Akhilesh Soni

Publications

1. Mixed-integer linear programming for scheduling unconventional oil field development

   Soni, Akhilesh, Linderoth, Jeff, Luedtke, James, and Rigterink, Fabian

   Optimization and Engineering, Sep 2021

   Abstract Paper

   The scheduling of drilling and hydraulic fracturing of wells in an unconventional oil field plays an important role in the profitability of the field. A key challenge arising in this problem is the requirement that neither drilling nor oil production can be done at wells within a specified neighborhood of a well being fractured. We propose a novel mixed-integer linear programming (MILP) formulation for determining a schedule for drilling and fracturing wells in an unconventional oil field. We also derive an alternative formulation which provides stronger relaxations. In order to apply the MILP model for scheduling large fields, we derive a rolling horizon approach that solves a sequence of coarse time-scale MILP instances to obtain a solution at the daily time scale.

2. Integer Programming Approaches To Subspace Clustering With Missing Data

   Soni, Akhilesh, Linderoth, Jeff, Luedtke, Jim, and Pimentel-Alarcón, Daniel

   OPT2021: 13th Annual Workshop on Optimization for Machine Learning, NeurIPS, Sep 2021

   Abstract Paper

   In the Subspace Clustering with Missing Data problem, we are given a collection of n data points, and each of the data points is observed only on a subset of its coordinates. The data points are assumed to be concentrated near a union of low-dimensional subspaces. The goal is to cluster the vectors as per their subspace membership. State-of-the-art algorithms can perform poorly on instances with a large amount of missing data o if the data matrix is nearly full-rank. We propose a novel integer programming-based method for SCMD. The approach is based on dynamically determining a set of candidate subspaces and optimally assigning points to selected subspaces. The problem structure is identical to the classical facility-location problem, with subspaces playing the role of facilities and data points that of customers. We propose a column-generation approach for identifying candidate subspaces combined with a Benders decomposition approach for solving the linear programming relaxation of the formulation. An empirical study demonstrates that the proposed approach can achieve better clustering accuracy than state-of-the-art methods when the data is high-rank or the percentage of missing data is high.

3. Regional decomposition for network design using Lagrangian relaxation

   Soni, Akhilesh, and Atakans, Semih

   In Preparation
4. Binary matrix completion over finite field

   Soni, Akhilesh, Linderoth, Jeff, Luedtke, Jim, and Pimentel-Alarcón, Daniel

   In Preparation