Iain Dunning

Computing in Operations Research Using Julia

The state of numerical computing is currently characterized by a divide between highly efficient yet typically cumbersome low-level languages such as C, C++, and Fortran and highly expressive yet typically slow high-level languages such as Python and MATLAB. This paper explores how Julia, a modern programming language for numerical computing that claims to bridge this divide by incorporating recent advances in language and compiler design (such as just-in-time compilation), can be used for implementing software and algorithms fundamental to the field of operations research, with a focus on mathematical optimization. In particular, we demonstrate algebraic modeling for linear and nonlinear optimization and a partial implementation of a practical simplex code. Extensive cross-language benchmarks suggest that Julia is capable of obtaining state-of-the-art performance.Data, as supplemental material, are available at http://dx.doi.org/10.1287/ijoc.2014.0623 .

Multistage Robust Mixed-Integer Optimization with Adaptive Partitions

We present a new partition-and-bound method for multistage adaptive mixed-integer optimization (AMIO) problems that extends previous work on finite adaptability. The approach analyzes the optimal solution to a static (nonadaptive) version of an AMIO problem to gain insight into which regions of the uncertainty set are restricting the objective function value. We use this information to construct partitions in the uncertainty set, leading to a finitely adaptable formulation of the problem. We use the same information to determine a lower bound on the fully adaptive solution. The method repeats this process iteratively to further improve the objective until a desired gap is reached. We provide theoretical motivation for this method, and characterize its convergence properties and the growth in the number of partitions. Using these insights, we propose and evaluate enhancements to the method such as warm starts and smarter partition creation. We describe in detail how to apply finite adaptability to multistage AMIO problems to appropriately address nonanticipativity restrictions. Finally, we demonstrate in computational experiments that the method can provide substantial improvements over a nonadaptive solution and existing methods for problems described in the literature. In particular, we find that our method produces high-quality solutions versus the amount of computational effort, even as the problem scales in the number of time stages and the number of decision variables.

A Course on Advanced Software Tools for Operations Research and Analytics

It is increasingly important for researchers and practitioners to be familiar with methods and software tools for analyzing large data sets, formulating and solving large-scale mathematical optimization models, and sharing solutions using interactive media. Unfortunately, advanced software tools are seldom included in curricula of graduate-level operations research OR and analytics programs. We describe a course consisting of eight three-hour modules intended to introduce masters and Ph.D. students to advanced software tools for OR and analytics: machine learning in R, data wrangling, visualization, big data, algebraic modeling with JuMP, high-performance and distributed computing, Internet and databases, and advanced mixed integer linear programming MILP techniques. For each module, we outline content, provide course materials, summarize student feedback, and share lessons learned from two iterations of the course. Student feedback was very positive, and all students reported that the course equipped them with software skills useful for their own research. We believe our course materials could serve as a template for the development of effective OR and analytics software tools courses and discuss how they could be adapted to other educational settings.

What Works Best When? A Systematic Evaluation of Heuristics for Max-Cut and QUBO

Though empirical testing is broadly used to evaluate heuristics, there are shortcomings with how it is often applied in practice. In a systematic review of Max-Cut and quadratic unconstrained binar...