Recent advances in process automation and optimization search technology have made it easier than ever to perform automated design studies and discover innovative solutions. But we still have to define the problem we want to solve and then decide how to represent that problem in our models. These two tasks are sometimes challenging, and they rely heavily on experience and intuition. In this article, as well as some future ones, we will share some of our experience in defining and representing various types of optimization problems. Hopefully you will find some of these techniques useful in your applications.
A common design scenario is to optimize the number and location of certain design features to satisfy performance goals and requirements. For the sake of discussion, let’s consider a specific example of this type of problem. Continue reading
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What are the three most important things to consider when buying a house? Location. Location. Location. The repetition intentionally over-emphasizes this point: if the location of your new real estate purchase is not good, then the details of the home don’t really matter.
A spacious kitchen and updated bathrooms are nice, but even a perfect house located near the end of a busy airport runway will not bring a high value in the real estate market. For this reason, many savvy investors buy the worst house in a great neighborhood and then upgrade it to suit their tastes, rather than buying the best house in a mediocre neighborhood.
So should you spend money to improve your current residence, or use those funds to move to a different neighborhood altogether? Clearly, the answer depends on the quality of your current location. Continue reading
You may have heard the story about the woman who always sliced about one inch off the end of a large roast before placing it in the pan to be cooked. When asked why she did this, she did not know the reason. But she was sure that it was important, because her mother always did exactly the same thing.
Now curious, the woman called her mother to ask why it is important to cut off the end of a roast before cooking it. Her mother did not know the reason, but she was confident that it was important, because her mother always did exactly the same thing.
A phone call to the woman’s grandmother finally revealed the true reason why two subsequent generations of cooks always cut off the end of a roast before cooking it. The grandmother explained, “A long time ago, the only size of roast at the local store was too large to fit in my pan. So I had to cut a bit off the end in order to cook it. I haven’t had to do that in years!”
I’ll bet the entire family had a good laugh about this situation. Many years ago, there was a really good reason to cut off the end of the roast, but that reason didn’t exist anymore. Yet that step in the process was passed down to future generations, as though it were crucial to the success of the meal.
There are probably many situations in which current limitations give rise to a process that continues to be used long after those limitations are gone. Often the facts become blurred and the philosophical reasoning becomes stronger, so no one questions whether the process is valid. A paradigm is created that is not easily broken. Continue reading
In 1997, IBM’s Deep Blue computer won a six-game chess match against world champion Gary Kasparov. More recently, IBM’s Watson supercomputer defeated two of the greatest Jeopardychampions of all time during a three-day competition.
Despite these impressive exhibitions, machines cannot think like humans – yet. For example, given different sets of information, humans have a natural ability to detect patterns and perceive order. Computers, on the other hand, must be told what types of pattern structures to look for.
But Deep Blue and Watson have demonstrated that when the rules of the game are well defined and the desired patterns are known, humans can program computers to solve these problems better or faster than our own minds can solve them.
Another example is engineering design optimization, where mathematical computer algorithms are being used to optimize engineered systems and components. In this context, the roles of mind and machine are still being debated. Unlike in chess or Jeopardy, no one has proposed a suitable competition to determine whether machines can outperform humans on design optimization tasks.
In my opinion, it is not a question of mind versus machine. The more important issue is how we can best leverage mind plus machine. While there is some overlap in their skill sets, the most powerful capabilities of the human mind complement those of computers. Continue reading
Change is often viewed as the result of a scientific discovery or the development of a breakthrough technology. But there’s usually a lot more to the story. To quote Paul Saffo – technology doesn’t drive change, it enables change.
When the chainsaw was first introduced, I wonder how many lumberjacks tried dragging it back and forth against a tree, expecting it to work the same way as a hand saw. Figuring out the best use of a new technology is just as important, and sometimes as difficult, as developing the technology in the first place.
Too often, the real value of a new technology becomes enslaved by old notions about how things work or what is possible. To realize the full advantages of a new technology, we need to look at things differently and accept new possibilities. Continue reading
“Be formless, shapeless, like water. Now, you put water into a cup, it becomes the cup. Put it into a teapot, it becomes the teapot. Now, water can flow, or creep, or drip, or crash. Be water, my friend.” – Bruce Lee
When martial artist Bruce Lee offered the above advice about being adaptable, I doubt that he was referring to mathematical optimization. But these words of wisdom are certainly relevant to optimization algorithms.
Searching a design space is a lot like navigating a mountain range, and we know that no two mountain ranges are alike.
Even while traveling within a given range, you are likely to encounter several different types of terrain – smooth and rolling in some areas, rocky and rugged in other areas. Many design spaces are like this, as well.
Yet most optimization search algorithms use a fixed strategy for every problem, even though it is often impossible to predict the characteristics of a newly defined design space. Continue reading
“The world is changing very fast. Big will not beat small anymore. It will be the fast beating the slow.” – Rupert Murdoch
When computer aided engineering (CAE) analysis techniques, like the finite element method, were first introduced, their primary role was to investigate why a design failed. Surely, this understanding would help designers avoid such failures in the future.
But soon, manufacturing companies realized that it was smarter to use CAE tools to predict whether a design would fail, before manufacturing. This gave designers the chance to make changes to designs and avoid most failures in the first place. This pass/fail test is still in place at many companies, in the form of scheduled iterations of computer aided design (CAD) drawings followed by CAE simulations.
Often, companies decide on a fixed number of manual CAD/CAE design iterations ahead of time. I’ve often wondered how project managers know exactly how many iterations it will take to arrive at the best design. Naturally, they haven’t figured the last-minute redesign “fire drills” and disorganized patchwork of final design changes into that preset number of design iterations. Continue reading
The goal of a mathematical optimization study is to find the optimal solution to a problem. And, when the problem at hand is simple enough to solve within the available time, we can achieve this goal consistently.
However, often we don’t have enough time or computing resources to carry out the number of design evaluations that would be needed to find the optimal solution. In these cases, we have no choice but to relax our goal and to seek the greatest possible design improvement within the available time.
A more direct statement of this would be, “Give me the best design you can find by Tuesday!” Continue reading
Most of us have heard the advice, “Change only one variable at a time to understand how that variable affects your system.”
Sometimes this advice is correct, but only in a very local sense. For example, if we want to estimate how sensitive a system is to a change in variable A, then we can hold all other variables constant and change variable A very slightly. The change in the system response divided by the change in variable A is an estimate of the sensitivity derivative at the original design point.
But, the key word in the previous sentence is “point,” because derivatives are defined at a point. If we select a different starting design point, and then repeat the above exercise, we would expect to get a different value for the sensitivity derivative.
Let’s examine this idea further. If we hold variable B constant at value B1, changing variable A will have a certain influence on the system response. But if we hold variable B constant at value B2, the effect of variable A might be very different than before. If so, then the effect of variable A depends on the value of variable B. When this occurs, we say that there is an interaction between variables A and B. We can easily generalize this argument to many variables. Continue reading