This paper presents a framework for classifying and comparing instances of integer linear programs (ILPs) based on their mathematical structure. It has long been observed that the structure of ILPs can play an important role in determining the effectiveness of certain solution techniques; those that work well for one class of ILPs are often found to be effective in solving similarly structured problems. In this work, the structure of a given ILP instance is captured via a graph-based representation, where decision variables and constraints are described by nodes, and edges denote the presence of decision variables in certain constraints. Using machine learning techniques for graph-structured data, we introduce two approaches for leveraging the graph representations for relating ILPs. In the first approach, a graph convolutional network (GCN) is used to classify ILP graphs as having come from one of a known number of problem classes. The second approach makes use of latent features learned by the GCN to compare ILP graphs to one another directly. As part of the latter approach, we introduce a formal measure of graph-based structural similarity. A series of empirical studies indicate strong performance for both the classification and comparison procedures. Additional properties of ILP graphs, namely, losslessness and permutation invariance, are also explored via computational experiments. History: Accepted by Pascal Van Hentenryck, Area Editor for Computational Modeling: Methods & Analysis. Supplemental Material: The software that supports the findings of this study is available within the paper and its Supplemental Information ( https://pubsonline.informs.org/doi/suppl/10.1287/ijoc.2023.0255 ) as well as from the IJOC GitHub software repository ( https://github.com/INFORMSJoC/2023.0255 ). The complete IJOC Software and Data Repository is available at https://informsjoc.github.io/ .

VeRoViz is an open-source vehicle routing visualization package consisting of both Python and web-based components. It was developed to streamline the workflow for vehicle routing researchers by simplifying and automating many of the tedious tasks associated with generating realistic test problems. VeRoViz also provides new functionality to produce customizable visualizations of complex vehicle routing problems. These visualization tools—including Gantt charts, static maps, and dynamic 3-D videos—assist researchers in validating models and communicating results. Additionally, a comprehensive collection of utility functions within VeRoViz provides researchers with useful tools to assess features of their problems. This paper provides an overview of VeRoViz and highlights the flexibility and ease-of-use of the toolkit. Summary of Contribution: This paper describes an open-source software package designed to assist vehicle routing researchers. The software package, named VeRoViz (vehicle routing visualization), streamlines the process of collecting and visualizing data relevant to vehicle routing research. This includes capturing road network travel times (and distances) between locations, displaying turn-by-turn vehicle routes, generating Gantt charts of vehicle assignments, and producing 3-D “movies” of vehicle routing solutions. The VeRoViz suite consists of three components. First, a web-based interface allows researchers (and instructors) to quickly “sketch” elements of a vehicle routing problem, providing visual representations of nodes and arcs on a map. Second, the VeRoViz Python package provides an extensive collection of functions that assist operations researchers in collecting data and displaying solutions. Finally, an HTML/JavaScript plugin is available for displaying time-dynamic 3-D visualization of vehicle routes. VeRoViz is not a vehicle routing solver; it is a software suite that complements and supports researchers who are developing solution approaches to increasingly realistic vehicle routing problems (e.g., problems related to drone delivery, electric vehicles, or dynamic delivery requests).

Operations researchers have long drawn insight from the structure of constraint coefficient matrices (CCMs) for mixed integer programs (MIPs). We propose a new question: Can pictorial representations of CCM structure be used to identify similar MIP models and instances? In this paper, CCM structure is visualized using digital images, and computer vision techniques are used to detect latent structural features therein. The resulting feature vectors are used to measure similarity between images and, consequently, MIPs. An introductory analysis examines a subset of the instances from strIPlib and MIPLIB 2017, two online repositories for MIP instances. Results indicate that structure-based comparisons may allow for relationships to be identified between MIPs from disparate application areas. Additionally, image-based comparisons reveal that ostensibly similar variations of an MIP model may yield instances with markedly different mathematical structures. Summary of Contribution: This paper presents a methodology for comparing mixed integer programs (MIPs) from any research domain based on the structure of the constraint coefficient matrices for one or more instances of a model. Specifically, computer vision and deep learning techniques are used to extract structural features and measure the similarity between these images. This process is agnostic to application area and instead focuses solely on mathematical structure. As a result, this methodology offers a fundamentally new way for operations researchers to view MIP similarity and highlights similarities between research problems that may have previously been viewed as unrelated.

The single row layout problem is a common and well-studied practical facility layout problem. The problem seeks the arrangement of a fixed number of facilities along one row that minimizes the objective of total material handling cost. In this paper, a single row layout problem with shared clearance between facilities is proposed. The shared additional clearance may be considered on one or both sides of each facility. To solve this problem tabu search is combined with a heuristic rule to solve problems of realistic size. Tabu search is used to find the sequence of facilities while the heuristic rule is determines the additional clearance for each facility. The proposed solution approach is applied to several problem instances involving 10, 20 and 30 facilities, and is compared against a popular mathematical programming solver (CPLEX). Computational results show that our approach is able to obtain high quality solutions and outperforms CPLEX under limited computational time for problems of realistic sizes.

Facility layout problems have drawn much attention over the years, as evidenced by many different versions and formulations in the manufacturing context. This paper is motivated by semiconductor manufacturing, where the floor space is highly expensive (such as in a cleanroom environment) but there is also considerable material handling amongst machines. This is an integrated optimization task that considers both material movement and manufacturing area. Specifically, a new approach combining multiobjective tabu search with linear programming is proposed for an extended double row layout problem, in which the objective is to determine exact locations of machines in both rows to minimize material handling cost and layout area where material flows are asymmetric. First, a formulation of this layout problem is established. Second, an optimization framework is proposed that utilizes multiobjective tabu search and linear programming to determine a set of non-dominated solutions, which includes both sequences and positions of machines. This framework is applied to various manufacturing situations, and compared with an exact approach and a popular multiobjective genetic algorithm optimization algorithm. Experimental results show that the proposed approach is able to obtain sets of Pareto solutions that are far better than those obtained by the alternative approaches.

Unmanned aerial vehicles (UAVs) have become increasingly valuable military assets, and reliance upon them will continue to increase. Despite lacking an onboard pilot, UAVs require crews of up to three human operators. These crews are already experiencing high workload levels, which is a problem that will be likely compounded as the military envisions a future where a single operator controls multiple UAVs. To accomplish this goal, effective scheduling of UAVs and human operators is crucial to future mission success. We present a mathematical model for simultaneously routing UAVs and scheduling human operators, subject to operator workload considerations. This model is thought to be the first of its kind. Numerical examples demonstrate the dangers of ignoring the human element in UAV routing and scheduling.