On Friday, September 30, our student chapter of the Society for Industrial and Applied Mathematics (SIAM) once again hosted their bi-annual picnic. Faculty members and graduate students enjoyed an evening of mixing while partaking of pulled pork from the Smokin’ Pig, pasta from Brioso, and chicken tenders and popcorn chicken as well as delicious homemade desserts and side dishes.
Camille Zerfas, graduate student, won the dessert competition with her Key Lime Pie, followed by graduate student Drew Lipman’s Cookie Bars. Amy Cox, wife of Dr. Chris Cox, won the side dish competition with her Baked Beans, followed by Dr. Sean Sather-Wagstaff’s Arugula Salad.
The next SIAM picnic will occur in the spring on the evening of Friday, April 8, 2015.
SIAM would like to consider offering more vegetarian menu options, so please submit suggestions by email to a SIAM officer.
More information about our SIAM chapter can be found here.
Packing Optimization of Free-Form Objects in Engineering Design*
Margaret Wiecek, Professor of Mathematical Sciences of the Operations Research (OR) subfaculty, and Georges Fadel, Professor of Mechanical and Manufacturing Systems and ExxonMobil Employees’ Chaired Professor of the Clemson Engineering Design Applications and Research (CEDAR) group, have been collaborating on complex systems design and optimization for seventeen years. They have developed and established Clemson’s expertise in multidisciplinary, multilevel, and multiobjective optimization for engineering design with special interest in automotive design.
Figure 1. CAD representation of the underhood
One part of their research program involves packing for engineering design that involves the development of models and methods to determine the arrangement of a set of subsystems or components within some enclosure to achieve a set of objectives without violating spatial or performance constraints. Packing problems, also known as layout optimization problems are challenging because they are highly multimodal, are characterized by models that lack closed-form mathematical representations, and require expensive computational procedures. The time needed to resolve intersection calculations increases exponentially with the number of objects to be packed while the space available for the placement of these components becomes less and less available. Figure 1 depicts a computer-aided design (CAD) representation of a vehicle underhood to reflect the realism of the underhood packing problem.
Figure 2. Compact packing of boxes in a nonconvex trunk.
Profs. Fadel and Wiecek deal with the packing problem from three different perspectives. The first one is motivated by geometric considerations and does not require optimization. An outer shell or envelope is constructed for each object to be packed while its internal details are ignored. Additionally, an inner shell or envelope is constructed for an enclosure within which the objects are packed. According to the other two perspectives, known as compact packing and noncompact packing, the packing problem is formulated as an optimization problem whose optimal solution is the optimal packing arrangement.
Figure 3. Compact free-form packing with full-rotational freedom in a nonconvex trunk.
Methods for geometric representation of objects have been employed in effective algorithms that convert CAD representations to formats used in the fast calculation of intersections or overlap between objects. These methods have given a foundation for the development of models and algorithms for compact and noncompact packing. The solution approaches to packing problems rely on exact algorithms as well as on heuristic methods whenever the level of complexity precludes development of effective exact algorithms. The developed heuristic algorithms have made it possible to solve very difficult optimization problems once thought intractable.
Figure 4. Nonconpact underhood packing with a water (grey) container in an initial position.
The compact packing consists in placing free-form objects with full rotational freedom inside an arbitrarily shaped enclosure so that the volume of the objects inside the enclosure or their number is maximized. The problem is mathematically represented as a single-objective optimization problem since compactness is the only criterion of interest to designers. Figure 2 depicts an optimal arrangement of rectangular boxes representing a set of suitcases of prescribed dimensions inside a nonconvex trunk space. An optimal arrangement of free-form objects with full rotational freedom is shown in Figure 3.
In noncompact packing, the designers are interested in optimizing other objectives evaluating the performance of packing. In automotive design, in addition to compactness the objectives such as balance, maintainability, and survivability of the vehicle are of interest. The mathematical formulation of the problem assumes the form of a multiobjective optimization problem. In the traditional noncompact packing the shapes of components are fixed prior to the packing process during which only their positions and orientations are optimized. However, the ability of packing with morhpable components, i.e., the components that change their shape while their shape and functional requirements are respected, leads to far better packing arrangements. The effect of a morphing water container is shown in Figures 4 and 5. In Figure 4 the water container starts expanding to attempt to reach a specified volume and occupy the available space. Figure 5 shows a bigger container which slightly affects the location of the other components.
Figure 5. Nonco5mpact underhood packing with a water container expanding to a target volume and filling the avilable space.
