A Computational Comparison of Optimization Methods for the Golomb Ruler Problem

The Golomb ruler problem is defined as follows: Given a positive integer n, locate n marks on a ruler such that the distance between any two distinct pair of marks are different from each other and the total length of the ruler is minimized. The Golomb ruler problem has applications in information theory, astronomy and communications, and it can be seen as a challenge for combinatorial optimization algorithms. Although constructing high quality rulers is well-studied, proving optimality is a far more challenging task. In this paper, we provide a computational comparison of different optimization paradigms, each using a different model (linear integer, constraint programming and quadratic integer) to certify that a given Golomb ruler is optimal. We propose several enhancements to improve the computational performance of each method by exploring bound tightening, valid inequalities, cutting planes and branching strategies. We conclude that a certain quadratic integer programming model solved through a Benders decomposition and strengthened by two types of valid inequalities performs the best in terms of solution time for small-sized Golomb ruler problem instances. On the other hand, a constraint programming model improved by range reduction and a particular branching strategy could have more potential to solve larger size instances due to its promising parallelization features

Machine Learning for Cutting Planes in Integer Programming: A Survey

We survey recent work on machine learning (ML) techniques for selecting cutting planes (or cuts) in mixed-integer linear programming (MILP). Despite the availability of various classes of cuts, the task of choosing a set of cuts to add to the linear programming (LP) relaxation at a given node of the branch-and-bound (B&B) tree has defied both formal and heuristic solutions to date. ML offers a promising approach for improving the cut selection process by using data to identify promising cuts that accelerate the solution of MILP instances. This paper presents an overview of the topic, highlighting recent advances in the literature, common approaches to data collection, evaluation, and ML model architectures. We analyze the empirical results in the literature in an attempt to quantify the progress that has been made and conclude by suggesting avenues for future research.Comment: Accepted in IJCAI 2023 Survey Trac

On the Separation of Topology-Free Rank Inequalities for the Max Stable Set Problem

In the context of finding the largest stable set of a graph, rank inequalities prescribe that a stable set can contain, from any induced subgraph of the original graph, at most as many vertices as the stability number of the former. Although these inequalities subsume many of the valid inequalities known for the problem, their exact separation has only been investigated in few special cases obtained by restricting the induced subgraph to a specific topology. In this work, we propose a different approach in which, rather than imposing topological restrictions on the induced subgraph, we assume the right-hand side of the inequality to be fixed to a given (but arbitrary) constant. We then study the arising separation problem, which corresponds to the problem of finding a maximum weight subgraph with a bounded stability number. After proving its hardness and giving some insights on its polyhedral structure, we propose an exact branch-and-cut method for its solution. Computational results show that the separation of topology-free rank inequalities with a fixed right-hand side yields a substantial improvement over the bound provided by the fractional clique polytope (which is obtained with rank inequalities where the induced subgraph is restricted to a clique), often better than that obtained with Lovasz's Theta function via semidefmite programming

Learning to Configure Separators in Branch-and-Cut

Cutting planes are crucial in solving mixed integer linear programs (MILP) as they facilitate bound improvements on the optimal solution. Modern MILP solvers rely on a variety of separators to generate a diverse set of cutting planes by invoking the separators frequently during the solving process. This work identifies that MILP solvers can be drastically accelerated by appropriately selecting separators to activate. As the combinatorial separator selection space imposes challenges for machine learning, we learn to separate by proposing a novel data-driven strategy to restrict the selection space and a learning-guided algorithm on the restricted space. Our method predicts instance-aware separator configurations which can dynamically adapt during the solve, effectively accelerating the open source MILP solver SCIP by improving the relative solve time up to 72% and 37% on synthetic and real-world MILP benchmarks. Our work complements recent work on learning to select cutting planes and highlights the importance of separator management

University Nanosatellite Distributed Satelllite Capabilities to Support TechSat 21

A new way to perform space missions utilizes the concept of clusters of satellites that cooperate to perform the function of a larger, single satellite. Each smaller satellite communicates with the others and shares the processing, communications, and payload or mission functions. The required functionality is thus spread across the satellites in the cluster, the aggregate forming a virtual satellite . The Air Force Research Laboratory (AFRL) initiated the TechSat 21 program to explore the basic technologies required to enable such distributed satellite systems. For this purpose, Space Based Radar (SBR) was selected as a reference mission to help identify technology requirements and to allow an easy comparison to a conventional approach. A summary of the basic mission and the performance requirements is provided. The satellite cluster approach to space missions requires science and technology advances in several key areas. Each of these challenges is described in some detail, with specific stressing requirements driven by the SBR reference mission. These TechSat 21 research and technology areas are being studied in a coordinated effort between several directorates within AFRL and the Air Force Office of Scientific Research. In support of TechSat 21, the Air Force Office of Scientific Research and the Defense Advanced Research Projects Agency are jointly funding 10 universities with grants of $50k/year over two years to design and assemble 10–12 nanosatellites (approx 10kg each) for launch in November 2001. The universities are conducting creative low-cost space experiments to explore the military usefulness of nanosatellites in such areas as formation flying, enhanced communications, miniaturized sensors and thrusters, and attitude control. AFRL is developing a deployment structure and providing advanced microsatellite hardware, and NASA Goddard is providing advanced crosslink communication and navigation hardware and flight algorithms to demonstrate formation flying. Numerous industry partners are also supporting the universities with hardware, design expertise, and test facilities. Areas of particular interest to the TechSat 21 program include autonomous operation and simplified ground control of satellite clusters, intersatellite communications, distributed processing, and formation control. This paper summarizes both hardware and computational challenges that have been identified in both the TechSat 21 and the university nanosatellite programs for implementing operational satellite subsystems to accomplish these tasks

Armstrong Flight Research Center Research Technology and Engineering Report 2015

I am honored to endorse the 2015 Neil A. Armstrong Flight Research Centers Research, Technology, and Engineering Report. The talented researchers, engineers, and scientists at Armstrong are continuing a long, rich legacy of creating innovative approaches to solving some of the difficult problems and challenges facing NASA and the aerospace community.Projects at NASA Armstrong advance technologies that will improve aerodynamic efficiency, increase fuel economy, reduce emissions and aircraft noise, and enable the integration of unmanned aircraft into the national airspace. The work represented in this report highlights the Centers agility to develop technologies supporting each of NASAs core missions and, more importantly, technologies that are preparing us for the future of aviation and space exploration.We are excited about our role in NASAs mission to develop transformative aviation capabilities and open new markets for industry. One of our key strengths is the ability to rapidly move emerging techniques and technologies into flight evaluation so that we can quickly identify their strengths, shortcomings, and potential applications.This report presents a brief summary of the technology work of the Center. It also contains contact information for the associated technologists responsible for the work. Dont hesitate to contact them for more information or for collaboration ideas