incremental Particle Swarm Optimizer (IPSO).

### Parameters
#### problem (dict)
- **fitness_function** (func) - objective function to be minimized
- **ndim_problem** (int) - number of dimensionality
- **upper_boundary** (array_like) - upper boundary of search range
- **lower_boundary** (array_like) - lower boundary of search range

#### options (dict)
- **max_function_evaluations** (int) - maximum of function evaluations (default: np.inf)
- **max_runtime** (float) - maximal runtime to be allowed (default: np.inf)
- **seed_rng** (int) - seed for random number generation
- **n_individuals** (int) - swarm (population) size (default: 20)
- **constriction** (float) - constriction factor (default: 0.729)
- **cognition** (float) - cognitive learning rate (default: 2.05)
- **society** (float) - social learning rate (default: 2.05)
- **max_ratio_v** (float) - maximal ratio of velocities w.r.t. search range (default: 0.5)

### Method
IPSO(problem, options)

### Request Example
```python
import numpy
from pypop7.benchmarks.base_functions import rosenbrock
from pypop7.optimizers.pso.ipso import IPSO

problem = {
    'fitness_function': rosenbrock,
    'ndim_problem': 2,
    'lower_boundary': -5*numpy.ones((2,)),
    'upper_boundary': 5*numpy.ones((2,))
}

options = {
    'max_function_evaluations': 5000,
    'seed_rng': 2022
}

ipso = IPSO(problem, options)
results = ipso.optimize()
print(f"IPSO: {results['n_function_evaluations']}, {results['best_so_far_y']}")
```

### Response
#### Success Response (200)
- **n_function_evaluations** (int) - number of function evaluations performed
- **best_so_far_y** (float) - best fitness value found so far

#### Response Example
```json
{
  "n_function_evaluations": 5000,
  "best_so_far_y": 2.29225104244031e-07
}
```
```

--------------------------------

### Running Experiments with PyPop7

Source: https://pypop.readthedocs.io/en/latest/_sources/tutorials/tutorials.rst.txt

This code demonstrates how to initialize and run experiments using a selected optimizer from PyPop7. It measures and prints the total runtime. Ensure 'start', 'end', and 'ndim_problem' are defined in the params dictionary.

```python
experiments = Experiments(params['start'], params['end'], params['ndim_problem'])
experiments.run(Optimizer)
print('Total runtime: {:7.5e}.'.format(time.time() - start_runtime))
```

--------------------------------

### Install pypop7 using pip

Source: https://pypop.readthedocs.io/en/latest/_sources/installation.rst.txt

Use this command to install the latest stable version of pypop7 from the Python Package Index (PyPI).

```bash
pip install pypop7
```

--------------------------------

### Create and Activate Conda Virtual Environment

Source: https://pypop.readthedocs.io/en/latest/installation.html

Steps to create a new conda virtual environment, activate it, install Python, and then install PyPop7. The Python version can be adjusted as needed.

```shell
conda deactivate  # close exiting virtual env, if exists
conda create -y --prefix env_pypop7  # free to change name of virtual env
conda activate ./env_pypop7  # on Windows OS
conda activate env_pypop7/  # on Linux
conda activate env_pypop7  # on MacOS
conda install -y --prefix env_pypop7 python=3.8.12  # create new virtual env
pip install pypop7
conda deactivate  # close current virtual env `env_pypop7`

```

--------------------------------

### Initialize and Run FEP Optimizer

Source: https://pypop.readthedocs.io/en/latest/_modules/pypop7/optimizers/ep/fep.html

Demonstrates how to initialize the FEP optimizer with problem and option parameters, and then run the optimization process. Ensure 'seed_rng' is explicitly set for reproducibility.

