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## Step By Step Modeling Of PuzzlOr Electrifying Problem
PuzzlOr problems are nice because they are simplified versions of real world problems of interest. Last December problem is a simplified version of an interesting logistics problem. A variety of method can be used to attack them, see for instance this interesting post by Isaac Slavitt where he tried both a brute force search and simulated annealing. Not surprisingly, I will try CPLEX on it. Here is the statement of the problem A new city is being built which will include 20 distinct neighborhoods as shown by the house... [More]
Tags: opl programming optimization modeling analytics |

## Un Peu de Math avec CPLEX
There is one thing I didn't disclose in my previous post (Un Peu de Math) on the Analytic Bridge Mathematical Competition : I used CPLEX to refine and validate various hypothesis. As usual, my first try wasn't very convincing, and I had to rely on better understanding of the problem to solve it efficiently. Let me start with a statement of the optimization problem to be solved. A permutation x is a function such that x(i) is in the set {0,1,...,n-1} for all i in that set.... [More]
Tags: modeling mathematics |

## More On Absolute Value
I needed to model an absolute value in a MIP model. I could have used one of the methods described in the very good review by Paul Rubin , but another method seemed better suited to my special case. I am given a binary variable z and an integer variable x such that 0 <= x <= 2 z = abs(x-1) The rest of the model is such that we cannot assume we minimize z. This is therefore a non convex constraint. The method I used works for any function of x . In order to model z = f(x) we introduce one binary x i... [More]
Tags: modeling |

## D-Wave vs CPLEX Comparison. Part 2: QUBO
Can we improve CPLEX performance for yet another test series used in McGeoch&Wang paper , namely the native QUBO instances? According to the paper, these instances were random instances constructed to match what the D-Wave hardware can solve directly. These are problems of the form minimize sum ij Q ij x i x j where all the variables x i are binary. Such problems are called QUBO (Quadratic Unconstrained Binary Optimization ) problems. CPLEX release 12.3 didn't do very well according to the paper (although it was... [More]
Tags: modeling qubo optimization d-wave |

## D-Wave vs CPLEX Comparison. Part 1: QAP
Why am I discussing again the D-Wave quantum computer vs CPLEX comparison paper published by Cathy McGeoch and Carrie Wong ? Mainly because it looked like an interesting challenge to redo the CPLEX experiments to see if we could get better results. Here are new results for the quadratic assignment problem test series. Our results for the other tests series in will be reported in subsequent posts. To cut a long story short, our results are better than those in the paper. ... [More]
Tags: optimization modeling analytics d-wave |

## The Orange Juice Algorithm
Update on May 20. A recent Network World paper discloses that Coca Cola is indeed using our optimization software for the orange juice application I originally described in the blog entry below. A nice, recent, article in BloombergBusinessweek describes a very interesting use of mathematical optimization at Coke. Optimization is used to ensure that their Minute Maid and Simply Orange orange juices always taste the same. This paper caused some buzz because it is said that a problem of up to one quintillion... [More]
Tags: analytics optimization solution modeling |

## Looking Under The Hood
Go to market (GTM) is something you must understand very quickly if you try to live from selling what you do. For optimization, we converged on a very simple view at IBM. There are two categories of customers, those who understand the technology, and those who don't. The formers are operations research (OR) practitioners and OR academics. The latter are line of business (LOB) people. Understanding how the technology work is not so much important to them. What is important is to understand what it enables. The OR market is well served by... [More]
Tags: optimization modeling |

## Making Dreams Come True (Or Not)
Last week, in my What Is The Solution When There Is No Solution entry, I commented about the fact that not all business requirements were actual constraints and that some of these are probably wishes that business people dream to fulfill. Making the difference between wishes and hard constraints is key to success. Indeed, handling wishes as hard constraints may result in infeasible models, which would be useless to the business people that come to you for help. It turns out that there is a surprisingly simple way to detect that some... [More]
Tags: optimization modeling analytics |

## What Is The Solution When There Is No Solution ?
Optimization is like a Ferarri, when you drive it correctly you can
achieve incredible performance . But you must understand what it can
do and what it can't do or you will crash. Same is true for optimization. I'm starting a series of posts on various
pitfalls that people using optimization can fall into. This is the what it can't do part . This will complement posts where I brag about the value of optimization, which are centered around what it can do . Today's topic is about the difference between an exact answer , and a useful... [More]
Tags: overconstrained infeasibility modeling optimization |