We seek the best traffic allocation scheme for the edge-cloud computing
network that satisfies constraints and minimizes the cost based on burstable
billing. First, for a fixed network topology, we formulate a family of integer
programming problems with random parameters describing the various traffic
demands. Then, to overcome the difficulty caused by the discrete feature of the
problem, we generalize the Gumbel-softmax reparameterization method to induce
an unconstrained continuous optimization problem as a regularized continuation
of the discrete problem. Finally, we introduce the Gumbel-softmax sampling
network to solve the optimization problems via unsupervised learning. The
network structure reflects the edge-cloud computing topology and is trained to
minimize the expectation of the cost function for unconstrained continuous
optimization problems. The trained network works as an efficient traffic
allocation scheme sampler, remarkably outperforming the random strategy in
feasibility and cost function value. Besides testing the quality of the output
allocation scheme, we examine the generalization property of the network by
increasing the time steps and the number of users. We also feed the solution to
existing integer optimization solvers as initial conditions and verify the
warm-starts can accelerate the short-time iteration process. The framework is
general with solid performance, and the decoupled feature of the random neural
networks is adequate for practical implementations.

本研究提出了一种基于 Gumbel-softmax 重参数化方法的边缘 - 云计算网络最佳流量分配方案的求解方法，可通过无监督学习训练出 Gumbel-softmax 采样网络来解决离散优化问题，并且该方法适用于波动性计费且在可行性和成本函数价值方面都表现出优异的性能。

基于神经网络的边缘云计算分位数优化

Neural Quantile Optimization for Edge-Cloud Computing

Integer programming problems (IPs) are challenging to be solved efficiently
due to the NP-hardness, especially for large-scale IPs. To solve this type of
IPs, Large neighborhood search (LNS) uses an initial feasible solution and
iteratively improves it by searching a large neighborhood around the current
solution. However, LNS easily steps into local optima and ignores the
correlation between variables to be optimized, leading to compromised
performance. This paper presents a general adaptive constraint partition-based
optimization framework (ACP) for large-scale IPs that can efficiently use any
existing optimization solver as a subroutine. Specifically, ACP first randomly
partitions the constraints into blocks, where the number of blocks is
adaptively adjusted to avoid local optima. Then, ACP uses a subroutine solver
to optimize the decision variables in a randomly selected block of constraints
to enhance the variable correlation. ACP is compared with LNS framework with
different subroutine solvers on four IPs and a real-world IP. The experimental
results demonstrate that in specified wall-clock time ACP shows better
performance than SCIP and Gurobi.

本文提出了一个基于自适应约束分区的优化框架，旨在解决解决大规模整数规划问题时可能会陷入局部最优解的问题。与现有的大邻域搜索算法相比，该框架可以更高效地利用任何现有优化求解器作为子例程来优化决策变量。实验结果表明，该框架在规定的墙钟时间内显示出比 SCIP 和 Gurobi 更好的性能。