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publications
Variable Ordering for Decision Diagrams: A Portfolio Approach
Published in Constraints 2022, 2022
We compare the performance of different portfolios of variable orderings on an algorithm that uses decision diagrams to compute lower bounds on the chromatic number of a graph.
Recommended citation: Karahalios and van-Hoeve (2022). "Variable Ordering for Decision Diagrams." Constraints 2022. https://link.springer.com/article/10.1007/s10601-021-09325-6
From Cliques to Colorings and Back Again
Published in Constraint Programming 2022, 2022
We present an exact algorithm for graph coloring and maximum clique problems based on SAT technology.
Recommended citation: Heule, Marijn JH, Anthony Karahalios, and Willem-Jan van Hoeve (2022). "From Cliques to Colorings and Back Again." Constraints 2022. https://drops.dagstuhl.de/opus/volltexte/2022/16655/pdf/LIPIcs-CP-2022-26.pdf
Column Elimination for Capacitated Vehicle Routing Problems
Published in CPAIOR 2023, 2023
We solve an LP over iteratively improving state-space relaxations to exactly solve the CVRP. Through experimental results, we show our method is competitive with state-of-the-art BCP methods
Recommended citation: A. Karahalios, and W.-J. van Hoeve. "Column Elimination for Capacitated Vehicle Routing Problems" CPAIOR 2023. https://sites.google.com/view/cpaior2023/home?authuser=0
talks
Variable Ordering for Decision Diagrams: A Portfolio Approach
Published:
Studying the use of portfolios of variable orderings on the performance of a decision diagram based algorithm for finding graph coloring lower bounds
Graph Coloring With Decision Diagrams: An Analysis Of Variable Ordering
Published:
A decision diagram approach was recently introduced to generate lower bounds for the graph coloring problem. It uses compilation via iterative refinement, which requires a variable ordering to be specified in advance. Oftentimes no single variable ordering dominates all others for a set of problem instances. This work provides an analysis and experimental evaluation of different variable ordering strategies including using portfolios of variable orderings.
Graph Coloring using Decision Diagrams with Zykov Branching
Published:
A recent work by van Hoeve introduced a decision diagram based iterative refinement algorithm for finding multi-path solutions to optimization problems. We study the addition of branch and bound to this algorithm, including the well-known Zykov branching rule for graph coloring.
From Cliques to Colorings and Back Again
Published:
We present an exact algorithm for graph coloring and maximum clique problems based on SAT technology.
Comparing Column Elimination and Column Generation
Published:
A method called Column Elimination was recently introduced to generate both lower bounds and optimal solutions for the graph coloring problem. Based on dynamic programming and decision diagrams, this exact method begins with a relaxed state space and refines this space at each iteration. Our work provides methodological and computational comparisons between Column Elimination and Column Generation; it uses the Capacitated Vehicle Routing Problem (CVRP) as a case study.
teaching
MBA Math Bootcamp TA
Teaching Assistant, Carnegie Mellon University, Tepper School of Business, 2021
TA for MBA Math Bootcamp focusing on Calculus and Probability
45-751 Optimization (MBA) Spring 2022
Teaching Assistant, Carnegie Mellon University, Tepper School of Business, 2022
TA for MBA Optimization course that covers fundamental optimization tools for quantitative analysis in the management sciences. The central topics of study are linear integer and nonlinear programming. Special emphasis is placed on linear programming particularly on modeling business applications and on sensitivity analysis. The course follows a practical spreadsheet-based approach to provide hands-on experience with software such as Excel Solver.
46-888 Optimization for Prescriptive Analytics (MBA) Summer 2022
Teaching Assistant, Carnegie Mellon University, Tepper School of Business, 2022
TA for MBA Optimization course that focuses on developing such optimization models for operational and strategic decision making. We will consider applications such as resource allocation, network design, and capacity planning, in a variety of business areas including finance, operations, logistics, and marketing. We will primarily focus on deterministic optimization models (i.e., we don’t use probability models or stochastic processes), and use linear, integer, and nonlinear programming as optimization methodologies. We solve problems in these fields using CPLEX in Python.
70-460 Mathematical Models for Consulting (Undergrad) Fall 2022
Instructor, Carnegie Mellon University, Tepper School of Business, 2022
Instructor for upper-level undergraduate optimization elective course. Fulfilled my teaching requirement for Tepper PhD students by teaching this class of 22 students. The course material includes column generation, integer programming, robust optimization, and a project where teams use these advanced modeling techniques to solve a real world problem. Models are implemented in both Excel and Python using Gurobi.