OMADS 1.1.0

"Python package for DFO; an implementation of the MADS basic variant."

OMADS

MADS-poll step: A python implementation for the mesh adaptive direct search (MADS) method; ORTHO-MADS algorithm

---

Version 1.1.0

---

License & copyright

© Ahmed H. Bayoumy

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 the libraries listed in the requirements.txt, OMADS/BASIC.py 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 BASIC.py call.

python ./OMADS/BASIC.py ../../tests/unconstrained/rosenbrock.json

Input parameters

Input parameters are serialized in a JSON template using predefined attributes (keywords) under three dictionaries; evaluator, param, and options. 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: uber bounds vector
  • var_names: list of design variables name
  • scaling: scaling factor
  • post_dir: the location of the post directory where the results file shall be saved if requested

---

• 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

---

Benchmarking

To benchmark OMADS, per se, you need to install the non-linear optimization benchmarking project NOBM 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}

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