```python
import numpy  # engine for numerical computing
from pypop7.benchmarks.base_functions import rosenbrock  # function to be minimized
from pypop7.optimizers.ep.fep import FEP
problem = {'fitness_function': rosenbrock,  # to define problem arguments
           'ndim_problem': 2,
           'lower_boundary': -5.0*numpy.ones((2,)),
           'upper_boundary': 5.0*numpy.ones((2,))}
options = {'max_function_evaluations': 5000,  # to set optimizer options
           'seed_rng': 2022,
           'sigma': 3.0}  # global step-size may need to be tuned
fep = FEP(problem, options)  # to initialize the optimizer class
results = fep.optimize()  # to run its optimization/evolution process
# to return the number of function evaluations and the best-so-far fitness
print(f"FEP: {results['n_function_evaluations']}, {results['best_so_far_y']}")
```

--------------------------------

### Initialize BES Optimizer

Source: https://pypop.readthedocs.io/en/latest/_modules/pypop7/optimizers/rs/bes.html

Demonstrates how to initialize the BES optimizer with problem and option configurations, including setting parameters like learning rate and gradient estimation factor.

```python
import numpy
from pypop7.benchmarks.base_functions import rosenbrock  # function to be minimized
from pypop7.optimizers.rs.bes import BES
problem = {'fitness_function': rosenbrock,  # define problem arguments
           'ndim_problem': 100,
           'lower_boundary': -2*numpy.ones((100,)),
           'upper_boundary': 2*numpy.ones((100,))}
options = {'max_function_evaluations': 10000*101,  # set optimizer options
           'seed_rng': 2022,
           'n_individuals': 10,
           'c': 0.1,
           'lr': 0.000001}
bes = BES(problem, options)  # initialize the optimizer class
results = bes.optimize()  # run the optimization process
# return the number of used function evaluations and found best-so-far fitness
print(f"BES: {results['n_function_evaluations']}, {results['best_so_far_y']}")
```

--------------------------------

### MAES Optimizer Usage Example

Source: https://pypop.readthedocs.io/en/latest/tutorials/tutorials.html

Example demonstrating how to instantiate and run the extended MAESPLOT optimizer for a given problem and options. It visualizes the collected data using a plot function.

```python
if __name__ == '__main__':
    ndim_problem = 15
    problem = {'fitness_function': func_lens,
               'ndim_problem': ndim_problem,
               'lower_boundary': -5.0*np.ones((ndim_problem,)),
               'upper_boundary': 5.0*np.ones((ndim_problem,))}
    options = {'max_function_evaluations': 7e3,
               'seed_rng': 2022,
               'x': d_init*np.ones((ndim_problem,)),
               'sigma': 0.3,
               'saving_fitness': 50,
               'is_restart': False}
    results = MAESPLOT(problem, options).optimize()
    plot(results['xs'])
```

--------------------------------

### ENES Optimizer Example

Source: https://pypop.readthedocs.io/en/latest/_modules/pypop7/optimizers/nes/enes.html

Example of using the ENES optimizer to minimize the Rosenbrock function. Demonstrates problem definition, option setting, optimizer initialization, and running the optimization process.

```python
import numpy  # engine for numerical computing
from pypop7.benchmarks.base_functions import rosenbrock  # function to be minimized
from pypop7.optimizers.nes.enes import ENES
problem = {'fitness_function': rosenbrock,  # define problem arguments
           'ndim_problem': 2,
           'lower_boundary': -5*numpy.ones((2,)),
           'upper_boundary': 5*numpy.ones((2,))}
options = {'max_function_evaluations': 5000,  # set optimizer options
           'seed_rng': 2022,
           'mean': 3*numpy.ones((2,))}
ENES = ENES(problem, options)  # initialize the optimizer class
results = ENES.optimize()  # run the optimization process
# return the number of function evaluations and best-so-far fitness
print(f"ENES: {results['n_function_evaluations']}, {results['best_so_far_y']}")
```

--------------------------------

### Initialize and Run CSA Optimizer

Source: https://pypop.readthedocs.io/en/latest/_modules/pypop7/optimizers/sa/csa.html

Example of initializing the CSA optimizer with problem and option parameters, then running the optimization process. It demonstrates setting up the problem, defining options like maximum function evaluations and random seed, and printing the optimization results.

