Person-Based Optimization of Signal Timing

2017 ◽  
Vol 2620 (1) ◽  
pp. 31-42 ◽  
Author(s):  
Zhengyao Yu ◽  
Vikash V. Gayah ◽  
Eleni Christofa
Keyword(s):  
Robust Optimization ◽  
Signal Timing ◽  
Optimization Approach ◽  
Optimization Strategy ◽  
Passenger Cars ◽  
Case Scenario ◽  
Worst Case ◽  
Arrival Times ◽  
Cycle Lengths ◽  
Traffic Signal Timing

Recent studies have proposed the use of person-based frameworks for the optimization of traffic signal timing to minimize the total passenger delay experienced by passenger cars and buses at signalized intersections. The efficiency and applicability of existing efforts, however, have been limited by an assumption of fixed cycle lengths and deterministic bus arrival times. An existing algorithm for person-based optimization of signal timing for isolated intersections was extended to accommodate flexible cycle lengths and uncertain bus arrival times. To accommodate flexible cycle lengths, the mathematical program was redefined to minimize total passenger delay within a fixed planning horizon that allowed cycle lengths to vary within a feasible range. Two strategies were proposed to accommodate uncertain bus arrival times: ( a) a robust optimization approach that conservatively minimized delays experienced in a worst-case scenario and ( b) a blended strategy that combined deterministic optimization and rule-based green extensions. The proposed strategies were tested with numerical simulations of an intersection in State College, Pennsylvania. Results revealed that the flexible cycle length algorithm could significantly reduce bus passenger delay and total passenger delay, with negligible increases in car passenger delay. These results were robust to changes in both bus and car flows. For bus arrival times, the robust optimization strategy seemed to be more effective at low levels of uncertainty and the blended strategy at higher levels of uncertainty. The anticipated benefits decreased with increases in the intersection flow ratio because of the lower flexibility of signal timing at the intersection.

Risk-Based Robust Bidding Strategies for EVs’ Aggregators in Day-ahead Markets with Uncertainty

2020 ◽  
Author(s):  
Ahmed Abdelmoaty ◽  
Wessam Mesbah ◽  
Mohammad A. M. Abdel-Aal ◽  
Ali T. Alawami
Keyword(s):  
Robust Optimization ◽  
Electricity Market ◽  
Real Life ◽  
Optimization Approach ◽  
Case Scenario ◽  
Worst Case ◽  
Bidding Strategies ◽  
Wind Generators ◽  
Proposed Model ◽  
Optimal Bidding

In the recent electricity market framework, the profit of the generation companies depends on the decision of the operator on the schedule of its units, the energy price, and the optimal bidding strategies. Due to the expanded integration of uncertain renewable generators which is highly intermittent such as wind plants, the coordination with other facilities to mitigate the risks of imbalances is mandatory. Accordingly, coordination of wind generators with the evolutionary Electric Vehicles (EVs) is expected to boost the performance of the grid. In this paper, we propose a robust optimization approach for the coordination between the wind-thermal generators and the EVs in a virtual<br>power plant (VPP) environment. The objective of maximizing the profit of the VPP Operator (VPPO) is studied. The optimal bidding strategy of the VPPO in the day-ahead market under uncertainties of wind power, energy<br>prices, imbalance prices, and demand is obtained for the worst case scenario. A case study is conducted to assess the e?effectiveness of the proposed model in terms of the VPPO's profit. A comparison between the proposed model and the scenario-based optimization was introduced. Our results confirmed that, although the conservative behavior of the worst-case robust optimization model, it helps the decision maker from the fluctuations of the uncertain parameters involved in the production and bidding processes. In addition, robust optimization is a more tractable problem and does not suffer from<br>the high computation burden associated with scenario-based stochastic programming. This makes it more practical for real-life scenarios.<br>

scholarly journals Risk-Based Robust Bidding Strategies for EVs’ Aggregators in Day-ahead Markets with Uncertainty

2020 ◽  
Author(s):  
Ahmed Abdelmoaty ◽  
Wessam Mesbah ◽  
Mohammad A. M. Abdel-Aal ◽  
Ali T. Alawami
Keyword(s):  
Robust Optimization ◽  
Electricity Market ◽  
Real Life ◽  
Optimization Approach ◽  
Case Scenario ◽  
Worst Case ◽  
Bidding Strategies ◽  
Wind Generators ◽  
Proposed Model ◽  
Optimal Bidding

