Jason J. Sauppe

Branch-and-bound algorithms

The branch-and-bound (B&B) algorithmic framework has been used successfully to find exact solutions for a wide array of optimization problems. B&B uses a tree search strategy to implicitly enumerate all possible solutions to a given problem, applying pruning rules to eliminate regions of the search space that cannot lead to a better solution. There are three algorithmic components in B&B that can be specified by the user to fine-tune the behavior of the algorithm. These components are the search strategy, the branching strategy, and the pruning rules. This survey presents a description of recent research advances in the design of B&B algorithms, particularly with regards to these three components. Moreover, three future research directions are provided in order to motivate further exploration in these areas.

Balance Optimization Subset Selection (BOSS): An Alternative Approach for Causal Inference with Observational Data

Scientists in all disciplines attempt to identify and document causal relationships. Those not fortunate enough to be able to design and implement randomized control trials must resort to observational studies. To make causal inferences outside the experimental realm, researchers attempt to control for bias sources by postprocessing observational data. Finding the subset of data most conducive to unbiased or least biased treatment effect estimation is a challenging, complex problem. However, the rise in computational power and algorithmic sophistication leads to an operations research solution that circumvents many of the challenges presented by methods employed over the past 30 years.

Complexity and approximation results: For the balance optimization subset selection model for causal inference in observational studies

Matching is widely used in the estimation of treatment effects in observational studies. However, the matching paradigm may be too restrictive in many cases because exact matches often do not exist in the available data. One mechanism for overcoming this issue is to relax the requirement of exact matching on some or all of the covariates (attributes that may affect the response to treatment) to a requirement of balance on the covariate distributions for the treatment and control groups. The balance optimization subset selection (BOSS) model can be used to identify a control group featuring optimal covariate balance. This paper explores the relationship between the matching and BOSS models and shows how BOSS subsumes matching. Complexity and approximation results are presented for the resulting models. Computational results demonstrate some of the important trade-offs between matching and BOSS. Data, as supplemental material, are available at http://dx.doi.org/10.1287/ijoc.2013.0583. There is a video associated with this paper. Click here to view the Video Overview. To save the file, right click and choose “Save Link As” from the menu.

A Network Simplex Algorithm for the Equal Flow Problem on a Generalized Network

A network simplex algorithm is described for the minimum-cost network flow problem on a generalized network, with the additional constraint that there exist sets of arcs that must carry equal amounts of flow. This problem can be modeled as a linear programming problem and solved using the standard simplex algorithm. However, because of the structure of the problem, more efficient algorithms are possible that solve the problem by operating directly on the network itself. One such algorithm is described that leads to improved asymptotic performance per iteration over the standard simplex algorithm, as long as the number of side constraints is small relative to the size of the network. Computational results are given comparing this algorithm to CPLEXs primal simplex solver on randomly generated graphs.

A wide branching strategy for the graph coloring problem

Branch-and-price algorithms for the graph coloring problem use an exponentially sized independent set-based integer programming formulation to produce usually tight lower bounds to enable more aggressive pruning in the branch-and-bound tree. One major problem inherent to any branch-and-price scheme for graph coloring is that to avoid destroying the pricing problem structure during column generation, difficult-to-implement branching rules that modify the underlying graph must be used. This paper proposes an alternative branching strategy that does not change the graph to solve the pricing problem but rather modifies the search tree to require fewer calls to difficult instances of the pricing problem. This approach, called wide branching, generates many subproblems at each node in the branch-and-price tree; this significantly reduces the length of any path through the search tree. In contrast, traditional deep branching only creates two subproblems per node, assigning a variable to either 0 or 1. A delayed ...

An algorithm to solve the proportional network flow problem

The proportional network flow problem is a generalization of the equal flow problem on a generalized network in which the flow on arcs in given sets must all be proportional. This problem appears in several natural contexts, including processing networks and manufacturing networks. This paper describes a transformation on the underlying network that reduces the problem to the equal flow problem; this transformation is used to show that algorithms that solve the equal flow problem can be directly applied to the proportional network flow problem as well, with no increase in asymptotic running time. Additionally, computational results are presented for the proportional network flow problem demonstrating equivalent performance to the same algorithm for the equal flow problem.

Bias in Balance Optimization Subset Selection: Exploration through examples

Abstract When estimating a treatment effect from observational data, researchers encounter bias regardless of estimation methods. In this paper, we focus on a particular method of estimation called Balance Optimization Subset Selection (BOSS). This paper investigates all the possible cases that may lead to bias in the context of BOSS, provides examples for those cases and tries to mitigate the bias. While doing so, we define a balance hierarchy and a correct imbalance measure which corresponds to the form of the response functions. In addition, new imbalance measures drawn from the Cramer-von Mises test statistic are introduced. The cases of insufficient data and suboptimality that can arise in causal analysis with BOSS are also presented.

Identifying NCAA tournament upsets using Balance Optimization Subset Selection

Abstract The NCAA basketball tournament attracts over 60 million people who fill out a bracket to try to predict the outcome of every tournament game correctly. Predictions are often made on the basis of instinct, statistics, or a combination of the two. This paper proposes a technique to select round-of-64 upsets in the tournament using a Balance Optimization Subset Selection model. The model determines which games feature match-ups that are statistically most similar to the match-ups in historical upsets. The technique is then applied to the tournament in each of the 13 years from 2003 to 2015 in order to select two games as potential upsets each year. Of the 26 selected games, 10 (38.4%) were actual upsets, which is more than twice as many as the expected number of correct selections when using a weighted random selection method.

Forecasting the 2012 and 2014 Elections Using Bayesian Prediction and Optimization

This article presents a data-driven Bayesian model used to predict the state-by-state winners in the Senate and presidential elections in 2012 and 2014. The Bayesian model takes into account the proportions of polled subjects who favor each candidate and the proportion who are undecided, and produces a posterior probability that each candidate will win each state. From this, a dynamic programming algorithm is used to compute the probability mass functions for the number of electoral votes that each presidential candidate receives and the number of Senate seats that each party receives. On the final day before the 2012 election, the model gave a probability of (essentially) one that President Obama would be reelected, and that the Democrats would retain control of the U.S. Senate. In 2014, the model gave a final probability of .99 that the Republicans would take control of the Senate.

Assigning Panels to Meeting Rooms at the National Science Foundation

The National Science Foundation provides funding for scientific research throughout the United States. Its program directors solicit requests for funding through calls for proposals and then assemble panels of experts to review these requests. The program directors are responsible for reserving meeting rooms for each of the panels. Our work automates much of the room reservation process by constructing and solving an optimization model that determines how panels should be assigned to available rooms to maximize the utilization of available meeting rooms. The model accommodates multiday panels, differences between the rooms (e.g., capacity, projector support), and double-booking constraints for both rooms and panel organizers. Staff members at the National Science Foundation are currently using this software, and have employed it to successfully schedule engineering directorate panels for the 2014–2015 review year.