```python
import numpy  # engine for numerical computing
from pypop7.benchmarks.base_functions import rosenbrock  # function to be minimized
from pypop7.optimizers.sa.csa import CSA
problem = {'fitness_function': rosenbrock,  # define problem arguments
           'ndim_problem': 2,
           'lower_boundary': -5*numpy.ones((2,)),
           'upper_boundary': 5*numpy.ones((2,))}
options = {'max_function_evaluations': 5000,  # set optimizer options
           'seed_rng': 2022,
           'x': 3*numpy.ones((2,)),
           'sigma': 1.0,
           'temperature': 100}
csa = CSA(problem, options)  # initialize the optimizer class
results = csa.optimize()  # run the optimization process
# return the number of function evaluations and best-so-far fitness
print(f"CSA: {results['n_function_evaluations']}, {results['best_so_far_y']}")
```

--------------------------------

### Initialize and Run EMNA Optimizer

Source: https://pypop.readthedocs.io/en/latest/_modules/pypop7/optimizers/eda/emna.html

Demonstrates how to initialize the EMNA optimizer with problem and option settings and then run the optimization process. It shows how to define the problem, set optimizer options, and print the results.

```python
import numpy
from pypop7.benchmarks.base_functions import rosenbrock  # function to be minimized
from pypop7.optimizers.eda.emna import EMNA
problem = {'fitness_function': rosenbrock,  # define problem arguments
           'ndim_problem': 2,
           'lower_boundary': -5*numpy.ones((2,)),
           'upper_boundary': 5*numpy.ones((2,))}
options = {'max_function_evaluations': 5000,  # set optimizer options
           'seed_rng': 2022}
emna = EMNA(problem, options)  # initialize the optimizer class
results = emna.optimize()  # run the optimization process
# return the number of function evaluations and best-so-far fitness
print(f"EMNA: {results['n_function_evaluations']}, {results['best_so_far_y']}")
```

--------------------------------

### Initialize Simulated Annealing Optimizer

Source: https://pypop.readthedocs.io/en/latest/_modules/pypop7/optimizers/sa/nsa.html

Initializes the optimizer's state, including the starting point for the search. If no starting point is provided, a random one is generated within specified boundaries.

```python
def initialize(self, args=None):
        if self.x is None:  # starting point
            x = self.rng_initialization.uniform(self.initial_lower_boundary, self.initial_upper_boundary)
        else:
            x = np.copy(self.x)
        assert len(x) == self.ndim_problem
        y = self._evaluate_fitness(x, args)
        self.parent_x, self.parent_y = np.copy(x), np.copy(y)
        return y
```

--------------------------------

### SNES Optimizer Initialization and Usage

Source: https://pypop.readthedocs.io/en/latest/nes/snes.html

Demonstrates how to initialize and use the SNES optimizer with a sample problem and options.

```APIDOC
## SNES Optimizer

### Description
Initializes and runs the Separable Natural Evolution Strategies (SNES) optimizer.

### Class Signature
`SNES(problem, options)`

### Parameters
#### `problem` (dict)
- **fitness_function** (func) - Objective function to be minimized.
- **ndim_problem** (int) - Dimensionality of the problem.
- **upper_boundary** (array_like) - Upper boundary of the search range.
- **lower_boundary** (array_like) - Lower boundary of the search range.

#### `options` (dict)
- **max_function_evaluations** (int) - Maximum number of function evaluations (default: np.inf).
- **max_runtime** (float) - Maximum runtime allowed in seconds (default: np.inf).
- **seed_rng** (int) - Seed for random number generation.
- **n_individuals** (int) - Number of offspring/descendants (offspring population size).
- **n_parents** (int) - Number of parents/ancestors (parental population size).
- **mean** (array_like) - Initial starting point. If not provided, a random sample is drawn.
- **sigma** (float) - Initial global step-size (mutation strength).

