Discrete optimization

About: Discrete optimization is a research topic. Over the lifetime, 4598 publications have been published within this topic receiving 158297 citations. The topic is also known as: discrete optimisation.

Optimization of Computer Networks: Modeling and Algorithms: A Hands-On Approach

Abstract: This book covers the design and optimization of computer networks applying a rigorous optimization methodology, applicable to any network technology. It is organized into two parts. In Part 1 the reader will learn how to model network problems appearing in computer networks as optimization programs, and use optimization theory to give insights on them. Four problem types are addressed systematically – traffic routing, capacity dimensioning, congestion control and topology design.

Design of Highly Uniform Magnetic Field Coils Based on a Particle Swarm Optimization Algorithm

Abstract: An innovative design method is proposed for highly uniform magnetic field coils using a particle swarm optimization (PSO) algorithm. We use an optimization approach instead of the conventional method of solving closed-form equations to obtain the coil geometric parameters. We apply a PSO algorithm to the optimization of the coil structure and set an appropriate penalty function and boundary conditions. A discrete optimization is employed to avoid obtaining parameters with a large number of decimal places. Compared with the conventional design method, our method solves the problem of how to design a coil set to produce a highly uniform magnetic field under various structural and process constraints. The coil designed by this method can produce a highly uniform magnetic field for a larger effective space. This is significant for miniaturized applications, especially for miniature atomic sensors. The calculations show that the magnetic field deviations of the triaxial cylindrical coils designed by this innovative method are decreased by more than two orders of magnitude in the volume of interest (VOI) compared to conventional triaxial cylindrical coils. Our experimental measurements are consistent with theoretical values. Measurements show that relative magnetic field uniformities of the axial and radial coils reache $1.2\times 10^{-4}$ and $3.9\times 10^{-3}$ along the magnetic field axis in the range of $\pm 0.5R$ . In addition, this method can also be used to design gradient field coils or other shaped coils.

Resource Constrained Neural Network Architecture Search: Will a Submodularity Assumption Help?

Abstract: The design of neural network architectures is frequently either based on human expertise using trial/error and empirical feedback or tackled via large scale reinforcement learning strategies performed over distinct discrete architecture choices. In the latter case, the optimization is often non-differentiable and also not very amenable to derivative-free optimization methods. Most methods in use today require sizable computational resources. And if we want networks that additionally satisfy resource constraints, the above challenges are exacerbated because the search must now balance accuracy with certain budget constraints on resources. We formulate this problem as the optimization of a set function -- we find that the empirical behavior of this set function often (but not always) satisfies marginal gain and monotonicity principles -- properties central to the idea of submodularity. Based on this observation, we adapt algorithms within discrete optimization to obtain heuristic schemes for neural network architecture search, where we have resource constraints on the architecture. This simple scheme when applied on CIFAR-100 and ImageNet, identifies resource-constrained architectures with quantifiably better performance than current state-of-the-art models designed for mobile devices. Specifically, we find high-performing architectures with fewer parameters and computations by a search method that is much faster.