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Description:

OMADS 2408.0

OMADS
MADS: A python implementation for the mesh adaptive direct search (MADS) method; ORTHO-MADS algorithm. OMADS can solve both single- and multi-objective optimization problems.
For technical and code documentation, please visit OMADS Webpage.

Version 2.1.0

License & copyright
© Ahmed H. Bayoumy
Citation
If you use this code, please cite it as below.
@software{OMADS_AB,
author = {Bayoumy, A.},
title = {OMADS},
year = 2022,
publisher = {Github},
version = {2407},
url = {https://github.com/Ahmed-Bayoumy/OMADS}
}

How to use OMADS package
After installing the OMADS package from PYPI website, the functions and classes of OMADS basic
module can be imported directly to the python script as follows:
from OMADS import *

How to run OMADS from terminal
After installing OMADS the SEARCH, POLL, and MADS modules can be called directly from a
terminal window under the src directory. The path of the JSON template, which contains the problem input parameters,
should be entered as an input argument to the aforementioned modules call.
python ./OMADS/POLL.py ../../tests/unconstrained/rosenbrock.json
python ./OMADS/SEARCH.py ../../tests/unconstrained/rosenbrock.json
python ./OMADS/MADS.py ../../tests/unconstrained/rosenbrock.json

Input parameters
Input parameters are serialized in a JSON template using predefined attributes (keywords) under four dictionaries;
evaluator, param, options and search. Here is a brief description of each dictionary and its key attributes.

evaluator: in this dictionary, we define the blackbox location and the name of input and output files (if exist)

blackbox: blackbox executable file name, or the function name if this is an internal function defined within the BM_suite
internal: the name of the testing category that holds your internal/external test function or blackbox evaluator

con: internal constrained single-objective function
uncon: internal unconctrained single-objective function
exe: external executable blackbox evaluator

input: the name of the input file (considered if external executable was defined)
output: the name of the output file (considered if external executable was defined)

param: problem setup

baseline: this is the initial starting point (initial design vector)
lb: lower bounds vector
ub: upper bounds vector
var_names: list of design variables name
var_types: list of the variables type

R: real variable
I: integer variable
C_<set name>: categorical variable. A set name from the sets dict should be added after the underscore that follows C
D_<set name>: discrete variable. A set name from the sets dict should be added after the underscore that follows D

Sets: a dictionary where its keys refer to the set name and their value should be assigned to a list of values (the values can be of heterogeneous type)
scaling: scaling factor
post_dir: the location of the post directory where the results file shall be saved if requested
constraints_type: list of the constraints barrier type, i.e., progressive barrier (PB) and extreme barrier (EB)
LAMBDA: list of the initial Lagrangian multipliers assigned to the constraints
RHO: list of the initial penalty parameter
hmax: the maximum feasibility threshold
nobj: number of objectives
isPareto: boolean for running a Pareto study
meshType: specify whether to use granular or orthogonal mesh

GMESH: granular mesh
OMESH: orthogonal mesh

name: problem name (that name will be used for naming the output files)

options: algorithmic options

seed: the random generator seed that ensures results reproducibility. This should be an integer value
budget: the evaluation budget; the maximum number of evaluations for the blackbox defined
tol: the minimum poll size tolerance; the algorithm terminates once the poll size falls below this value
psize_init: initial poll size
display: a boolean for displaying verbose outputs per iteration in the terminal window
opportunistic: a boolean for enabling opportunistic search
check_cache: a boolean for checking if the current point is a duplicate by checking its hashed address (integer signature)
store_cache: a boolean for saving evaluated designs in the cache memory
collect_y: currently inactive (to be used when the code is integrated with the PyADMM MDO module)
rich_direction: a boolean that enables capturing a rich set of directions in a generalized pattern
precision: a string character input that controls the dtype decimal resolution used by the numerical library numpy

high: float128 1e-18
medium: float64 1e-15
low: float32 1e-8

save_results: a boolean for generating a MADS.csv file for the output results under the post directory
save_coordinates: saving poll coordinates (spinners) of each iteration in a JASON dictionary template that can be used for visualization
save_all_best: a boolean for saving only incumbent solutions
parallel_mode: a boolean for parallel computation of the poll set

search: the search step options

type: search type can take one of the following values

VNS: variable neighbor search
sampling: sampling search
BO: Bayesian optimization (TODO: not published yet as it is still in the testing and BM phase)
NM: Nelder-Mead (TODO: not published yet as it is still in the testing and BM phase)
PSO: particle swarm optimization (TODO: not published yet as it is in the testing phase)
CMA-ES: covariance matrix adaptation evolution strategy (TODO: not published yet as it is in the testing phase)

s_method: can take one of the following values

ACTIVE: Online active sampling using kernel density estimators (KDE)
LH: Latin Hypercube sampling\
RS: random sampling
HALTON: Halton sampling

ns: number of samples

Multiobjective MADS
The poll, search, and MADS algorithms are capable of solving both unconstrained and constrained multiobjective problems by conducting a Pareto study. The approximated Pareto front (non-dominated solutions) are saved in a separate CSV file named with the suffix Pareto "{problem_name}_Pareto.out". The figures below display the results of test functions chosen from the literature.
Constrained test functions

Unonstrained test functions

Benchmarking
To benchmark OMADS, per se, you need to install the non-linear optimization benchmarking project NOBM (will be installed automatically when you install OMADS) from
PYPI. Two benchmarking suits are provided under the BMDFO package -- BMDFO stands for
benchmarking derivative-free optimization algorithms. The benchmarking suits have different constrained and
unconstrained optimization problems with various characteristics. The BMDFO modules can be imported directly
to the python script as shown below:
from BMDFO import toy

For more details about the NOBM project and its use, check this link.
After running the benchmarking suite using various seed values, which are used to initialize the random number generator,
a BM_report.csv file will be created in the post directory under the examples folder.
Example
import OMADS
import numpy as np

def rosen(x, *argv):
x = np.asarray(x)
y = [np.sum(100.0 * (x[1:] - x[:-1] ** 2.0) ** 2.0 + (1 - x[:-1]) ** 2.0,
axis=0), [0]]
return y

eval = {"blackbox": rosen}
param = {"baseline": [-2.0, -2.0],
"lb": [-5, -5],
"ub": [10, 10],
"var_names": ["x1", "x2"],
"scaling": 10.0,
"post_dir": "./post"}
options = {"seed": 0, "budget": 100000, "tol": 1e-12, "display": True}

data = {"evaluator": eval, "param": param, "options":options}

out = {}
# out is a dictionary that will hold output data of the final solution. The out dictionary has three keys: "xmin", "fmin" and "hmin"

out = OMADS.main(data)

Results
--- Run Summary ---
Run completed in 0.0303 seconds
Random numbers generator's seed 0
xmin = [1.0, 1.0]
hmin = 1e-30
fmin = 0.0
#bb_eval = 185
#iteration = 46
nb_success = 4
psize = 9.094947017729282e-13
psize_success = 1.0
psize_max = 2.0

https://github.com/Ahmed-Bayoumy/OMADS/assets/22842095/5dc72c34-4722-4d93-8c84-d17f5595556d