### Example Usage
```python
import numpy
from pypop7.benchmarks.base_functions import rosenbrock
from pypop7.optimizers.nes.snes import SNES

problem = {
    'fitness_function': rosenbrock,
    'ndim_problem': 2,
    'lower_boundary': -5*numpy.ones((2,)),
    'upper_boundary': 5*numpy.ones((2,))
}

options = {
    'max_function_evaluations': 5000,
    'seed_rng': 2022,
    'mean': 3*numpy.ones((2,)),
    'sigma': 0.1
}

snes = SNES(problem, options)
results = snes.optimize()

print(f"SNES: {results['n_function_evaluations']}, {results['best_so_far_y']}")
```

### Returns
- **results** (dict) - Dictionary containing optimization results, including 'n_function_evaluations' and 'best_so_far_y'.
```

--------------------------------

### CSA Optimizer Initialize Method

Source: https://pypop.readthedocs.io/en/latest/_modules/pypop7/optimizers/sa/csa.html

Sets the initial starting point for the optimization. If no starting point is provided, it generates a random one within the defined boundaries. Evaluates the fitness of the initial point.

```python
    def initialize(self, args=None):
        if self.x is None:  # starting point
            x = self.rng_initialization.uniform(self.initial_lower_boundary, self.initial_upper_boundary)
        else:
            x = np.copy(self.x)
        assert len(x) == self.ndim_problem
        y = self._evaluate_fitness(x, args)
        self.parent_x, self.parent_y = np.copy(x), np.copy(y)
        return y
```

--------------------------------

### Run Experiment and Print Runtime

Source: https://pypop.readthedocs.io/en/latest/tutorials/tutorials.html

This snippet shows how to initialize an experiment, run an optimizer, and print the execution runtime. It's useful for performance measurement during optimization tasks.

```python
experiment = Experiment(index, f, self.seeds[i, index], self.ndim_problem)
experiment.run(optimizer)
print('    runtime: {:7.5e}.'.format(time.time() - start_time))
```

--------------------------------

### Example Usage of ENES Optimizer

Source: https://pypop.readthedocs.io/en/latest/_modules/pypop7/optimizers/nes/enes.html

Demonstrates how to use the ENES optimizer to minimize the Rosenbrock function.

```APIDOC
## Example: Minimizing Rosenbrock Function with ENES

Use the optimizer `ENES` to minimize the well-known test function
`Rosenbrock <http://en.wikipedia.org/wiki/Rosenbrock_function>`_:

```python
import numpy  # engine for numerical computing
from pypop7.benchmarks.base_functions import rosenbrock  # function to be minimized
from pypop7.optimizers.nes.enes import ENES

# Define problem arguments
problem = {
    'fitness_function': rosenbrock,
    'ndim_problem': 2,
    'lower_boundary': -5*numpy.ones((2,)),
    'upper_boundary': 5*numpy.ones((2,))
}

# Set optimizer options
options = {
    'max_function_evaluations': 5000,
    'seed_rng': 2022,
    'mean': 3*numpy.ones((2,))
}

# Initialize the optimizer class
ENES_optimizer = ENES(problem, options)

# Run the optimization process
results = ENES_optimizer.optimize()

# Print the number of function evaluations and best-so-far fitness
print(f"ENES: {results['n_function_evaluations']}, {results['best_so_far_y']}")
```

### Output Example

```
ENES: 5000, 0.00035668252927080496
```
```

--------------------------------

### DSCEM Initialize Method

Source: https://pypop.readthedocs.io/en/latest/_modules/pypop7/optimizers/cem/dscem.html

Prepares the optimizer for a new run or restart. It calculates the initial mean and allocates space for samples (population) and their fitness values.

```python
def initialize(self, is_restart=False):
        mean = self._initialize_mean(is_restart)
        x = np.empty((self.n_individuals, self.ndim_problem))  # samples (population)
        y = np.empty((self.n_individuals,))  # fitness (no evaluation)
        return mean, x, y
```

--------------------------------

### Initialize Optimization State

Source: https://pypop.readthedocs.io/en/latest/_modules/pypop7/optimizers/ds/cs.html

Sets the initial point and evaluates its fitness. Used at the start of optimization or after a restart.

