Mithun Goutham

Mithun Goutham, Meghna Menon, Sarah Garrow et al.

The convex hull cheapest insertion heuristic produces good solutions to the Euclidean Traveling Salesperson Problem, but it has never been extended to the non-Euclidean problem. This paper uses multidimensional scaling to first project the points from a non-Euclidean space into a Euclidean space, enabling the generation of a convex hull that initializes the algorithm. To evaluate the proposed algorithm, non-Euclidean spaces are created by adding separators to the TSPLIB data-set, or by using the L1 norm as a metric.

Mithun Goutham, Riccardo DalferroNucci, Stephanie Stockar et al.

Accurately estimating decision boundaries in black box systems is critical when ensuring safety, quality, and feasibility in real-world applications. However, existing methods iteratively refine boundary estimates by sampling in regions of uncertainty, without providing guarantees on the closeness to the decision boundary and also result in unnecessary exploration that is especially disadvantageous when evaluations are costly. This paper presents $\varepsilon$-Neighborhood Decision-Boundary Governed Estimation (EDGE), a sample efficient and function-agnostic algorithm that leverages the intermediate value theorem to estimate the location of the decision boundary of a black box binary classifier within a user-specified $\varepsilon$-neighborhood. To demonstrate applicability, a case study is presented of an electric grid stability problem with uncertain renewable power injection. Evaluations are conducted on three test functions, where it is seen that the EDGE algorithm demonstrates superior sample efficiency and better boundary approximation than adaptive sampling techniques and grid-based searches.