In the recent electricity market framework, the profit of the generation companies depends on the decision of the operator on the schedule of its units, the energy price, and the optimal bidding strategies. Due to the expanded integration of uncertain renewable generators which is highly intermittent such as wind plants, the coordination with other facilities to mitigate the risks of imbalances is mandatory. Accordingly, coordination of wind generators with the evolutionary Electric Vehicles (EVs) is expected to boost the performance of the grid. In this paper, we propose a robust optimization approach for the coordination between the wind-thermal generators and the EVs in a virtual<br>power plant (VPP) environment. The objective of maximizing the profit of the VPP Operator (VPPO) is studied. The optimal bidding strategy of the VPPO in the day-ahead market under uncertainties of wind power, energy<br>prices, imbalance prices, and demand is obtained for the worst case scenario. A case study is conducted to assess the e?effectiveness of the proposed model in terms of the VPPO's profit. A comparison between the proposed model and the scenario-based optimization was introduced. Our results confirmed that, although the conservative behavior of the worst-case robust optimization model, it helps the decision maker from the fluctuations of the uncertain parameters involved in the production and bidding processes. In addition, robust optimization is a more tractable problem and does not suffer from<br>the high computation burden associated with scenario-based stochastic programming. This makes it more practical for real-life scenarios.<br>

Operational Effects of the Consolidated Intersection Design on Urban and Suburban Arterials

2018 ◽  
Vol 2672 (17) ◽  
pp. 96-107
Author(s):  
Daniel J. Cook
Keyword(s):  
Travel Time ◽  
Signalized Intersections ◽  
Signal Timing ◽  
Left Turn ◽  
Vehicle Delay ◽  
Cycle Lengths ◽  
Expected Benefits ◽  
Traffic Signal Timing ◽  
Critical Phases ◽  
Pedestrian Crossing

Along urban and suburban arterials, closely-spaced signalized intersections are commonly used to provide access to adjacent commercial developments. Often, these signalized intersections are designed to provide full access to developments on both sides of the arterial and permit through, left-turn, and right-turn movements from every intersection approach. Traffic signal timing is optimized to reduce vehicle delay or provide progression to vehicles on the arterial, or both. However, meeting both of these criteria can be cumbersome, if not impossible, under high-demand situations. This research proposes a new design that consolidates common movements at three consecutive signalized intersections into strategic fixed locations along the arterial. The consolidation of common movements allows the intersections to cycle between only two critical phases, which, in turn, promotes shorter cycle lengths, lower delay, and better progression. This research tested the consolidated intersection concept by modeling a real-world site in microsimulation software and obtaining values for delay and travel time for multiple vehicle paths along the corridor and adjacent commercial developments in both existing and proposed conditions. With the exception of unsignalized right turns at the periphery of the study area, all non-displaced routes showed a reduction in travel time and delay. Additional research is needed to understand how additional travel through the commercial developments adjacent to the arterial may effect travel time and delay. Other expected benefits of the proposed design include a major reduction in conflict points, shorter pedestrian crossing and wait times, and the opportunity to provide pedestrian refuge areas in the median.

Comparison of Planning and Operational Analysis Procedures for Signalized Intersections from the Highway Capacity Manual

1996 ◽  
Vol 1555 (1) ◽  
pp. 59-64
Author(s):  
Mark R. Virkler ◽  
Shashi Gannavaram ◽  
Anand Ramabhadran
Keyword(s):  
Level Of Service ◽  
Signal Timing ◽  
Highway Capacity ◽  
Operational Procedure ◽  
Highway Capacity Manual ◽  
Operational Analysis ◽  
Planning Procedure ◽  
Adjustment Factors ◽  
Cycle Lengths ◽  
Traffic Signal Timing

