Optimization: Art, Science or Both?
Engineers are always in the pursuit of optimizing their designs. More and more they use mathematical optimization processes to accomplish this challenging goal. Below is a collection of ideas I find myself talking about the most when discussing with engineers who just started to use mathematical optimization to find better performing, robust and innovative designs.
1. Optimization is a Learning Tool
To do mathematical optimization, we first need to automate the analysis process. Once automated, we are free from mundane, non-value added, error-prone tasks of updating the simulation input, running the simulation and extracting the results. This also allows us to be able to simulate many more designs in the same amount of time that we could do a handful of them. These designs are generated using established mathematical processes to give us the most valuable information with the least amount of simulations. These two concepts combined help us to learn about our designs at a much faster rate than before. With learning, comes more questions about our designs: what if I change manufacturing; what if I consider thermal effects; what if I change the shape? We then re-employ optimization to look for answers to these questions. As you can see this question and answer cycle continues until our design time is up and having collected all this information, we are equipped to make better design decisions. I have yet to see a case where only one optimization approach is run and the engineer took the optimum found as the final design.
2. Have you sorted out your resources?
During optimization, many designs will be simulated. These simulations will require licenses, CPU’s, storage space and most importantly your time and effort. There are many ways to conduct a mathematical optimization study and they all require different levels of these resources. Some such as Genetic Algorithms require a longer time to run which may in turn require you to create a response surface to use it with instead of the exact simulation. However, creating a response surface does require decision making and effort. On the other side of the spectrum, you can use Global Response Surface Method that does not ask you make decisions that you may not be comfortable with making at this stage and they are efficient. So, make a list of your resources before planning on your optimization studies so that you can pick the most appropriate optimization process.
3. Incorporate your engineering knowledge while leaving room for new ideas
As engineers, you know about the design requirements, manufacturing, part supply, material behavior and consumer patterns. Try to input to the optimizer as much as you can so that the designs it suggests are meaningful, practical and feasible.
While doing this, one handicap is that you may end up restricting the design space too much by imposing too many requirements. This may result in a large number of search but no result.
It is a fine balance to give enough flexibility for design opportunities while putting boundaries for feasibility.
4. Reduce, Reuse, Recycle
This item goes hand in hand with the previous item but is focused on the optimization problem formulation and running.
When you are at school working at mathematical optimization problems, you are advised to include as many independent variables as possible since this results in the largest design space to explore leading into the most design improvement opportunities. When you are working on theoretical problems, this may be a good advice but when you are working on engineering problems, you are bounded by resources that will prevent us from doing so as the amount of simulations needed to do mathematical optimization is a function of design variables. This is where Reduce comes. Reduce the variables into a set that makes significant changes in the design outcome. Do not waste resources in simulating design variations that is not going to provide important information.
When you decide to run your next study, remember the first set of designs you have evaluated are still relevant. Reuse them.
If you decide to venture out to other design exploration approaches such as stochastics, again remember all the designs you have evaluated may still be relevant so recycle them.
5. What about that global optimum?
Oh, yes that global optimum…Unless you have a convex problem, you cannot guarantee finding a global optimum. Exploratory methods such as Genetic Algorithms attempts to remedy this issue but it also requires a large number of simulations which gets impractical very quickly. This is where one needs to remember the Pareto law. If I can get 80% of the improvement in 20% of the time; should I worry about the remaining 20% that will cost me 80% of the time?
After merging these discussion points with your own experiences, you may conclude that optimization is more of an art than science and I would not disagree with you. Art also appreciates simplicity!
Thanks for reading, until next time Explore, Study and Optimize!