```python
def initialize(self, args=None, is_restart=False):
        x = self._initialize_x(is_restart)  # initial point
        y = self._evaluate_fitness(x, args)  # fitness
        return x, y
```

--------------------------------

### Initialize and Run SNES Optimizer

Source: https://pypop.readthedocs.io/en/latest/nes/snes.html

Example of initializing the SNES optimizer with problem and option configurations, then running the optimization process. Ensure 'seed_rng' is explicitly set for reproducible results.

```python
1>>> import numpy  # engine for numerical computing
2>>> from pypop7.benchmarks.base_functions import rosenbrock  # function to be minimized
3>>> from pypop7.optimizers.nes.snes import SNES
4>>> problem = {'fitness_function': rosenbrock,  # define problem arguments
5...            'ndim_problem': 2,
6...            'lower_boundary': -5*numpy.ones((2,)),
7...            'upper_boundary': 5*numpy.ones((2,))}
8>>> options = {'max_function_evaluations': 5000,  # set optimizer options
9...            'seed_rng': 2022,
10...            'mean': 3*numpy.ones((2,)),
11...            'sigma': 0.1}  # the global step-size may need to be tuned for better performance
12>>> snes = SNES(problem, options)  # initialize the optimizer class
13>>> results = snes.optimize()  # run the optimization process
14>>> # return the number of function evaluations and best-so-far fitness
15>>> print(f"SNES: {results['n_function_evaluations']}, {results['best_so_far_y']}")
16SNES: 5000, 0.49730042657448875
```

--------------------------------

### Get Shubert Minimizers

Source: https://pypop.readthedocs.io/en/latest/_modules/pypop7/benchmarks/cases.html

Retrieves a list of minimizers for the Shaffer (Schaffer) test function. This data is used for validation.

```python
def get_y_shubert():
    """Get test data for **Schaffer** test function.
    """
    minimizers = [[-7.0835, 4.858], [-7.0835, -7.7083], [-1.4251, -7.0835], [5.4828, 4.858],
                  [-1.4251, -0.8003], [4.858, 5.4828], [-7.7083, -7.0835], [-7.0835, -1.4251],
                  [-7.7083, -0.8003], [-7.7083, 5.4828], [-0.8003, -7.7083], [-0.8003, -1.4251],
                  [-0.8003, 4.8580], [-1.4251, 5.4828], [5.4828, -7.7083], [4.858, -7.0835],
                  [5.4828, -1.4251], [4.858, -0.8003]]
    return minimizers
```

--------------------------------

### Run Optimization Experiments

Source: https://pypop.readthedocs.io/en/latest/_sources/tutorials/tutorials.rst.txt

This script demonstrates how to set up and run a series of optimization experiments using different algorithms from PyPop7. It includes argument parsing for experiment parameters and conditional imports for selected optimizers.

```python
import pickle
import time
import argparse
import numpy as np

from pypop7.optimizers.rs.prs import PRS as Optimizer


class Experiment(object):
    def __init__(self, index, fitness_function, seed, ndim_problem):
        self.index = index
        self.fitness_function = fitness_function
        self.seed = seed
        self.ndim_problem = ndim_problem
        self._file = 'results/{:s}/{:s}/{:d}D/{:d}.pickle'

    def run(self, optimizer):
        options = {'seed': self.seed,
                   'ndim_problem': self.ndim_problem,
                   'saving_fitness': 2000,
                   'verbose': 0}
        options['temperature'] = 100.0  # for simulated annealing (SA)
        solver = optimizer(problem, options)
        results = solver.optimize()
        file = self._file.format(solver.__class__.__name__,
                                 solver.fitness_function.__name__,
                                 solver.ndim_problem,
                                 self.index)
        with open(file, 'wb') as handle:  # data format (pickle)
            pickle.dump(results, handle, protocol=pickle.HIGHEST_PROTOCOL)