The 1994 update of the Highway Capacity Manual (HCM) includes a planning procedure to estimate the capacity condition of a signalized intersection (Xcm). The planning method results can also be extended to a planning application of the more data-intensive HCM operational procedure to estimate intersection critical flow-to-capacity ratio (Xc) and level of service with only planning-level data. Both the planning procedure and the planning application of the operational procedure involve default adjustment factors and synthesized traffic signal timing (called the “default signal timing”). Data from 166 Missouri intersections were used to determine how well the planning approaches predict operational analysis results. In general, the default signal timings had shorter cycle lengths than the timing plans used at pretimed signals. The shorter cycle lengths led to slightly higher flow-to-capacity ratios, since a higher proportion of each cycle was devoted to lost time. The default signal timings also had more equal flow-to-capacity ratios within critical lane groups. The shorter cycle lengths and more equal flow-to-capacity ratios led to a predicted level of service that was the same or better than that calculated for actual conditions. For the subject intersections, locally calibrated default adjustment factors yielded better predictions of flow-to-capacity ratios and level of service than the HCM defaults. The planning value for Xcm was often less than the actual Xc for operational analysis of actual conditions. This was to be expected since Xcm is based on the maximum allowable cycle length. The HCM planning procedure is expected to receive wide use in a variety of planning and design applications. Calibration of appropriate local default values should improve the accuracy of the planning procedure results.

scholarly journals Robust Optimization Approach to Process Flexibility Designs with Contribution Margin Differentials

2020 ◽  
Author(s):  
Shixin Wang ◽  
Xuan Wang ◽  
Jiawei Zhang
Keyword(s):  
Robust Optimization ◽  
Performance Measures ◽  
Broad Class ◽  
Problem Definition ◽  
Partial Ordering ◽  
Group Index ◽  
Optimization Approach ◽  
Worst Case ◽  
Process Flexibility ◽  
Long Chain

Problem definition: The theoretical investigation of the effectiveness of limited flexibility has mainly focused on a performance metric that is based on the maximum sales in units. However, this could lead to substantial profit losses when the maximum sales metric is used to guide flexibility designs while the products have considerably large profit margin differences. Academic/practical relevance: We address this issue by introducing margin differentials into the analysis of process flexibility designs, and our results can provide useful guidelines for the evaluation and design of flexibility configurations when the products have heterogeneous margins. Methodology: We adopt a robust optimization framework and study process flexibility designs from the worst-case perspective by introducing the dual margin group index (DMGI). Results and managerial implications: We show that a general class of worst-case performance measures can be expressed as functions of a design’s DMGIs and the given uncertainty set. Moreover, the DMGIs lead to a partial ordering that enables us to compare the worst-case performance of different designs. Applying these results, we prove that under the so-called partwise independently symmetric uncertainty sets and a broad class of worst-case performance measures, the alternate long-chain design is optimal among all long-chain designs with equal numbers of high-profit products and low-profit products. Finally, we develop a heuristic based on the DMGIs to generate effective flexibility designs when products exhibit margin differentials.

Feasibility Robust Optimization via Scenario Generation and Reduction

2018 ◽  
Author(s):  
Eliot Rudnick-Cohen ◽  
Jeffrey W. Herrmann ◽  
Shapour Azarm
Keyword(s):  
Robust Optimization ◽  
Optimization Problems ◽  
Computational Cost ◽  
Optimization Techniques ◽  
Scenario Generation ◽  
Test Problems ◽  
Optimization Approach ◽  
Uncertain Parameters ◽  
Worst Case ◽  
Robust Solution

Feasibility robust optimization techniques solve optimization problems with uncertain parameters that appear only in their constraint functions. Solving such problems requires finding an optimal solution that is feasible for all realizations of the uncertain parameters. This paper presents a new feasibility robust optimization approach involving uncertain parameters defined on continuous domains without any known probability distributions. The proposed approach integrates a new sampling-based scenario generation scheme with a new scenario reduction approach in order to solve feasibility robust optimization problems. An analysis of the computational cost of the proposed approach was performed to provide worst case bounds on its computational cost. The new proposed approach was applied to three test problems and compared against other scenario-based robust optimization approaches. A test was conducted on one of the test problems to demonstrate that the computational cost of the proposed approach does not significantly increase as additional uncertain parameters are introduced. The results show that the proposed approach converges to a robust solution faster than conventional robust optimization approaches that discretize the uncertain parameters.

