Design - Bell Helicopter

An important part of the design of a new helicopter is the flight test, where data is collected measuring the forces on different components of the helicopter. Before a helicopter design can be approved, one needs to know that the design can withstand these forces over the expected lifetime of the helicopter. A physical stress test is costly and time consuming, and it can only apply about a half-dozen forces. Therefore it is essential to choose the correct forces from the flight test, which will then be applied in the physical stress tests. The correct forces are the extreme (i.e., most important) forces in directions that cause wear and tear. Choosing these forces is difficult, since millions of data points are measured during the flight test and the data points are in high dimensions.

The testing team uses expert knowledge to determine which points are likely to be important. Data reduction is required, however. Our team hoped to find a blind data reduction method that would agree with the points found using expert knowledge. A research team consisting of a professor, postdoctoral fellows, undergraduate students, and graduate students worked with the team from Bell Helicopter using ideas from convex analysis and computational mathematics to find the required extreme points. The results of the blind algorithm agreed with the results provided by expert knowledge. The results were used in time to go ahead with the physical stress testing on a new model of helicopter.

Quantum gate design

The heart of a quantum computer is a simple quantum gate that has several inputs and outputs controlling a certain number of basic quanta of information known as qubits. The research group at the Institute for Quantum Science and Technology, led by Dr. Barry Sanders at the University of Calgary had developed a novel machine learning method, known as Subspace-selective Self-adaptive Differential Evolution, for creating the optimal design of a three qubit gate. Extending this to more qubits is a major computational challenge, which the group presented as a problem at the 2015 PIMS Industrial Problem Solving Workshop held at the University of Saskatchewan. A four qubit design leads to a hard optimization problem in \(4^4 = 256\) dimensions. A mathematical re-formulation of the design problem led to an algorithmically simpler feasible region problem. The result is a computationally efficient algorithm that solves the design in a matter of hours of compute time, rather than weeks or months.

Mining - Scheduling Ops

Managing a network of mines is a complex operation, each mine with its own unique character, producing a range of products at various capacities, with varying amounts of space for on-site inventory storage, often with processing facilities to refine products, and with unique transportation access and costs.

The Potash Corporation, headquarted in the Province of Saskatchewan, has mines at locations around the world and supplies a global market for fertilizer and crop nutrients that are essential in modern agriculture.

Scheduling of shut-downs and starts-up of each potash mine, and a variety of labour and fiscal constraints, can be a key step in determining the network operations. Ultimately the goal of a commercial mining operation is to maximize profits over a sustained period of time, taking into consideration the constraints of operation while responding to opportunities in the marketplace. The researchers at Potash Corp presented a challege to the participants of the 2015 PIMS Industrial Problem Solving Workshop, to come up with an effective software algorithm to aid in optimizing the operations of the mines. A key improvement was to provide feedback to the operators on how to adjust the algorithm on the fly, to provide useful and reliable results for real operations over a sustained period.