Technology makes man lazy

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Technology makes man lazy

A mix of operations research items and software tricks that I'll probably forget if I don't write them down somewhere. The terminology and some of the details in this post are specific to CPLEX, but I suspect that a number of other solvers will have something analogous to user cuts and lazy constraints, albeit perhaps under different names.

If the terminology is familiar to you, you can skip to the end of the post and find the one potentially useful nugget of information it contains. Let me start with an illustration of the feasible region of a hypothetical two variable pure integer linear program.

The polygon bounded in black including portions of the two axes is the feasible region of the linear program relaxation also known as the linear hull or LP hull. This is what you get if you relax the integrality restrictions while enforcing all functional constraints and variable bounds.

The blue dots are the integer lattice points inside the polygon, i. The blue polygon, the integer hull or IP hull, is the smallest convex set containing all integer-feasible solutions.

The IP hull is always a subset of the LP hull. Assuming a linear objective function, one of the vertices of the IP hull all of which are lattice points will be the optimal solution to the problem. User Cuts In CPLEX parlance, a cut is a constraint that is not part of the original model and does not eliminate any feasible integer solutions.

Cuts are typically added for one of two reasons: A user cut is simply a cut added by the user, rather than by CPLEX, frequently but not necessarily inside a callback.

The next figure illustrates a user cut red dashed line. The shaded triangle shows the portion of the original LP hull that is removed by the user cut. Note that no integer solutions were harmed in the construction of this diagram. Lazy Constraints In contrast to user cuts, lazy constraints are allowed to pare away integer-feasible solutions.

The next figure shows an example of a lazy constraint green line. The shaded polygon is again the portion of the LP and, in part, IP hull removed by the constraint. Note that, this time, three integer points are being rendered infeasible.

The implication of using lazy constraints is that the problem originally specified first figure is actually a relaxation of the true problem; adding the lazy constraints to that initial problem gives you the problem you really want to solve.

Why use lazy constraints? Three reasons come to mind. First, a full specification of the model may involve an extremely large number of constraints, many of which you anticipate will be redundant, or at least not binding near the optimal solution.

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If you knew in advance which of those constraints were redundant, you could simply omit them, but frequently you cannot identify redundant constraints at the outset.

Many modern solvers allow you to put a portion of the constraints what we are calling the "lazy" ones in a pool, where they are initially not a part of the active model. As solutions are generated, the solver checks to see if any lazy constraints are violated and, if so, adds them to the active set.

Lazy constraints that were previously added but have not been binding for a while may be returned to the pool. This is an attempt to reduce the computation time per iteration, and possibly the memory footprint of the problem.


A second and closely related reason to use lazy constraints is that there may in fact be so many constraints that you cannot afford the time or memory to generate them all at the outset. One approach to formulating the Traveling Salesman Problem as an integer program requires the use of subtour elimination constraints.

The number of such constraints grows exponentially with the number of nodes in the network. While they are easy to specify in a computer program, for decent size networks you simply cannot afford to list them all. An alternative is to treat them as lazy constraints and generate them on the fly, through a callback.

The third reason to use lazy constraints, specifically in a callback, is that you may not be able to identify them at the time the model is specified. The feasibility and optimality cuts generated during Benders decomposition fall into this category.

You discover them by solving one or more subproblems at certain points in the search for the solution to the master problem.These presentations appear to be breaking the FTC guidelines of endorsements, by stressing “what’s possible” instead of “what’s typical” and they don’t have the necessarily disclaimers..

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Biographical information

I gave you the FBI definition above. RC, also known as Delta or by his chosen nickname of Sev, was a clone of Mandalorian bounty hunter Jango Fett.

Born in 32 BBY on the watery world of Kamino, Sev was trained by the Mandalorian Cuy'val Dar training sergeant Walon Vau to become a clone commando in the Grand Army of the. LazyTown (Latibær in Icelandic) is an English-language Icelandic children's educational musical comedy program made by an international crew and performed by a cast from Iceland, the United States and the United Kingdom.

It is based upon a children's book from titled Áfram Latibær! and was created by Magnús Scheving, an aerobics champion who also plays the character Sportacus.

Technology makes man lazy

Writing sample of essay on a given topic "Technology Makes Man Lazy". Is Technology Making us Lazy? “Technology makes us weaker!” Man would not have made it to the moon.

Traffic would be horribly inefficient. We would still commute by boat. Technology: the progressives dream and the reactionary's nightmare. Advances in technology have been creating upheavals in society all the way back to the start of the Bronze age and further..

But things really shifted into high gear with the Industrial regardbouddhiste.comlogy started industrializing the United States around , changing it from an agricultural society into a manufacturing.

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