It seems impossible to get through a day without hearing the word "optimization." We want to maximize the profit, minimize the weight, minimize the cost; the list goes on. Of course, we all know how to optimize a mathematical function: Take the first derivative, equate it to zero, take the second derivative If only real problems were that simple.
There is no denying that engineering problems are becoming increasingly more complex and multidisciplinary. A typical approach to these problems is to create a potential solution based on innovation, intuition and creativity. We analyze the solution to investigate its performance and improve the design by modifying it with our intuition and creativity. We continue to iterate and "optimize,"--unfortunately, not until the "derivatives" are zero, but when a production deadline is reached.
Time is too often the critical deciding factor. To reduce this critical dependency and improve productivity, computational tools have been introduced--drafting, virtual modeling, analysis and simulation, rapid prototyping and 3D printing. These tools not only speed up the various design stages, they can carry out complex calculations and manufacturing that are otherwise not feasible. However, none of these tools can create new designs. The quality of a design remains primarily dependent on human creativity and intuition. This is why optimization is a truly revolutionary engineering tool: It can now "create" unintuitive designs that we have never thought of before.
There are optimization methods for all stages of design. High-fidelity topology optimization methods determine, from a block of material, the optimum geometrical shape that is readily manufacturable with modern technology (such as additive manufacturing). Starting from a set of random designs, optimization can select and modify the candidate designs to find the best configuration. Multidisciplinary design optimization can also consider highly coupled systems.
The best news for the engineering community is that optimization finds the solution where either the derivative is zero or it cannot be improved further. Whether we use the gradients to guide design to the optimum solution, use natural evolution to modify toward the best genes, or follow ants to find the food, we know we have found the design with the best performance. This provides an unprecedented competitive advantage to industry.
Of course, engineering optimization is also an intense research field that continues to address new challenges. For example, there is an explosion of research to build in redundancy into optimization by accounting for real-life uncertainties (termed robust and reliability optimization). With this technology, we can now look forward to avoiding over-engineered designs with blind reserve factors, and consider the specific uncertainties in design more intelligently.
Challenges to Overcome
However, we know from the "No Free Lunch" theorem (NFL doesn't just stand for National Football League!) that life is never that rosy. Why isn't everyone using optimization already? Well, we need to appreciate that optimization is simply a tool that provides the solution to the given problem. A correct definition of a problem can take several iterations, so it is unlikely that the first solution will be the final design.
In addition, optimization relies on the simulation to find the optimum. Two limitations arise:
1. The optimum solution is only as good as the simulation. In other words, unreliable simulation leads to a non-optimum design.
2. Some complex simulations can take days or weeks, even with the latest computer technology. Thus, iterative applications of these simulations in optimization can take too long.
Perhaps the most interesting challenge lies in the revolutionary nature of optimization. It can lead to solutions that are completely "outside the box" that no one has ever seen or thought of before. Too often, a reaction to such a solution is "no, it can't be right" and it is dismissed. Sure, it may not be right for the reasons outlined above, but it certainly deserves careful attention. Indeed, it is not uncommon for optimized structures to offer a 40% weight savings for those who have taken the brave step of embracing this approach.
Accepting an unintuitive design from optimization may take the courage to boldly go where no man has gone before, but the returns can be truly game changing.
Alicia Kim is a Senior Lecturer at the University of Bath, UK, and is currently based in Los Alamos National Laboratory on sabbatical.