class Experiments(object):
    def __init__(self, start, end, ndim_problem):
        self.start, self.end = start, end
        self.ndim_problem = ndim_problem
        self.functions = [cf.sphere, cf.cigar,
                          cf.discus, cf.cigar_discus,
                          cf.ellipsoid, cf.different_powers,
                          cf.schwefel221, cf.step,
                          cf.rosenbrock, cf.schwefel12]
        # set RNG seeds for repeatability
        self.seeds = np.random.default_rng(2022).integers(
            np.iinfo(np.int64).max, size=(len(self.functions), 50))

    def run(self, optimizer):
        for index in range(self.start, self.end + 1):
            print('* experiment: {:d} ***:'.format(index))
            for i, f in enumerate(self.functions):
                start_time = time.time()
                print('  * function: {:s}:'.format(f.__name__))
                experiment = Experiment(index, f, self.seeds[i, index], self.ndim_problem)
                experiment.run(optimizer)
                print('    runtime: {:7.5e}.'.format(time.time() - start_time))


if __name__ == '__main__':
    start_runtime = time.time()
    parser = argparse.ArgumentParser()
    # set starting index of experiments (from 0 to 49)
    parser.add_argument('--start', '-s', type=int)
    # set ending index of experiments (from 0 to 49)
    parser.add_argument('--end', '-e', type=int)
    # use any optimizer from PyPop7
    parser.add_argument('--optimizer', '-o', type=str)
    # set dimension of all fitness functions
    parser.add_argument('--ndim_problem', '-d', type=int, default=2000)
    args = parser.parse_args()
    params = vars(args)
    # ensure seeds between 0 (include) and 49 (include)
    assert isinstance(params['start'], int) and 0 <= params['start'] < 50
    assert isinstance(params['end'], int) and 0 <= params['end'] < 50
    assert isinstance(params['optimizer'], str)
    assert isinstance(params['ndim_problem'], int) and params['ndim_problem'] > 0
    if params['optimizer'] == 'PRS':  # 1952
        # PRS: Ashby's "Design for a Brain: The Origin of Adaptive Behavior"
        #   (1952 - 1st Edition / 1960 - 2nd Edition)
        #   https://link.springer.com/book/10.1007/978-94-015-1320-3
        from pypop7.optimizers.rs.prs import PRS as Optimizer
    elif params['optimizer'] == 'SRS':  # 2001
        from pypop7.optimizers.rs.srs import SRS as Optimizer
    elif params['optimizer'] == 'ARHC':  # 2008
        from pypop7.optimizers.rs.arhc import ARHC as Optimizer
    elif params['optimizer'] == 'GS':  # 2017
        from pypop7.optimizers.rs.gs import GS as Optimizer
    elif params['optimizer'] == 'BES':
        from pypop7.optimizers.rs.bes import BES as Optimizer
    elif params['optimizer'] == 'HJ':
        from pypop7.optimizers.ds.hj import HJ as Optimizer
    elif params['optimizer'] == 'NM':
        from pypop7.optimizers.ds.nm import NM as Optimizer
    elif params['optimizer'] == 'POWELL':
        from pypop7.optimizers.ds.powell import POWELL as Optimizer
    elif params['optimizer'] == 'FEP':
        from pypop7.optimizers.ep.fep import FEP as Optimizer
    elif params['optimizer'] == 'GENITOR':
        from pypop7.optimizers.ga.genitor import GENITOR as Optimizer
    elif params['optimizer'] == 'G3PCX':
        from pypop7.optimizers.ga.g3pcx import G3PCX as Optimizer
    elif params['optimizer'] == 'GL25':
        from pypop7.optimizers.ga.gl25 import GL25 as Optimizer
    elif params['optimizer'] == 'COCMA':
        from pypop7.optimizers.cc.cocma import COCMA as Optimizer
    elif params['optimizer'] == 'HCC':
        from pypop7.optimizers.cc.hcc import HCC as Optimizer
    elif params['optimizer'] == 'SPSO':
        from pypop7.optimizers.pso.spso import SPSO as Optimizer
    else:
        raise ValueError('Optimizer not found.')
    experiments = Experiments(params['start'], params['end'], params['ndim_problem'])
    experiments.run(Optimizer)
    print('Total runtime: {:7.5e}.'.format(time.time() - start_runtime))
```

--------------------------------

### Get Salomon Test Data

Source: https://pypop.readthedocs.io/en/latest/_modules/pypop7/benchmarks/cases.html

Returns None for the Salomon test function, indicating no specific test data is provided.

