arXiv subjects

Sangho Shim

Publications and source records attributed to Sangho Shim.

3 recordsLinked to original sources

arXiv2023

Redrawing the 2012 map of the Maryland congressional districts

Gerrymandering is the practice of drawing biased electoral maps that manipulate the voter population to gain an advantage. The most recent time gerrymandering became an issue was 2019 when the U.S. Federal Supreme Court decided that the court does not have the authority to dictate how to draw the district map and state legislators are the ones who should come up with an electoral district plan. We solve the political districting problem and redraw the 2012 map of Maryland congressional districts which raised the issue in 2019.

cs.CY↗

arXiv2022

Park-and-Ride Facility Location Selection under Nested Logit Demand Function

Park-and-ride facilities are car parks where users can transfer to public transportation. Commuters can use P&R facilities or choose to travel by car to their destinations, and individual choice behavior is assumed to follow a logit model. The P&R facility location problem identifies locations for a fixed number of P&R facilities from among potential locations such that the number of users of the P&R facilities is maximized. This problem has previously been formalized under a multinomial logit demand function. However, as it imposes the strong condition of the independence of irrelevant alternatives, the MNL model is unable to represent the real-world P&R facility location problem exactly. Respecting the nested structure of individual choice behavior, we generalize the MNL model to a nested logit model and develop two computational methods -- neighborhood search and randomized rounding -- to solve large-scale P&R facility location problems under the NL demand function. The neighborhood search method first finds one feasible solution and then improves the feasible solution to the next one along an edge of the polyhedron whose vertices are the feasible solutions. The neighborhood search method is randomized to create an adaptive randomized rounding procedure. Computational experiments verified that the computational methods were able to solve the nonlinear optimization problem under the NL demand function on 1,000 medium-scale instances to exact optimality rapidly. Specifically, the methods were verified to solve the MNL model to exact optimality 10,000 times faster than the mixed integer linear programming formulation described in the literature. We performed additional computational experiments to assess the performance of our computational methods on a variety of large-scale instances. Our computational analysis also elucidates the difference between the MNL and NL models.

math.OC↗

arXiv2022

Parallel Power System Restoration

Power system restoration is an essential activity for grid resilience, where grid operators restart generators, re-establish transmission paths, and restore loads after a blackout event. With a goal of restoring electric service in the shortest time, the core decisions in restoration planning are to partition the grid into sub-networks, each of which has an initial power source for black-start (called sectionalization problem), and then restart all generators in each network (called generator startup sequencing problem or GSS) as soon as possible. Due to the complexity of each problem, the sectionalization and GSS problems are usually solved separately, often resulting in a sub-optimal solution. Our paper develops models and computational methods to solve the two problems simultaneously. We first study the computational complexity of the GSS problem and develop an efficient integer linear programming formulation. We then integrate the GSS problem with the sectionalization problem and develop an integer linear programming formulation for the parallel power system restoration (PPSR) problem to find exact optimal solutions. To solve larger systems, we then develop bounding approaches that find good upper and lower bounds efficiently. Finally, to address computational challenges for very large power grids, we develop a randomized approach to find a high-quality feasible solution quickly. Our computational experiments demonstrate that the proposed approaches are able to find good solutions for PPSR in up to 2000-bus systems.

cs.CE↗