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Popular How-To's in Objective C category


 
How to create a solver in python
Scripts & Utilities

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...

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Articles Related To Objective C


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).

 

Optimization solver

A number of constrained optimization solvers are designed to solve the general nonlinear optimization problem.

  1. PSQP: This optimizer is a preconditioned sequential quadratic programming algorithm. This optimizer implements a sequential quadratic programming method with a BFGS variable metric update.
  2. SLSQP: This optimizer is a sequential least squares programming algorithm. SLSQP uses the Han–Powell quasi-Newton method with a BFGS update of the B-matrix and an L1-test function in the step-length algorithm. The optimizer uses a slightly modified version of Lawson and Hanson’s NNLS nonlinear least-squares solver.
  3. CONMIN: This optimizer implements the method of feasible directions. CONMIN solves the nonlinear programming problem by moving from one feasible point to an improved one by choosing at each iteration a feasible direction and step size that improves the objective function.
  4. COBYLA: It is an implementation of Powell’s nonlinear derivative–free constrained optimization that uses a linear approximation approach. The algorithm is a sequential trust–region algorithm that employs linear approximations to the objective and constraint functions.
  5. SOLVOPT: SOLVOPT is a modified version of Shor’s r–algorithm with space dilation to find a local minimum of nonlinear and non–smooth problems.
  6. KSOPT: This code reformulates the constrained problem into an unconstrained one using a composite Kreisselmeier–Steinhauser objective function to create an envelope of the objective function and set of constraints. The envelope function is then optimized using a sequential unconstrained minimization technique.
  7. NSGA2: This optimizer is a non-dominating sorting genetic algorithm that solves non-convex and non-smooth single and multiobjective optimization problems.
  8. ALGENCAN: It solves the general non-linear constrained optimization problem without resorting to the use of matrix manipulations. It uses instead an Augmented Lagrangian approach which is able to solve extremely large problems with moderate computer time.
  9. FILTERSD: It use of a Ritz values approach Linear Constraint Problem solver. Second derivatives and storage of an approximate reduced Hessian matrix is avoided using a limited memory spectral gradient approach based on Ritz values.

 

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)

 

Example:

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.

The global demand for data Science professionals is extremely high because of increasing relevance across various sectors. Data Science has become the most-sought skill because the data is piling along with a surge in different tech fields like Artificial Intelligence, machine learning and data Analytics. Hiring data scientist is being carried across numerous domains like e-commerce, education, retail, telecommunication and much more.

 

In the past years, analysts used excel tools to analyze data. Things are changing now! In this modern world, data-driven decision making is sparkling and technology is advanced in the data industry. The tools and technologies that modern Data Scientists employ are a combination of statistical and Machine Learning algorithms. They are used to discover patterns using predictive models. The future of Data Science is bright and the options for its implementation are extensive.

 

Data Scientists must consistently evolve at the edge of innovation and creativity. They must be aware of the types of models they create. These innovations will allow them to spend time discovering new things that may be of value. Subsequently, the advances in Data Science tools will help leverage existing Data Science talent to a greater extent.

 

So what does a Data Scientist do?

Data Scientists influence a pile of data in an innovative way to discover valuable trends and insights. This approach helps to identify opportunities by implementing research and management tools to optimize business processes by reducing the risks. Data Scientists are also responsible for designing and implementing processes for data mining, research and modeling purposes.

 

Data scientist performs research and analyses data and help companies flourish by predicting growth, trends and business insights based on a large amount of data. Basically, data scientists are massive data wranglers. They take a vast data and use their skills in mathematics, statistics and programming to scrub and organize the information. All their analysis combined with industrial knowledge helps to uncover hidden solutions to business challenges.

 

Generally, a data scientist needs to know what could be the output of the big data he/she is analyzing. He/she also needs to have a clearly defined plan on how the output can be achieved with the available resources and time. Most of all the data scientists must know the reason behind his attempt to analyze the big data.

 

To achieve all of the above, a data scientist may be required to:

 

Every organization has unique data problems with its own complexities. Solving different Data Science problems requires different skill sets. Data Science teams are groups of professionals with varied skill sets. They, as a team, solve some of the hardest data problems an organization might face. Each member contributes distinctive skill set required to complete a Data Science project from start to finish.

 

The Career Opportunities:

The careers associated with data science are generally categorized into five.

 

  1. Statisticians: Statisticians work usually for national governments, marketing research firms and research institutes. Extracting information from massive databases through numerous statistical procedures is what they do.
  2. Data Analyst: Telecommunication companies, manufacturing companies, financial companies etc. hire data scientists to analyze their data. A data analyst keeps track of various factors affecting company operation and make visual graphics.
  3. Big Data and Data Mining Engineer: Tech companies, retail companies and recreation companies use data scientists as data mining engineers. They have to gather and analyze huge amounts of data, typically from unstructured information.
  4. Business Intelligence Reporting Professional: They work for tech companies, financial companies, and consulting companies etc. Market research is the primary objective of this job. They also generate various reports from the structured data to improve the business.
  5. Project Manager: A project manager evaluates data and insights fetched from the operational departments and influences the business decisions. They have to plan the work and make sure everything goes in accordance with the plan.

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