Optimization deals with selecting the simplest option among a number of possible choices that are feasible or do not violate constraints. Python is used to optimize parameters in a model to best fit data, increase profitability of a possible engineering style, or meet another form of objective which will be described mathematically with variables and equations.
pyOpt is a Python-based package for formulating and solving nonlinear constrained optimization problems in an efficient, reusable and portable manner. Python programming uses object-oriented concepts, such as class inheritance and operator overloading, to maintain a distinct separation between the problem formulation and the optimization approach used to solve the problem.
All optimisation downside solvers inherit from the Optimizer abstract category. The category attributes include the solver name (name), an optimizer kind symbol (category), and dictionaries that contain the solver setup parameters (options) and message output settings (informs). The class provides ways to check and alter default solver parameters (getOption, setOption), as well as a method that runs the solver for a given optimisation problem (solve).
A number of constrained optimization solvers are designed to solve the general nonlinear optimization problem.
To solve an optimization problem with pyOpt an optimizer must be initialized. The initialization of one or more optimizers is independent of the initialization of any number of optimization problems. To initialize SLSQP, which is an open-source, sequential least squares programming algorithm that comes as part of the pyOpt package, use:
>>> slsqp = pyOpt.SLSQP()
This initializes an instance of SLSQP with the default options. The setOption method can be used to change any optimizer specific option, for example the internal output flag of SLSQP:
>>> slsqp.setOption('IPRINT', -1)
Now Schittkowski’s constrained problem can be solved using SLSQP and for example, pyOpt’s automatic finite difference for the gradients:
>>> [fstr, xstr, inform] = slsqp(opt_prob,sens_type='FD')
By default, the solution information of an optimizer is also stored in the specific optimization problem. To output solution to the screen one can use:
>>> print opt_prob.solution(0)
The problem is taken from the set of nonlinear programming examples by Hock and Schittkowski and it is defined as
=======================================================================
min − x1x2x3
x1,x2,x3
subjected to x1 + 2x2 + 2x3 − 72 ≤ 0
− x1 − 2x2 − 2x3 ≤ 0
0 ≤ x1 ≤ 42
0 ≤ x2 ≤ 42
0 ≤ x3 ≤ 42
The optimum of this problem is at (x1∗ , x2∗ , x3* ) = (24, 12, 12), with an objective function value of f ∗ = −3456, and constraint values g (x∗ ) = (0, −72).
#======================================================================
# Standard Python modules
#======================================================================
import os, sys, time
import pdb
#======================================================================
# Extension modules
#======================================================================
#from pyOpt import *
from pyOpt import Optimization
from pyOpt import PSQP
from pyOpt import SLSQP
from pyOpt import CONMIN
from pyOpt import COBYLA
from pyOpt import SOLVOPT
from pyOpt import KSOPT
from pyOpt import NSGA2
from pyOpt import ALGENCAN
from pyOpt import FILTERSD
#======================================================================
def objfunc(x):
f = -x[0]*x[1]*x[2]
g = [0.0]*2
g[0] = x[0] + 2.*x[1] + 2.*x[2] - 72.0
g[1] = -x[0] - 2.*x[1] - 2.*x[2]
fail = 0
return f,g, fail
#======================================================================
# Instantiate Optimization Problem
opt_prob = Optimization('Hock and Schittkowski Constrained Problem',objfunc)
opt_prob.addVar('x1','c',lower=0.0,upper=42.0,value=10.0)
opt_prob.addVar('x2','c',lower=0.0,upper=42.0,value=10.0)
opt_prob.addVar('x3','c',lower=0.0,upper=42.0,value=10.0)
opt_prob.addObj('f')
opt_prob.addCon('g1','i')
opt_prob.addCon('g2','i')
print opt_prob
# Instantiate Optimizer (PSQP) & Solve Problem
psqp = PSQP()
psqp.setOption('IPRINT',0)
psqp(opt_prob,sens_type='FD')
print opt_prob.solution(0)
# Instantiate Optimizer (SLSQP) & Solve Problem
slsqp = SLSQP()
slsqp.setOption('IPRINT',-1)
slsqp(opt_prob,sens_type='FD')
print opt_prob.solution(1)
# Instantiate Optimizer (CONMIN) & Solve Problem
conmin = CONMIN()
conmin.setOption('IPRINT',0)
conmin(opt_prob,sens_type='CS')
print opt_prob.solution(2)
# Instantiate Optimizer (COBYLA) & Solve Problem
cobyla = COBYLA()
cobyla.setOption('IPRINT',0)
cobyla(opt_prob)
print opt_prob.solution(3)
# Instantiate Optimizer (SOLVOPT) & Solve Problem
solvopt = SOLVOPT()
solvopt.setOption('iprint',-1)
solvopt(opt_prob,sens_type='FD')
print opt_prob.solution(4)
# Instantiate Optimizer (KSOPT) & Solve Problem
ksopt = KSOPT()
ksopt.setOption('IPRINT',0)
ksopt(opt_prob,sens_type='FD')
print opt_prob.solution(5)
# Instantiate Optimizer (NSGA2) & Solve Problem
nsga2 = NSGA2()
nsga2.setOption('PrintOut',0)
nsga2(opt_prob)
print opt_prob.solution(6)
# Instantiate Optimizer (ALGENCAN) & Solve Problem
algencan = ALGENCAN()
algencan.setOption('iprint',0)
algencan(opt_prob)
print opt_prob.solution(7)
# Instantiate Optimizer (FILTERSD) & Solve Problem
filtersd = FILTERSD()
filtersd.setOption('iprint',0)
filtersd(opt_prob)
print opt_prob.solution(8)
Solving non-linear global optimization problems could be tedious task sometimes. If the problem is not that complex then general purpose solvers could work. However, as the complexity of problem increases, general purpose global optimizers start to take time. That is when need to create your problem specific fast and direct global optimizer’s need arises.
We have an specialized team with PHD holders and coders to design and develop customized global optimizers. If you need help with one, please feel free to send your queries to us.
We first understand the problem and data by visualizing it. After that we create a solution to your needs.
Please do read to understand what a solver is and how it works - If you want to create your own simple solver. This is not exactly how every solver works, however, this will give you a pretty solid idea of what is a solver and how it is supposed to work.
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Python scipy provides a good number of optimizers/solvers. You can use these optimizers to solve various non-linear and linear equations. However, sometimes things might get tricky and you will not be able to calculate and provide jacobian to these solvers. We...
