arXiv subjects

Sunil Chopra

Publications and source records attributed to Sunil Chopra.

4 recordsLinked to original sources

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↗

arXiv2020

A Bounded Formulation for The School Bus Scheduling Problem

This paper proposes a new formulation for the school bus scheduling problem (SBSP) which optimizes school start times and bus operation times to minimize transportation cost. Our goal is to minimize the number of buses to serve all bus routes such that each route arrives in a time window before school starts. We present a new time-indexed integer linear programming (ILP) formulation for this problem. Based on a strengthened version of the linear relaxation of the ILP, we develop a dependent randomized rounding algorithm that yields near-optimal solutions for large-scale problem instances. We also generalize our methodologies to solve a robust version of the SBSP.

math.OC↗

arXiv2019

Generalizing the Covering Path Problem on a Grid

We study the covering path problem on a grid of R^{2}. We generalize earlier results on a rectangular grid and prove that the covering path cost can be bounded by the area and perimeter of the grid. We provide (2+ε) and (1+ε)-approximations for the problem on a general grid and on a convex grid, respectively.

cs.DS↗

arXiv2019

The Covering Path Problem on a Grid

This paper introduces the covering path problem on a grid (CPPG) which finds the cost-minimizing path connecting a subset of points in a grid such that each point that needs to be covered is within a predetermined distance of a point from the chosen subset. We leverage the geometric properties of the grid graph which captures the road network structure in many transportation problems, including our motivating setting of school bus routing. As defined in this paper, the CPPG is a bi-objective optimization problem comprised of one cost term related to path length and one cost term related to stop count. We develop a trade-off constraint which quantifies the trade-off between path length and stop count and provides a lower bound for the bi-objective optimization problem. We introduce simple construction techniques to provide feasible paths that match the lower bound within a constant factor. Importantly, this solution approach uses transformations of the general CPPG to either a discrete CPPG or continuous CPPG based on the value of the coverage radius. For both the discrete and continuous versions, we provide fast constant-factor approximations, thus solving the general CPPG.

math.OC↗