A Robust Data-Driven Approach for the Newsvendor Problem with Nonparametric Information

2021 ◽  
Author(s):  
Liang Xu ◽  
Yi Zheng ◽  
Li Jiang
Keyword(s):  
Robust Optimization ◽  
Real Data ◽  
Newsvendor Problem ◽  
Problem Definition ◽  
Data Driven ◽  
Optimization Approach ◽  
Worst Case ◽  
Demand Distribution ◽  
Robust Decisions ◽  
True Distribution

Problem definition: For the standard newsvendor problem with an unknown demand distribution, we develop an approach that uses data input to construct a distribution ambiguity set with the nonparametric characteristics of the true distribution, and we use it to make robust decisions. Academic/practical relevance: Empirical approach relies on historical data to estimate the true distribution. Although the estimated distribution converges to the true distribution, its performance with limited data is not guaranteed. Our approach generates robust decisions from a distribution ambiguity set that is constructed by data-driven estimators for nonparametric characteristics and includes the true distribution with the desired probability. It fits situations where data size is small. Methodology: We apply a robust optimization approach with nonparametric information. Results: Under a fixed method to partition the support of the demand, we construct a distribution ambiguity set, build a protection curve as a proxy for the worst-case distribution in the set, and use it to obtain a robust stocking quantity in closed form. Implementation-wise, we develop an adaptive method to continuously feed data to update partitions with a prespecified confidence level in their unbiasedness and adjust the protection curve to obtain robust decisions. We theoretically and experimentally compare the proposed approach with existing approaches. Managerial implications: Our nonparametric approach under adaptive partitioning guarantees that the realized average profit exceeds the worst-case expected profit with a high probability. Using real data sets from Kaggle.com, it can outperform existing approaches in yielding profit rate and stabilizing the generated profits, and the advantages are more prominent as the service ratio decreases. Nonparametric information is more valuable than parametric information in profit generation provided that the service requirement is not too high. Moreover, our proposed approach provides a means of combining nonparametric and parametric information in a robust optimization framework.

A Unified Classification Model Based on Robust Optimization

2013 ◽  
Vol 25 (3) ◽  
pp. 759-804 ◽  
Author(s):  
Akiko Takeda ◽  
Hiroyuki Mitsugi ◽  
Takafumi Kanamori
Keyword(s):  
Robust Optimization ◽  
Unified Model ◽  
Machine Learning Algorithms ◽  
Classification Model ◽  
Support Vector ◽  
Optimization Approach ◽  
Statistical Interpretation ◽  
Fisher Discriminant Analysis ◽  
Learning Methods ◽  
Worst Case

A wide variety of machine learning algorithms such as the support vector machine (SVM), minimax probability machine (MPM), and Fisher discriminant analysis (FDA) exist for binary classification. The purpose of this letter is to provide a unified classification model that includes these models through a robust optimization approach. This unified model has several benefits. One is that the extensions and improvements intended for SVMs become applicable to MPM and FDA, and vice versa. For example, we can obtain nonconvex variants of MPM and FDA by mimicking Perez-Cruz, Weston, Hermann, and Schölkopf's ( 2003 ) extension from convex ν-SVM to nonconvex Eν-SVM. Another benefit is to provide theoretical results concerning these learning methods at once by dealing with the unified model. We give a statistical interpretation of the unified classification model and prove that the model is a good approximation for the worst-case minimization of an expected loss with respect to the uncertain probability distribution. We also propose a nonconvex optimization algorithm that can be applied to nonconvex variants of existing learning methods and show promising numerical results.

scholarly journals Non-Convex Feasibility Robust Optimization Via Scenario Generation and Local Refinement

2019 ◽  
Vol 142 (5) ◽  
Author(s):  
Eliot Rudnick-Cohen ◽  
Jeffrey W. Herrmann ◽  
Shapour Azarm
Keyword(s):  
Robust Optimization ◽  
Optimization Problems ◽  
Computational Cost ◽  
Optimal Solution ◽  
Optimization Techniques ◽  
Scenario Generation ◽  
Test Problems ◽  
Optimization Approach ◽  
Uncertain Parameters ◽  
Worst Case

Abstract Feasibility robust optimization techniques solve optimization problems with uncertain parameters that appear only in their constraint functions. Solving such problems requires finding an optimal solution that is feasible for all realizations of the uncertain parameters. This paper presents a new feasibility robust optimization approach involving uncertain parameters defined on continuous domains. The proposed approach is based on an integration of two techniques: (i) a sampling-based scenario generation scheme and (ii) a local robust optimization approach. An analysis of the computational cost of this integrated approach is performed to provide worst-case bounds on its computational cost. The proposed approach is applied to several non-convex engineering test problems and compared against two existing robust optimization approaches. The results show that the proposed approach can efficiently find a robust optimal solution across the test problems, even when existing methods for non-convex robust optimization are unable to find a robust optimal solution. A scalable test problem is solved by the approach, demonstrating that its computational cost scales with problem size as predicted by an analysis of the worst-case computational cost bounds.

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