## Date of Award

December 2021

## Document Type

Dissertation

## Degree Name

Doctor of Philosophy (PhD)

## Department

Industrial Engineering

## Committee Member

J. Cole Smith

## Committee Member

Yongjia Song

## Committee Member

J. Cole Smith

## Committee Member

Brian C. Dean

## Committee Member

Thomas C. Sharkey

## Abstract

This work deals with three different combinatorial optimization problems: minimizing the total size of a pair of binary decision diagrams (BDDs) under a certain structural property, a variant of the facility location problem, and a dynamic version of the Shortest-Path Interdiction (DSPI) problem. However, these problems all have the following core idea in common: They all stem from representing an optimization problem as a decision diagram. We begin from cases in which such a diagram representation of reasonable size might exist, but finding a small diagram is difficult to achieve. The first problem develops a heuristic for enforcing a structural property for a collection of BDDs, which allows them to be merged into a single one efficiently. In the second problem, we consider a specific combinatorial problem that allows for a natural representation by a pair of BDDs. We use the previous result and ideas developed earlier in the literature to reformulate this problem as a linear program over a single BDD. This approach enables us to obtain sensitivity information, while often enjoying runtimes comparable to a mixed integer program solved with a commercial solver, after we pay the computational overhead of building the diagram (e.g., when re-solving the problem using different costs, but the same graph topology). In the last part, we examine DSPI, for which building the full decision diagram is generally impractical. We formalize the concept of a game tree for the DSPI and design a heuristic based on the idea of building only selected parts of this exponentially-sized decision diagram (which is not binary any more). We use a Monte Carlo Tree Search framework to establish policies that are near optimal. To mitigate the size of the game tree, we leverage previously derived bounds for the DSPI and employ an alpha–beta pruning technique for minimax optimization. We highlight the practicality of these ideas in a series of numerical experiments.

## Recommended Citation

Bochkarev, Alexey, "Selected Topics in Network Optimization: Aligning Binary Decision Diagrams for a Facility Location Problem and a Search Method for Dynamic Shortest Path Interdiction" (2021). *All Dissertations*. 2915.

https://open.clemson.edu/all_dissertations/2915