```python
def get_y_salomon():
    """Get test data for **Salomon** test function.
    """
    return None
```

--------------------------------

### Get Michalewicz Test Data

Source: https://pypop.readthedocs.io/en/latest/_modules/pypop7/benchmarks/cases.html

Returns None for the Michalewicz test function, indicating no specific test data is provided.

```python
def get_y_michalewicz():
    """Get test data for **Michalewicz** test function.
    """
    return None
```

--------------------------------

### COEA Optimizer Initialization and Usage

Source: https://pypop.readthedocs.io/en/latest/cc/coea.html

Demonstrates how to initialize and use the COEA optimizer for a given problem and options, including running the optimization process and printing results.

```APIDOC
## COEA Class

### Description
CoOperative Co-Evolutionary Algorithm (COEA). This is a modified version using real-valued representation for continuous optimization and the GENITOR suboptimizer.

### Parameters

#### problem (dict)
Arguments for the problem definition:
- 'fitness_function' (func) - Objective function to be minimized.
- 'ndim_problem' (int) - Number of dimensions of the problem.
- 'upper_boundary' (array_like) - Upper boundary of the search range.
- 'lower_boundary' (array_like) - Lower boundary of the search range.

#### options (dict)
Optimizer options:
- 'max_function_evaluations' (int, default: np.inf) - Maximum number of function evaluations.
- 'max_runtime' (float, default: np.inf) - Maximum runtime allowed in seconds.
- 'seed_rng' (int) - Seed for random number generation.
- 'n_individuals' (int, default: 100) - Number of individuals (population size).

### Request Example
```python
import numpy
from pypop7.benchmarks.base_functions import rosenbrock
from pypop7.optimizers.cc.coea import COEA

problem = {
    'fitness_function': rosenbrock,
    'ndim_problem': 2,
    'lower_boundary': -5.0*numpy.ones((2,)),
    'upper_boundary': 5.0*numpy.ones((2,))
}

options = {
    'max_function_evaluations': 5000,
    'seed_rng': 2022,
    'x': 3.0*numpy.ones((2,))
}

coea = COEA(problem, options)
results = coea.optimize()
print(f"COEA: {results['n_function_evaluations']}, {results['best_so_far_y']}")
```

### Response
#### Success Response (dict)
- 'n_function_evaluations' (int) - Number of function evaluations performed.
- 'best_so_far_y' (float) - The best objective function value found.

#### Response Example
```json
{
  "n_function_evaluations": 5000,
  "best_so_far_y": 0.4308
}
```
```

--------------------------------

### Get LevyMontalvo Test Data

Source: https://pypop.readthedocs.io/en/latest/_modules/pypop7/benchmarks/cases.html

Returns None for the LevyMontalvo test function, indicating no specific test data is provided.

```python
def get_y_levy_montalvo():
    """Get test data for **LevyMontalvo** test function.
    """
    return None
```

--------------------------------

### Get Skew-Rastrigin Test Data

Source: https://pypop.readthedocs.io/en/latest/_modules/pypop7/benchmarks/cases.html

Retrieves test data for the Skew-Rastrigin function. Use this data to test optimization algorithms.

```python
def get_y_skew_rastrigin(ndim):
    """Get test data for **Skew-Rastrigin** test function.
    """
    y = [[4.0, 1.0, 0.0, 100.0, 400.0],
         [404.0, 101.0, 0.0, 200.0, 800.0],
         [804.0, 201.0, 0.0, 201.0, 804.0],
         [0.0, 400.0, 4.0, 202.0, 3000.0, 1020.0, 1317.0]]
    return y[ndim]
```