A genetic algorithm (GA) is a heuristic optimization technique. The method tries to mimic natural selection and evolution by starting with a population of random candidates. Candidates are evaluated for "fitness" by plugging them into the objective function. The characteristics of the better candidates are combined to create a new
This article uses an example to introduce to genetic algorithms (GAs) for optimization. It discusses two operators (mutation and crossover) that are important in implementing a genetic algorithm. It discusses choices that you must make when you implement these operations. Some programmers love using genetic algorithms. Genetic algorithms are heuristic
Sometimes we can learn as much from our mistakes as we do from our successes. Recently, I needed to solve an optimization problem for which the solution vector was a binary vector subject to a constraint. I was in a hurry. Without thinking much about what I was doing, I
Many optimization problems in statistics and machine learning involve continuous parameters. For example, maximum likelihood estimation involves optimizing a log-likelihood function over a continuous domain, possibly with constraints. Recently, however, I had to solve an optimization problem for which the solution vector was a 0/1 binary variable. To solve the
I previously wrote about one way to solve the partition problem in SAS. In the partition problem, you divide (or partition) a set of N items into two groups of size k and N-k such that the sum of the items' weights is the same in each group. For example,
The partition problem has many variations, but recently I encountered it as an interactive puzzle on a computer. (Try a similar game yourself!) The player is presented with an old-fashioned pan-balance scale and a set of objects of different weights. The challenge is to divide (or partition) the objects into
Machine Learning models are becoming widely used to formulate and describe processes’ key metrics across different industry fields. There is also an increasing need for the integration of these Machine Learning (ML) models with other Advanced Analytics methodologies, such as Optimization. Specifically, in the manufacturing industry, SAS explored state-of-the-art science
Linear programming (LP) and mixed integer linear programming (MILP) solvers are powerful tools. Many real-world business problems, including facility location, production planning, job scheduling, and vehicle routing, naturally lead to linear optimization models. Sometimes a model that is not quite linear can be transformed to an equivalent linear model to reduce
Note from Udo Sglavo on mathematical optimization: When data scientists look at the essence of analytics and wonder about their daily endeavor, it often comes down to supporting better decisions. Peter F. Drucker, the founder of modern management, stated: "Whenever you see a successful business, someone once made a courageous decision."
A good public transportation system is crucial to develop smart cities, particularly in great metropolitan areas. Network optimization algorithms can be applied to better understand urban mobility, particularly based on a multimodal public transportation network.
A year ago we could not imagine stadiums being empty during the most exciting sports events, but it is a common sight now. The entertainment sector is one of the hardest hit sectors because of the COVID-19 pandemic [1]. Social distancing requirements made it impossible to have viewers in stadiums
We will use prescriptive analytics and optimization to select a stock portfolio that maximizes returns while taking risk tolerance into account.
Many of us are currently working from home and getting adjusted to this new way of working. If you’re an employee working on the shop floor of a manufacturing facility, however, working from home is not an option. Among the many hard decisions manufacturing leaders have had to make during
Football fans around the world have something exciting to look forward to, with the European Championship scheduled to take place in June and July 2020. Twenty teams out of 24 have already qualified for the tournament, and after last Saturday's draw, the teams and fans are now getting ready to
After a marathon of a season, 162 games in each team's schedule to be precise, the stakes for Major League Baseball are higher in October, and postseason play is underway. Whether it's the renewal of an old rivalry, redemption for last year's runners up, or rooting for this season's breakout
One of the strengths of the SAS/IML language is its flexibility. Recently, a SAS programmer asked how to generalize a program in a previous article. The original program solved one optimization problem. The reader said that she wants to solve this type of problem 300 times, each time using a
A simple example of how you can combine SAS and open-source technologies to solve real business issues.
An important application of nonlinear optimization is finding parameters of a model that fit data. For some models, the parameters are constrained by the data. A canonical example is the maximum likelihood estimation of a so-called "threshold parameter" for the three-parameter lognormal distribution. For this distribution, the objective function is
Major European football (soccer) leagues came to an end after an intensive year. Manchester City claimed the Premier League title after a high-intensity title race against Liverpool. It is unbelievable that Liverpool would have won 25 out of the last 27 PL titles with 97 points. Luckily, the Reds
Learn how Bayesian optimization works through a simple demo.
Customer risk rating models play a crucial role in complying with the Know Your Customer (KYC) and Customer Due Diligence (CDD) requirements, which are designed to assess customer risk and prevent fraud. Today, the most common form of the Customer Risk Rating model is a score-based risk rating model. This
There is one equation every retail store, call center, traffic, airport or hospital manager should know by heart. No, it’s not E = mc². The one I had in mind is this: W = 1 / (μ – λ) It may not look like much, but it can mean the
Burger and fries, wine and cheese, peanut butter and jelly … some things just go better together. For organizations embarking on digital transformation, AI and IoT just go better together. These two distinct technologies; AI and IoT (or AIoT) are a natural fit. To take an analogy from the human
When solving optimization problems, it is harder to specify a constrained optimization than an unconstrained one. A constrained optimization requires that you specify multiple constraints. One little typo or a missing minus sign can result in an infeasible problem or a solution that is unrelated to the true problem. This
This article shows how to perform an optimization in SAS when the parameters are restricted by nonlinear constraints. In particular, it solves an optimization problem where the parameters are constrained to lie in the annular region between two circles. The end of the article shows the path of partial solutions
In the oil industry you can make or lose money based on how good your forecasts are, so I’ve pulled together six papers that discuss different ways in which you can leverage analytics to optimize your output and more accurately predict your production performance. Written by employees at oil and
Ballpark Chasers A cross-country trip is pretty much an all-American experience, and so is baseball. Traveling around the country to see all 30 Major League Baseball (MLB) stadiums is not a new idea; there's even a social network between so-called "Ballpark Chasers" where people communicate and share their journeys. Even
Data analysts often fit a probability distribution to data. When you have access to the data, a common technique is to use maximum likelihood estimation (MLE) to compute the parameters of a distribution that are "most likely" to have produced the observed data. However, how can you fit a distribution
When you run an optimization, it is often not clear how to provide the optimization algorithm with an initial guess for the parameters. A good guess converges quickly to the optimal solution whereas a bad guess might diverge or require many iterations to converge. Many people use a default value
SAS will be represented by more than 20 attendees at the INFORMS Annual Meeting at the George R. Brown Convention Center (GBCC) in Houston, Texas. Officially the conference runs from Sunday, Oct. 22 through Wednesday, Oct. 25, but our activities in Houston start even earlier. Technology Workshops on Saturday, October
