Solving the Top-percentile traffic routing problem by Approximate Dynamic Programming

Internet Service Providers (ISPs) have the ability to route their traffic over different network providers. This study investigates the optimal routing strategy under multihoming in the case where network providers charge ISPs according to top-percentile pricing (i.e. based on the ?th highest volume of traffic shipped). We call this problem the Top-percentile Traffic Routing Problem (TpTRP). The TpTRP is a multistage stochastic optimization problem. Routing decision for every time period should be made before knowing the amount of traffic that is to be sent. The stochastic nature of the problem forms the critical difficulty of this study. Solution approaches based on Stochastic Integer Programming or Stochastic Dynamic Programming (SDP) suffer from the curse of dimensionality, which restricts their applicability. To overcome this, we suggest to use Approximate Dynamic Programming, which exploits the structure of the problem to construct continuous approximations of the value functions in SDP. Thus, the curse of dimensionality is largely avoided

Local solutions of the optimal power flow problem

The existence of locally optimal solutions to the AC optimal power flow problem (OPF) has been a question of interest for decades. This paper presents examples of local optima on a variety of test networks including modified versions of common networks. We show that local optima can occur because the feasible region is disconnected and/or because of nonlinearities in the constraints. Standard local optimization techniques are shown to converge to these local optima. The voltage bounds of all the examples in this paper are between ±5% and ±10% off-nominal. The examples with local optima are available in an online archive (http://www.maths.ed.ac.uk/optenergy/LocalOpt/) and can be used to test local or global optimization techniques for OPF. Finally we use our test examples to illustrate the behavior of a recent semi-definite programming approach that aims to find the global solution of OPF

MILP formulation for controlled islanding of power networks

This paper presents a flexible optimization approach to the problem of intentionally forming islands in a power network. A mixed integer linear programming (MILP) formulation is given for the problem of deciding simultaneously on the boundaries of the islands and adjustments to generators, so as to minimize the expected load shed while ensuring no system constraints are violated. The solution of this problem is, within each island, balanced in load and generation and satisfies steady-state DC power flow equations and operating limits. Numerical tests on test networks up to 300 buses show the method is computationally efficient. A subsequent AC optimal load shedding optimization on the islanded network model provides a solution that satisfies AC power flow. Time-domain simulations using second-order models of system dynamics show that if penalties were included in the MILP to discourage disconnecting lines and generators with large flows or outputs, the actions of network splitting and load shedding did not lead to a loss of stability

Optimization-Based Islanding of Power Networks Using Piecewise Linear AC Power Flow

In this paper, a flexible optimization-based framework for intentional islanding is presented. The decision is made of which transmission lines to switch in order to split the network while minimizing disruption, the amount of load shed, or grouping coherent generators. The approach uses a piecewise linear model of AC power flow, which allows the voltage and reactive power to be considered directly when designing the islands. Demonstrations on standard test networks show that solution of the problem provides islands that are balanced in real and reactive power, satisfy AC power flow laws, and have a healthy voltage profile

a multicenter multicohort phase ii study of trastuzumab deruxtecan ds 8201a in subjects with her2 expressing metastatic colorectal cancer

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a multicenter multicohort phase 2 study of trastuzumab deruxtecan ds 8201a in subjects with her2 expressing metastatic colorectal cancer trial in progress

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Combining Survival and Toxicity Effect Sizes from Clinical Trials: NCCTG 89-20-52 (Alliance)

Background: How can a clinician and patient incorporate survival and toxicity information into a single expression of comparative treatment benefit? Sloan et al. recently extended the ½ standard deviation concept for judging the clinical importance of findings from clinical trials to survival and tumor response endpoints. A new method using this approach to combine survival and toxicity effect sizes from clinical trials into a quality-adjusted effect size is presented.Methods: The quality-adjusted survival effect size (QASES) is calculated as survival effect size (ESS) minus the calibrated toxicity effect sizes (EST) (QASES=ESS-EST). This combined effect size can be weighted to adjust for the relative emphasis placed by the patient on survival and toxicity effects.Results: As an example, consider clinical trial NCCTG 89-20-52 which randomized patients to once-daily thoracic radiotherapy (ODTRT) versus twice-daily treatment of thoracic radiotherapy (TDRT) for the treatment of lung cancer. The ODTRT vs. TDRT arms had median survival time of 22 vs. 20 months (p=0.49) and toxicity rate of 39% vs. 54%, (p<0.05). The QASES of 0.18 standard deviations translates to a quality-adjusted survival difference of 5.7 months advantage for the ODRT arm over the TDRT treatment arm (22(16.3) months), p<0.05). Similar results are presented for the four possible case combinations of significant/non-significant survival and toxicity benefits using completed clinical trials.Conclusions: We used a novel approach to re-analyze clinical trial data to produce a single estimate for each treatment that combines survival and toxicity data. The QASES approach is an intuitive and mathematically simple yet robust approach