Jonathan Peter Lorraine

Machine learning models are often tuned by nesting optimization of model weights inside the optimization of hyperparameters. We give a method to collapse this nested optimization into joint stochastic optimization of weights and hyperparameters. Our process trains a neural network to output approximately optimal weights as a function of hyperparameters. We show that our technique converges to locally optimal weights and hyperparameters for sufficiently large hypernetworks. We compare this method to standard hyperparameter optimization strategies and demonstrate its effectiveness for tuning thousands of hyperparameters.

Designed an algorithm for finding a point to add a Voronoi diagram, with an associated Voronoi cell that has maximal area. The algorithm was applied to compute an optimal LCBO placement in Toronto. The locations value was confirmed by LCBO representatives. Work was completed as a research internship and supported by NSERC.

This paper considers two covering location problems on a network where the demand is distributed along the edges. The first is the classical maximal covering location problem. The second problem is the obnoxious version where the coverage should be minimized subject to some distance constraints between the facilities. It is first shown that the finite dominating set for covering problems with nodal demand does not carry over to the case of edge based demands. Then, a solution approach for the single facility problem is presented. Afterwards, the multi-facility problem is discussed and several discretization results for tree networks are presented for the case that the demand is constant on each edge; unfortunately, these results do not carry over to general networks as a counter example shows. To tackle practical problems, the conditional version of the problem is considered and a greedy heuristic is introduced. Afterwards, numerical tests are presented to underline the practicality of the algorithms proposed and to understand the conditions under which accurate modeling of edge-based demand and a continuous edge-based location space are particularly important.

In this paper we develop a novel methodology to simultaneously optimize locations and designs for a set of new facilities facing competition from some preexisting facilities. Known as the Competitive Facility Location and Design Problem (GFLDP), this model was previously only solvable when a limited number of design scenarios was pre-specified. Our methodology removes this limitation and allows for solving of much more realistic models. The results are illustrated with a small case study.