Wireless powered mobile-edge computing (MEC) has recently emerged as a promising paradigm to enhance the data processing capability of low-power networks, such as wireless sensor networks and internet of things (IoT). In this paper, we consider a wireless powered MEC network that adopts a binary offloading policy, so that each computation task of wireless devices (WDs) is either executed locally or fully offloaded to an MEC server. Our goal is to acquire an online algorithm that optimally adapts task offloading decisions and wireless resource allocations to the time-varying wireless channel conditions. This requires quickly solving hard combinatorial optimization problems within the channel coherence time, which is hardly achievable with conventional numerical optimization methods. To tackle this problem, we propose a Deep Reinforcement learning-based Online Offloading (DROO) framework that implements a deep neural network as a scalable solution that learns the binary offloading decisions from the experience. It eliminates the need of solving combinatorial optimization problems, and thus greatly reduces the computational complexity especially in large-size networks. To further reduce the complexity, we propose an adaptive procedure that automatically adjusts the parameters of the DROO algorithm on the fly. Numerical results show that the proposed algorithm can achieve near-optimal performance while significantly decreasing the computation time by more than an order of magnitude compared with existing optimization methods. For example, the CPU execution latency of DROO is less than @math second in a @math -user network, making real-time and optimal offloading truly viable even in a fast fading environment.
There are many related works that jointly model the computing mode decision problem and resource allocation problem in MEC networks as the MIP problems. For instance, @cite_22 proposed a coordinate descent (CD) method that searches along one variable dimension at a time. @cite_23 studies a similar heuristic search method for multi-server MEC networks, which iteratively adjusts binary offloading decisions. Another widely adopted heuristic is through convex relaxation, e.g., by relaxing integer variables to be continuous between @math and @math @cite_6 or by approximating the binary constraints with quadratic constraints @cite_27 . Nonetheless, on one hand, the solution quality of the reduced-complexity heuristics is not guaranteed. On the other hand, both search-based and convex relaxation methods require considerable number of iterations to reach a satisfying local optimum and are inapplicable for fast fading channels.
@cite_27 @cite_22 @cite_23 @cite_6
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One central issue in practically deploying network coding is the adaptive and economic allocation of network resource. We cast this as an optimization, where the net-utility-the difference between a utility derived from the attainable multicast throughput and the total cost of resource provisioning-is maximized. By employing the MAX of flows characterization of the admissible rate region for multicasting, this paper gives a novel reformulation of the optimization problem, which has a separable structure. The Lagrangian relaxation method is applied to decompose the problem into subproblems involving one destination each. Our specific formulation of the primal problem results in two key properties. First, the resulting subproblem after decomposition amounts to the problem of finding a shortest path from the source to each destination. Second, assuming the net-utility function is strictly concave, our proposed method enables a near-optimal primal variable to be uniquely recovered from a near-optimal dual variable. A numerical robustness analysis of the primal recovery method is also conducted. For ill-conditioned problems that arise, for instance, when the cost functions are linear, we propose to use the proximal method, which solves a sequence of well-conditioned problems obtained from the original problem by adding quadratic regularization terms. Furthermore, the simulation results confirm the numerical robustness of the proposed algorithms. Finally, the proximal method and the dual subgradient method can be naturally extended to provide an effective solution for applications with multiple multicast sessions Designing mobile edge computing (MEC) systems by jointly optimizing communication and computation resources, which can help increase mobile batteries' lifetime and improve quality of experience for computation-intensive and latency-sensitive applications, has received significant interest. In this paper, we consider energy-efficient resource allocation schemes for a multi-user mobile edge computing system with inelastic computation tasks and non-negligible task execution durations. First, we establish a mathematical model to characterize the offloading of a computation task from a mobile to the base station (BS) equipped with MEC servers. This computation-offloading model consists of three stages, i.e., task uploading, task executing, and computation result downloading, and allows parallel transmissions and executions for different tasks. Then, we formulate the weighted sum energy consumption minimization problem to optimally allocate the task operation sequence, the uploading and downloading time durations as well as the starting times for uploading, executing and downloading, which is a challenging mixed discrete- continuous optimization problem and is NP-hard in general. We propose a method to obtain an optimal solution and develop a low-complexity algorithm to obtain a suboptimal solution, by connecting the optimization problem to a three-stage flow-shop scheduling problem and utilizing Johnson's algorithm as well as convex optimization techniques. Finally, numerical results show that the proposed sub-optimal solution outperforms existing comparison schemes. Abstract The problem of locating hub facilities and allocating non-hub nodes to those hubs arises frequently in the design of communication networks, airline passenger flow and parcel delivery networks. In this paper we consider uncapacitated multiple and single allocation p -hub median problems. We develop new mixed 0 1 linear formulations with tight linear programming relaxations. The approach is tested on a well known and heavily used benchmark data set of real-world problems with resulting LP relaxations ranging from 10010 to 391 250 variables and from 2 101 to 31 901 constraints, which proved to be difficult linear programs. Yet, this approach proved to be very effective: in almost all instances the linear programming solution was integer. In cases with fractional solutions, the integrality was achieved by adding a small partial set of integrality constraints. Therefore, we extended the range of optimally solvable instances of these NP-hard hub location problems, which have defied researchers for the last ten years. As an additional result for the single allocation case we were able to establish optimality of all heuristic solutions obtained via tabu search algorithm from a previous study. For the more difficult single allocation p -hub median problem we also used the best known heuristic solution as a guidance in adding integrality constraints. This novel linkage between optimal and heuristic solutions has a potential impact in a number of other problem settings, where efficient heuristic solutions exist and are probably, but not provably optimal. We develop a mathematical programming approach for the classicalPSPACE-hard restless bandit problem in stochastic optimization. We introduce a hierarchy ofN (whereN is the number of bandits) increasingly stronger linear programming relaxations, the last of which is exact and corresponds to the (exponential size) formulation of the problem as a Markov decision chain, while the other relaxations provide bounds and are efficiently computed. We also propose a priority-index heuristic scheduling policy from the solution to the firstorder relaxation, where the indices are defined in terms of optimal dual variables. In this way we propose a policy and a suboptimality guarantee. We report results of computational experiments that suggest that the proposed heuristic policy is nearly optimal. Moreover, the second-order relaxation is found to provide strong bounds on the optimal value.