Browsing by Author "Cavers, Michael"
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Item Open Access On a 2-path problem(2016) Song, Haotian; Zinchenko, Yuriy; Bauer, Kristine; Cavers, MichaelAn electric power supplier needs to build a transmission line between 2 jurisdictions. Ideally, the design of the new electric power line would be such that it optimizes some user-defined utility function, for example, minimizes the construction cost or the environmental impact. Due to reliability considerations, the power line developer has to install not just one, but two transmission lines, separated by a certain distance from one to another, so that even if one of the lines fails, the end user will still receive electricity along the second line. We discuss how such a problem can be modelled and prove the general graph-based problem to be NP-hard. At the same time, we propose a polynomial-time approximation scheme to handle this problem. Although the worst-case performance of the latter scheme is not fully understood yet, we note that under two mild practical assumptions, the scheme yields the optimal solution to the original problem. The novel scheme appears to be extremely efficient numerically. Our implementation scheme vastly outperforms more conventional solution methods, such as mixed-integer based models. In turn, this allows us to solve realistically sized problems on graphs nearing a hundred thousand nodes.Item Open Access Student-weighted Multiple Choice Tests(2015-05-12) Ling, Joseph; Cavers, MichaelLarge-enrolment courses routinely administer multiple choice tests. Well-thought-out multiple choice tests are excellent assessment instruments, but their format allows for guessing. Furthermore, the opportunity for students to highlight their levels of mastery of material is not necessarily present. Frary (1989) reviews multiple choice methods that attempt to capture student knowledge in each question. In this workshop, we will discuss one such format of multiple choice testing known as Confidence Weighting (Echternacht, 1972). In this model, students are given a certain freedom to assign relative weights to individual questions representing their belief in the correctness of their response. The purpose of this is to allow students to demonstrate their level of confidence on their true knowledge of the material. Thus, students with identical responses to the questions may receive different overall scores depending on their indicated degree of confidence for each question. We experimented using this method in two first-year calculus courses during three semesters in 2014. During this workshop, we describe our experience along with issues encountered while using this model. The session will be interactive allowing for participants to share ideas and their personal experiences with various multiple-choice models. The model described here has not been widely used and we hope to explore questions and possible issues that may arise with the workshop participants. The outcome will be ideas for improvements to the Confidence Weighting method that can be applied in future courses. Variations on this method will also be explored and discussed (Lang, 2014).