When mathematical optimization was first introduced to the engineering design world, an optimization expert typically sat with the design engineer to help them apply optimization techniques to their design applications retroactively. Depending on the application, this exercise often became a full-blown project on its own. For a large number of design variables, do a screening Design of Experiments (DOE) first. If there is a computationally demanding simulation, do a space filling DOE and then create a metamodel and use this instead of the exact simulation. If there is only little room for improvement, then use a global search method; but of course global search is expensive so first create a metamodel, which means running a space filling DOE, but which method to run? The questions and scenarios were plentiful with answers reflecting the experts’ personal opinion.
Optimization experts, despite happily finding jobs, were not necessarily content with this situation as it reduced the likelihood that optimization techniques were employed in engineering, thus not fully exploiting its potential. The ultimate challenge was to find a one-click optimization that would work efficiently for a range of problems: local – global, single objective – multi objective, continuous – discrete, and linear – nonlinear.
With that ultimate goal in mind, the method development team at Altair has been working on an optimization method that requires minimal understanding of optimization theory, but still helps the engineer achieve his or her goal. Global response surface method (GRSM) delivered with HyperStudy® 12.0 represents the culmination of this effort.
What is GRSM?
GRSM combines an adaptive response-surface-based optimization with global search. As a result, it is both efficient and the search is not limited to a local region. GRSM first employs advanced strategies to sample the design space with a small number of designs regardless of the problem size. Using these sample designs, it constructs a response surface. The algorithm finds the optimum on this surface, and validates it with an exact simulation. It then adds this design to the sample set, adding a number of new samples as well. The response surface is then updated, and the algorithm finds the optimum in this new surface. GRSM repeats this loop until the user-defined number of designs is evaluated. Note that these evaluations can be run in parallel to reduce the wall time of the study. Furthermore, a number of concurrent evaluations may be dynamically controlled using the multi-execute option in HyperStudy.
GRSM works for both single and multi-objective optimization formulations, as well as handles both continuous and discrete variables. Aside from its wide range of applicability, GRSM’s most notable feature is that the user only needs to enter the number of designs they can afford to evaluate. There are no other method parameters that must be fine-tuned.
Performance of GRSM is tested on the design application covered in HyperStudy tutorial HS-4415: Optimization Study of a Landing Beam Using Excel. This tutorial presents an ideal test case as it deals with a real nonlinear engineering problem, yet runs quickly, allowing us to test many scenarios. To challenge the optimization method, the problem size is expanded to have 30 design variables, 18 constraints and one objective function. Design variable bounds are also enlarged to +-25%. An adaptive response surface method (ARSM) and a global exploration method, genetic algorithm (GA), are both run for comparison. The results are summarized in the table below.
Looking at the table above, GA requires many more runs than the other two methods. A conclusion about a method’s behavior may not be drawn based upon only one example. However, it is typical that GA will require many more runs compared to ARSM and GRSM.
Again, in this example, ARSM had difficulty finding a feasible design until it ran to 539 runs. When it was allowed to run that long, it found a slightly better design than GRSM (0.7% better). Conversely, GRSM could find a good design with a small number of runs (50). When it was allowed to run longer, it significantly improved the design.
It would be wrong to generalize these results as method characteristics but we do expect GA to run a lot longer than other methods and GRSM to find good designs with relatively low effort, both in terms of number of evaluations and in terms of human effort in running the study.
For another useful reference on GRSM, please refer to the article in the Altair blog entitled “HyperStudy Global Response Surface Method” by Joseph Pajot.
It is critical to make design study approaches like optimization usable by engineers. This requires revolutionizing the software user interface to be powerful yet intuitive, flexible yet easy; and refining methods to be robust, efficient, and effective. In the HyperStudy team, we have been investing a great deal of effort toward achieving these goals. This paper summarizes one such initiative to make optimization approachable, GRSM.
GRSM is truly a one-click optimizer, as the only method setting the user must provide is the number of evaluations they can afford. GRSM is effective at finding good designs with reasonable effort regardless of the size of the problem. Each application has its own characteristics, hence each method will behave differently for different applications. In the example covered, GRSM found good designs with 50 runs and achieved even better results if allowed to run longer. GA required significantly more effort, and ARSM required more evaluations to find a feasible design.
Try GRSM in your next design challenge and let us know what you think!