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Full-Text Articles in Physical Sciences and Mathematics
Iterated Local Search Algorithms For Bike Route Generation, Aidan Pieper
Iterated Local Search Algorithms For Bike Route Generation, Aidan Pieper
Honors Theses
Planning routes for recreational cyclists is challenging because they prefer longer more scenic routes, not the shortest one. This problem can be modeled as an instance of the Arc Orienteering Problem (AOP), a known NP-Hard optimization problem. Because no known algorithms exist to solve this optimization problem efficiently, we solve the AOP using heuristic algorithms which trade accuracy for speed. We implement and evaluate two different Iterated Local Search (ILS) heuristic algorithms using an open source routing engine called GraphHopper and the OpenStreetMap data set. We propose ILS variants which our experimental results show can produce better routes at the …
Modular Scheduling System For Westside School District, Tyler Bienhoff
Modular Scheduling System For Westside School District, Tyler Bienhoff
Honors Theses
Westside School district offers a modular scheduling system for their high school that is more similar to a college schedule than the typical high school system. Due to the complexity of their master schedule each semester, there are no commercially available products that can assist in creating a schedule. Hence, this thesis discusses a scheduling algorithm and management system that was built specifically for Westside High School with the potential to be expanded for use by other interested schools. The first part of the paper is focused on gathering input from students and faculty for which courses and how many …
Extensions Of The Morse-Hedlund Theorem, Eben Blaisdell
Extensions Of The Morse-Hedlund Theorem, Eben Blaisdell
Honors Theses
Bi-infinite words are sequences of characters that are infinite forwards and backwards; for example "...ababababab...". The Morse-Hedlund theorem says that a bi-infinite word f repeats itself, in at most n letters, if and only if the number of distinct subwords of length n is at most n. Using the example, "...ababababab...", there are 2 subwords of length 3, namely "aba" and "bab". Since 2 is less than 3, we must have that "...ababababab..." repeats itself after at most 3 letters. In fact it does repeat itself every two letters. …
Mechanism Design, Matching Theory And The Stable Roommates Problem, Yashaswi Mohanty
Mechanism Design, Matching Theory And The Stable Roommates Problem, Yashaswi Mohanty
Honors Theses
This thesis consists of two independent albeit related chapters. The first chapter introduces concepts from mechanism design and matching theory, and discusses potential applications of this theory, particularly in relation to dorm allocations in colleges. The second chapter investigates a subset of the dorm allocation problem, namely that of matching roommates. In particular, the paper looks at the probability of solvability of random instances of the stable roommates game under the condition that preferences are not completely random and exogenous but endogenously determined through a dependence on room choice. These probabilities are estimated using Monte-Carlo simulations and then compared with …