At the same time, most optimization algorithms still refuse to accept input from engineers to help guide their mathematical search. The assumption is that the human brain cannot possibly decipher complex relationships among multiple system responses that depend upon large numbers of connected variables. Unfortunately, this is true.

Is this a case of irreconcilable differences? Or is it simply an example of everyone wanting to be the teacher, and no one wanting to be the student? I’m reminded of the Latin proverb:

Surely engineering intuition can benefit from the results of mathematical exploration, and vice-versa. It seems almost obvious.“By learning you will teach; by teaching you will learn.”

So why do engineers and optimization algorithms prefer to work solo? I don’t believe they prefer this. I think it is more a matter of not knowing how to collaborate, or not having the tools to facilitate this interaction.

Fortunately, modern optimization software tools like HEEDS now have features that encourage engineers to learn from the intermediate results of an optimization study and to share intuition-based insights with the optimization algorithm

Consider the following example:

- An engineer uses intuition and experience to define the goals of an optimization problem and a baseline (starting) design.
- An optimization search algorithm then begins to explore the design space to uncover mathematical relationships that can lead to an optimized design, all the while sharing its progress and discoveries with the engineer.
- While monitoring, validating and interpreting these intermediate search results, the engineer starts to learn what makes some designs better than others. This new understanding causes the engineer’s intuition to practically blurt out, “If design B is better than design A, then design C should be even better!” Of course, the optimization algorithm might eventually discover design C on its own, but it would surely take a lot longer to do so.
- The engineer shares his insight with the optimization algorithm, which happily accepts the input and puts it to use immediately. If the engineer was correct, then the algorithm now has new information that will accelerate its search. If the engineer’s intuition did not lead to a better design, then the algorithm has only spent one design evaluation to discover this, and the new data may still have some valuable nuggets that can be exploited later in the search.
- The circular process of
*exploring*→*monitoring*→*interpreting*→*sharing*is continuous throughout the search process, leading to better designs in much less time than was previously possible. - The enhanced communication between the engineer and the optimization algorithm builds a strong interdependent relationship between the two, leveraging the strength of each.

Further, this is not one of those nice ideas that looks good on paper but doesn’t work well in practice. This technique has already been used very successfully on many challenging design problems, including composite aircraft, crashworthy cars and insulated vaccine carriers.

There is now overwhelming evidence that a more intimate coupling of intuition with a hybrid, adaptive optimization algorithm can solve many challenging problems previously thought to be intractable.

Of course, in order to find the best solutions many optimization algorithms tend to explore a design space broadly, even spending some time in those regions of the space that don’t yield any good designs. So the process helps us to understand not only what makes a good design, but also why some designs perform poorly. This reminds me of another important proverb:

“Wise men learn by other men's mistakes, fools by their own.”

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