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Register a new userLarge-Scale Traffic Signal Offset Optimization
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Added by
Richard Zhang
Publication date
2019
fields
Informatics Engineering
and research's language is
English
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The offset optimization problem seeks to coordinate and synchronize the timing of traffic signals throughout a network in order to enhance traffic flow and reduce stops and delays. Recently, offset optimization was formulated into a continuous optimization problem without integer variables by modeling traffic flow as sinusoidal. In this paper, we present a novel algorithm to solve this new formulation to near-global optimality on a large-scale. Specifically, we solve a convex relaxation of the nonconvex problem using a tree decomposition reduction, and use randomized rounding to recover a near-global solution. We prove that the algorithm always delivers solutions of expected value at least 0.785 times the globally optimal value. Moreover, assuming that the topology of the traffic network is tree-like, we prove that the algorithm has near-linear time complexity with respect to the number of intersections. These theoretical guarantees are experimentally validated on the Berkeley, Manhattan, and Los Angeles traffic networks. In our numerical results, the empirical time complexity of the algorithm is linear, and the solutions have objectives within 0.99 times the globally optimal value.
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Bayesian hybrid models fuse physics-based insights with machine learning constructs to correct for systematic bias. In this paper, we compare Bayesian hybrid models against physics-based glass-box and Gaussian process black-box surrogate models. We consider ballistic firing as an illustrative case study for a Bayesian decision-making workflow. First, Bayesian calibration is performed to estimate model parameters. We then use the posterior distribution from Bayesian analysis to compute optimal firing conditions to hit a target via a single-stage stochastic program. The case study demonstrates the ability of Bayesian hybrid models to overcome systematic bias from missing physics with less data than the pure machine learning approach. Ultimately, we argue Bayesian hybrid models are an emerging paradigm for data-informed decision-making under parametric and epistemic uncertainty.
The basic reproduction number $R_0$ is a fundamental quantity in epidemiological modeling, reflecting the typical number of secondary infections that arise from a single infected individual. While $R_0$ is widely known to scientists, policymakers, and the general public, it has received comparatively little attention in the controls community. This note provides two novel characterizations of $R_0$: a stability characterization and a geometric program characterization. The geometric program characterization allows us to write $R_0$-constrained and budget-constrained optimal resource allocation problems as geometric programs, which are easily transformed into convex optimization problems. We apply these programs to a case study of allocating vaccines and antidotes, finding that targeting $R_0$ instead of the spectral abscissa of the Jacobian matrix (a common target in the controls literature) leads to qualitatively different solutions.
This paper studies the distributed optimization problem where the objective functions might be nondifferentiable and subject to heterogeneous set constraints. Unlike existing subgradient methods, we focus on the case when the exact subgradients of the local objective functions can not be accessed by the agents. To solve this problem, we propose a projected primal-dual dynamics using only the objective functions approximate subgradients. We first prove that the formulated optimization problem can only be solved with an approximate error depending upon the accuracy of the available subgradients. Then, we show the exact solvability of this optimization problem if the accumulated approximation error is not too large. After that, we also give a novel componentwise normalized variant to improve the transient behavior of the convergent sequence. The effectiveness of our algorithms is verified by a numerical example.
The wake effect is one of the leading causes of energy losses in offshore wind farms (WFs). Both turbine placement and cooperative control can influence the wake interactions inside the WF and thus the overall WF power production. Traditionally, greedy control strategy is assumed in the layout design phase. To exploit the potential synergy between the WF layout and control so that a system-level optimal layout can be obtained with the greatest energy yields, the layout optimization should be performed with cooperative control considerations. For this purpose, a novel two-stage WF layout optimization model is developed in this paper. Cooperative WF control of both turbine yaw and axis-induction are considered. However, the integration of WF control makes the layout optimization much more complicated and results in a large-scale nonconvex problem, hindering the application of current layout optimization methods. To increase the computational efficiency, we leverage the hierarchy and decomposability of the joint optimization problem and design a decomposition-based hybrid method (DBHM). Case studies are carried out on different WFs. It is shown that WF layouts with higher energy yields can be obtained by the proposed joint optimization compared to traditional separate layout optimization. Moreover, the computational advantages of the proposed DBHM on the considered joint layout optimization problem are also demonstrated.
Optimization in distributed networks plays a central role in almost all distributed machine learning problems. In principle, the use of distributed task allocation has reduced the computational time, allowing better response rates and higher data reliability. However, for these computational algorithms to run effectively in complex distributed systems, the algorithms ought to compensate for communication asynchrony, network node failures and delays known as stragglers. These issues can change the effective connection topology of the network, which may vary over time, thus hindering the optimization process. In this paper, we propose a new distributed unconstrained optimization algorithm for minimizing a convex function which is adaptable to a parameter server network. In particular, the network worker nodes solve their local optimization problems, allowing the computation of their local coded gradients, which will be sent to different server nodes. Then within this parameter server platform each server node aggregates its communicated local gradients, allowing convergence to the desired optimizer. This algorithm is robust to network s worker node failures, disconnection, or delaying nodes known as stragglers. One way to overcome the straggler problem is to allow coding over the network. We further extend this coding framework to enhance the convergence of the proposed algorithm under such varying network topologies. By using coding and utilizing evaluations of gradients of uniformly bounded delay we further enhance the proposed algorithm performance. Finally, we implement the proposed scheme in MATLAB and provide comparative results demonstrating the effectiveness of the proposed framework
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