About the Blog

 

Introduction 

This is a blog about optimization algorithms and their Python implementations.

Why this Blog?

I want to share what I've learned with others.  Each topic will include some background, an example and links to complete, working Python code.  I don't plan on covering a lot of theory since there is typically a lot of that on the web.  Links to key refences will be included.  I often use code shared by others on the web and when I do, I will reference these sources.   

Being retired, I'm not looking for my next job and I don't need to "monetize" what I'm publishing here.  I just feel that someone out there might appreciate or be helped by what I've done.  




Comments

Post a Comment

Popular posts from this blog

Minimum Distance to f(x) with Scipy Optimize

Image
  Shortest Distance Between f(x) and a Point ¶ In this notebook, I show a simple demonstration of using Scipy Optimize to find shortest distance from a given point $(𝑥_p,𝑦_p)$ to a curve: 𝑦 = 𝑓(𝑥). I will need to import a few Python libraries for this. In [1]: import numpy as np import scipy.optimize as optimize import matplotlib.pyplot as plt Scipy Optimize has an impressive array of functions to support common optimization problems. For this problem, I will use scipy.minimize to find the minimum distance. minimize requires an objective function and an initial guess for $x_{opt}$. f(x) is the "curve" we want to find the shortest distance to. This can be any continuous function of x. In [2]: def f ( x ): return np . cos ( x ) # + np.sin(x) def dist ( x ): """ Returns the Euclidean distance from (xp, yp) to (x, f(x)) """ y = f ( x ) dist ...
Read more

Minimize (or Maximize) a Function of One Variable

Image
Maximize Volume of a Box ¶ For someone new to optimization, finding the minima or maxima of a simple function is probably one of the first challenges you will face. Sometimes you can solve them with a bit of calculus. When that isn't feasible, you can use numerical methods to find a solution. In this notebook I will investigate the problem of minimizing (or maximizing) a function of one variable (a scalar function). The problem I will use to illustrate this optimization task is maximizing the volume of an open top box cut from a fixed size rectangle. The Problem ¶ Given a sheet of paper that is 8.5 inches by 11 inches, a box will be formed by cutting squares from each corner as shown below. The box if formed by folding up the resulting four tabs at the dashed fold lines. We want to find the dimension x that will give us the maximum volume for the open top box. The formula for the box volume is straightforward: $$Vol = x(8.5 - 2x)(11 - 2x)$$ We can expand this into a ...
Read more

2D Bin Packing with a Genetic Algorithm

Image
This is a follow up to a previous notebook where I used a guillotine heuristic to solve a 2D bin packing problem. In my previous notebook, I sorted the parts by descending area before applying the guillotine heuristic. As I pointed out, this sorting choice can have a significant impact on packing performance. I've used genetic (evolutionary) optimization algorithms (GA) in other applications and thought they might be effective in solving the bin packing problems. GA overcomes the sorting dilemma by randomly trying many different orderings of the parts. Genetic Algorithms ¶ The basic ideas and steps in genetic optimization are: Create an intial population . Parts are randomly sampled from the original parts list (without replacement) then some are rotated based on chance. This is repeated until $N_{pop}$ parts lists have been created. This collection of ordered parts lists is called a population. Evaluate this poulation for fitness . Each parts list is provided to a ...
Read more