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Ravi Shankar SEO Expert, India
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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.

PHP (recursive acronym for PHP: Hypertext Pre-processor) is a widely-used open source general-purpose scripting language that is especially suited for web development and can be embedded into HTML.

PHP is one of the main languages used in dynamic web development. It’s one of the oldest language and a common component in the LAMP stack (Linux, Apache, MySQL, PHP). If you want to create a website or any back-end web service, PHP is one of the main languages you can choose from. If you need revisions to an existing application that runs on a Linux server, it’s common for the back-end coding to be done with PHP.

About PHP Developers

PHP developers are often simply called “back-end engineers.” A PHP developer is responsible for writing server-side web application logic. PHP developers usually develop back-end components, connect the application with the other (often third-party) web services, and support the front-end developers by integrating their work with the application.

They’re turn client’s specifications into a workable, tangible product that runs on a web server. Although PHP can run in a Windows environment, it’s more commonly used on Linux servers with Apache running as the web client. Many PHP developers package their applications this way with Linux and Apache to make it easier for the client to host it.

PHP developers code the functionality and brings an app to life. Collaborating with designers, they ensure that the front-end application is appealing to users. You may find that some PHP developers have front-end design skills, but often times, they work with UI and UX designers to create a user interface that’s engaging and supported by solid back-end functionality.

What Can You Expect from a PHP Developer?

It is a PHP Developer's job to write, test and maintain the code for web pages and computer graphics programs. They use PHP, a widely used scripting language, to build websites, programs and applications that computers follow to perform functions. They are also responsible for writing, troubleshooting, testing and maintaining the source code for computer programs. If needed, PHP Developers also assist team members in problem solving.

A PHP developer should be able to visualize your application and what you need based on your conversations and documentation (if you have any). They should be able to understand your business so that they can provide you with an application that supports your goals and business logic.

PHP developers mainly create two types of applications: web apps with a database background, and APIs that provide your existing software and data to mobile apps and other developers. PHP code powers the back end of a web app, so a PHP developer will design and architect your code and the way it works to support the front end. APIs are often used when developers or apps need to query your internal data, and they allow you to provide this data to the outside world. For instance, your app might pull a list of tweets from Twitter’s API. A PHP developer will read the API documentation and implement it into your website. APIs are also used with some mobile apps to power the app’s data services.

Deliverables could be full source code files, or some developers help you upload the code to your web server of your choice choice. If you’re building a website from scratch, it’s vital that you choose a developer with the skills necessary to tackle a project from the ground up. A senior-level developer will know how to manage a project (they might assign a project manager), set expectations, estimate costs, and give you organized, scalable code that you can work with for years.

Just like other development areas, PHP developers have a variety of skill sets and levels. Senior-level PHP experts often have several other languages in their arsenal. They should be able to design a full application from the ground up. Junior-level developers have a few years of experience, but they often need to work with, or have their work reviewed by, a senior-level developer to ensure that code is efficient and properly written.

Defining Your Project

A developer can only do as good of a job as the specifications or information they get from the client. Communication is key so that your PHP developer fully understands your concepts and goals. When you post a project, you must be able to communicate key elements so that you can get the best estimates from the best developers.

Before you post a project request or talk to developers, you should sit down and map out your idea. This can be done using images, presentations, or other types of documentation. For instance, you can draw your own wireframes and then explain each concept in writing. Developers bidding on your project can get a better idea of what needs to be done and estimate far more accurately.

It can be difficult for a client to understand the duration of a project and its cost, but a developer can sit down and discuss project scope, a reasonable timeline, and any deliverables that you can expect during the project’s development process.

Writing a Project Description

Once you know what you want from your end product, it’s time to write your project description. You need to be concise but provide enough detail to attract top developers. You can attach documents and provide video links to your project description to help developers better understand your goals.

Below is one sample of how a PHP project description may look. Keep in mind that many people use the term “job description,” but a full job description is only needed for employees. When engaging a freelancer as an independent contractor, you typically just need a statement of work, job post, or any other document that describes the work to be done.

Title: PHP Developer Needed to Build E-Commerce Website

Description: We need a PHP developer to build an e-commerce platform for our website. We have a rough wireframe document that explains the front end and the back end. We need help determining back-end architecture, so we want a developer to determine the way it will be built. We currently have hosting and need help uploading the code after it’s finished. The e-commerce store will host our product catalogue, take orders, allow customers to sign up, and then send email reminders to customers that left products in their shopping cart.

You can modify this description to better fit what you’re looking for, but it gives the basic requirements that a PHP development project might have.

PHP projects can take a long time, so expect a big project to take several months. PHP projects may require sit-downs to understand your requirements, design, coding, prototyping, and testing. All of these extend the deadline and can require several months for larger projects. A developer might even add a small percentage of time to the duration to ensure that deadlines are met. As with any project, the more descriptive your post is and the more you communicate with your programmer, the smoother the process will be.

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