Engineering design of a complex system, that is composed of subsystems and components, requires interaction among several engineering disciplines (such as fluid dynamics, thermodynamics, structures, controls, and others) that are involved in the design process of the system. Because system and component designs are typically assigned to independent engineering teams with complementary background and expertise, packing for a distributed or decentralized design process has also been studied.
Figures 6 and 7 depict optimal packings of six components (battery, engine, radiator, coolant reservoir, air filter, and brake booster) within the underhood of a hybrid electric vehicle, while one of these components, the battery, is being designed under demanding thermal criteria. The design process is distributed between two design teams: the vehicle-level team responsible for packing of the underhood and the component-level team who designs the battery. When high importance is assigned to the vehicle level, the battery is placed on the left (the rectangular box in Figure 6). In contrast, when high importance is assigned to the battery level, the battery is not only placed on the right but also changes its shape (the long rectangular box in Figure 7), while the other components also change places due to the different location and shape of the battery. The vehicle performs differently with each packing arrangement.
Figure 6. Noncompact distributed underhood packing with high importance given to the vehicle level.
Drs. Fadel and Wiecek will direct their future research toward more advanced packing problems such as packing with multiple morphable components or with the consideration of wiring, hoses, and pipes. Maintaining the interdisciplinary character of work by integrating engineering and sciences perspective is likely to continue leading them to new significant accomplishments in their future studies on packing optimization.
Figure 7. Noncompact distributed underhood packing with high importance given to the battery level.
(*) G.M. Fadel and M.M. Wiecek, “Packing Optimization of Free-Form Objects in Engineering Design,” in Optimal Packings with Applications edited by J. D. Pintér and G. Fasano, Springer, 2015, pp.37—66.
I told a friend that one thing I’ve noticed lately is how fast time seems to fly by. His response was that the best advice he’d received when faced with time pressure is to ‘walk slowly and drink lots of water’. At face value that saying seems a bit absurd as a way to deal with a heavy workload. Upon more reflection I decided it was actually a good motto because it suggests a need to pace oneself and take measures to stay healthy. I expect that the high level of activity we all experience in our department will get even more frenetic as the reorganization shifts into advanced gear. Keeping channels of communication open during this period will help make the transition as smooth as possible. So I’m thankful that Sean Sather-Wagstaff offered to edit the department newsletter. He told me that a main reason for his offer is to get to know members of the various subfaculties. Sean is going to feature one or two subfaculties in each newsletter. Please be sure to provide material for inclusion, when asked. Connie McClain, the newest member of our administrative staff, is working with Sean to put the newsletter together. We are very fortunate to have Connie (at the desk behind the glass panel nearest Martin M) and Alison Ward (at the opposite end, i.e. at the desk nearest Martin E) recently join the administrative group.
Another aspect of communication is taking advantage of social events. I’m enjoying our Wednesday afternoon coffee breaks (hosted by Felice Manganiello). The Welcome Back reception at the Outdoor Lab was fun, and the speaker Rich Ringeisen (at the far right in the picture of our emeritus faculty members at the reception) was both entertaining and thought-provoking. Rich reminded us of the benefits of an active colloquium series. It not only enriches us, it also gets the word out about good things in our department when visitors return home and tell others what they saw here. Towards that end, we’re working with Physics to host a Sobcyzk colloquium in the Spring.
I’m glad to see that our department’s long-held tradition of spring and fall picnics for graduate students, faculty, and their families, sponsored by our SIAM student chapter, continues. Each Fall we welcome newcomers, and the highlight of the Spring picnic is the graduate student awards.
Also on the social front, we’re working to increase participation in the annual Homecoming gathering. I’ve included a picture from this year’s event. We had a strong team effort in putting this on. Near the center of the photo you can see Timo Heister cooking on the McKnew’s grill, with Kevin James helping.
Please consider donating to the Math Sciences enhancement fund. Some generous friends of the department, including retired faculty, give regularly. There are some recurring expenses that cannot be paid for (or at least are not fully covered) from accounts that are used for day-to-day operating expenses. Donations to the enhancement fund help with undergraduate student awards, some of the expenses associated with faculty recruiting, seminars and colloquia, and scholarships that are promised to winners of the Clemson Calculus Challenge if and when they enroll here. Checks should be made out to the Clemson University Foundation.
I’m thankful for the opportunity to be the i-chair (that sounds a little cooler than ‘interim chair’, doesn’t it?). There are many things done by our students, faculty, and staff worth bragging about. Soon you’ll see a revamped department website that will help us in that regard. This newsletter is a good step in the right direction too.
