Energy-Efficient Service Placement for Latency-Sensitive Applications in Edge Computing

Edge computing is a promising solution to host artificial intelligence (AI) applications that enable real-time insights on user-generated and device-generated data. This requires edge computing resources (storage and compute) to be widely deployed close to end devices. Such edge deployments require a large amount of energy to run as edge resources are typically overprovisioned to flexibly meet the needs of time-varying user demand with a low latency. Moreover, AI applications rely on deep neural network (DNN) models that are increasingly larger in size to support high accuracy. These DNN models must be efficiently stored and transferred, so as to minimize their energy consumption. In this article, we model the problem of energy-efficient placement of services (namely, DNN models) for AI applications as a multiperiod optimization problem. The formulation jointly places services and schedules requests such that the overall energy consumption is minimized and latency is low. We propose a heuristic that efficiently solves the problem while taking into account the impact of placing services across time periods. We assess the quality of the proposed heuristic by comparing its solution to a lower bound of the problem, obtained by formulating and solving a Lagrangian relaxation of the original problem. Extensive simulations show that our proposed heuristic outperforms baseline approaches in achieving a low energy consumption by packing services on a minimal number of edge nodes, while at the same time keeping the average latency of served requests below a configured threshold in nearly all time periods.Peer reviewe

New Conic Optimization Techniques for Solving Binary Polynomial Programming Problems

Polynomial programming, a class of non-linear programming where the objective and the constraints are multivariate polynomials, has attracted the attention of many researchers in the past decade. Polynomial programming is a powerful modeling tool that captures various optimization models. Due to the wide range of applications, a research topic of high interest is the development of computationally efficient algorithms for solving polynomial programs. Even though some solution methodologies are already available and have been studied in the literature, these approaches are often either problem specific or are inapplicable for large-scale polynomial programs. Most of the available methods are based on using hierarchies of convex relaxations to solve polynomial programs; these schemes grow exponentially in size becoming rapidly computationally expensive. The present work proposes methods and implementations that are capable of solving polynomial programs of large sizes. First we propose a general framework to construct conic relaxations for binary polynomial programs, this framework allows us to re-derive previous relaxation schemes and provide new ones. In particular, three new relaxations for binary quadratic polynomial programs are presented. The first two relaxations, based on second-order cone and semidefinite programming, represent a significant improvement over previous practical relaxations for several classes of non-convex binary quadratic polynomial problems. The third relaxation is based purely on second-order cone programming, it outperforms the semidefinite-based relaxations that are proposed in the literature in terms of computational efficiency while being comparable in terms of bounds. To strengthen the relaxations further, a dynamic inequality generation scheme to generate valid polynomial inequalities for general polynomial programs is presented. When used iteratively, this scheme improves the bounds without incurring an exponential growth in the size of the relaxation. The scheme can be used on any initial relaxation of the polynomial program whether it is second-order cone based or semidefinite based relaxations. The proposed scheme is specialized for binary polynomial programs and is in principle scalable to large general combinatorial optimization problems. In the case of binary polynomial programs, the proposed scheme converges to the global optimal solution under mild assumptions on the initial approximation of the binary polynomial program. Finally, for binary polynomial programs the proposed relaxations are integrated with the dynamic scheme in a branch-and-bound algorithm to find global optimal solutions

A Branch-and-Cut Algorithm based on Semidefinite Programming for the Minimum k-Partition Problem

The minimum k-partition (MkP) problem is a well-known optimization problem encountered in various applications most notably in telecommunication and physics. Formulated in the early 1990s by Chopra and Rao, the MkP problem is the problem of partitioning the set of vertices of a graph into k disjoint subsets so as to minimize the total weight of the edges joining vertices in different partitions. In this thesis, we design and implement a branch-and-cut algorithm based on semidefinite programming (SBC) for the MkP problem. We describe and study the properties of two relaxations of the MkP problem, the linear programming and the semidefinite programming relaxations. We then derive a new strengthened relaxation based on semidefinite programming. This new relaxation provides tighter bounds compared to the other two discussed relaxations but suffers in term of computational time. We further devise an iterative clustering heuristic (ICH), a novel heuristic that finds feasible solution to the MkP problem and we compare it to the hyperplane rounding techniques of Goemans and Williamson and Frieze and Jerrum for k=2 and for k=3 respectively. Our computational results support the conclusion that ICH provides a better feasible solution for the MkP. Furthermore, unlike the hyperplane rounding, ICH remains very effective in the presence of negative edge weights. Next we describe in detail the design and implementation of a branch-and-cut algorithm based on semidefinite programming (SBC) to find optimal solution for the MkP problem. The ICH heuristic is used in our SBC algorithm to provide feasible solutions at each node of the branch-and-cut tree. Finally, we present computational results for the SBC algorithm on several classes of test instances with k=3, 5, and 7. Complete graphs with up to 60 vertices and sparse graphs with up to 100 vertices arising from a physics application were considered

A Branch-and-Cut Algorithm based on Semidefinite Programming for the Minimum k-Partition Problem

The minimum k-partition (MkP) problem is the problem of partitioning the set of vertices of a graph into k disjoint subsets so as to minimize the total weight of the edges joining vertices in the same partition. The main contribution of this paper is the design and implementation of a branch-and-cut algorithm based on semidefinite programming (SBC) for the MkP problem. The two key ingredients for this algorithm are: the combination of semidefinite programming (SDP) with polyhedral results; and the iterative clustering heuristic (ICH) that finds feasible solutions for the MkP problem. We compare ICH to the hyperplane rounding techniques of Goemans and Williamson and of Frieze and Jerrum, and the computational results support the conclusion that ICH consistently provides better feasible solutions for the MkP problem. ICH is used in our SBC algorithm to provide feasible solutions at each node of the branch-and-bound tree. The SBC algorithm computes globally optimal solutions for dense graphs with up to 60 vertices, for grid graphs with up to 100 vertices, and for different values of k, providing the best exact approach to date for k > 2