With the emergence of ride-sharing companies that offer transportation on demand at a large scale and the increasing availability of corresponding demand data sets, new challenges arise to develop ...routing optimization algorithms that can solve massive problems in real time. In “Online Vehicle Routing: The Edge of Optimization in Large-Scale Applications,” D. Bertsimas, P. Jaillet, and S. Martin present a novel and generalizable backbone algorithm that uses integer optimization to find high-quality solutions to large routing optimization problems. The algorithm, together with the real-time routing optimization software framework developed and shared by the authors, can dispatch thousands of taxis serving more than 25,000 customers per hour. An extensive study with historical simulations of Yellow Cabs in New York City is used to both show that the algorithm improves on the performance of existing heuristics and to provide insights on the optimization opportunities of a large ride-sharing fleet.
With the emergence of ride-sharing companies that offer transportation on demand at a large scale and the increasing availability of corresponding demand data sets, new challenges arise to develop routing optimization algorithms that can solve massive problems in real time. In this paper, we develop an optimization framework, coupled with a novel and generalizable backbone algorithm, that allows us to dispatch in real time thousands of taxis serving more than 25,000 customers per hour. We provide evidence from historical simulations using New York City routing network and yellow cab data to show that our algorithms improve upon the performance of existing heuristics in such real-world settings.
The online supplement is available at
https://doi.org/10.1287/opre.2018.1763
.
We consider the question of variable selection in linear regressions, in the sense of identifying the correct direct predictors (those variables that have nonzero coefficients given all candidate ...predictors). Best subset selection (BSS) is often considered the “gold standard,” with its use being restricted only by its NP‐hard nature. Alternatives such as the least absolute shrinkage and selection operator (Lasso) or the Elastic net (Enet) have become methods of choice in high‐dimensional settings. A recent proposal represents BSS as a mixed‐integer optimization problem so that large problems have become computationally feasible. We present an extensive neutral comparison assessing the ability to select the correct direct predictors of BSS compared to forward stepwise selection (FSS), Lasso, and Enet. The simulation considers a range of settings that are challenging regarding dimensionality (number of observations and variables), signal‐to‐noise ratios, and correlations between predictors. As fair measure of performance, we primarily used the best possible F1‐score for each method, and results were confirmed by alternative performance measures and practical criteria for choosing the tuning parameters and subset sizes. Surprisingly, it was only in settings where the signal‐to‐noise ratio was high and the variables were uncorrelated that BSS reliably outperformed the other methods, even in low‐dimensional settings. Furthermore, FSS performed almost identically to BSS. Our results shed new light on the usual presumption of BSS being, in principle, the best choice for selecting the correct direct predictors. Especially for correlated variables, alternatives like Enet are faster and appear to perform better in practical settings.
The complexity of geometric scaling Deza, Antoine; Pokutta, Sebastian; Pournin, Lionel
Operations research letters,
January 2024, 2024-01-00, Volume:
52
Journal Article
Peer reviewed
Open access
Geometric scaling, introduced by Schulz and Weismantel in 2002, solves the integer optimization problem max{c⋅x:x∈P∩Zn} by means of primal augmentations, where P⊂Rn is a polytope. We restrict ...ourselves to the important case when P is a 0/1-polytope. Schulz and Weismantel showed that no more than O(nlog2n‖c‖∞) calls to an augmentation oracle are required. This upper bound can be improved to O(nlog2‖c‖∞) using the early-stopping policy proposed in 2018 by Le Bodic, Pavelka, Pfetsch, and Pokutta. Considering both the maximum ratio augmentation variant of the method as well as its approximate version, we show that these upper bounds are essentially tight by maximizing over a n-dimensional simplex with vectors c such that ‖c‖∞ is either n or 2n.
This paper proposes an integrated framework for wind farm maintenance that combines i) predictive analytics methodology that uses real-time sensor data to predict future degradation and remaining ...lifetime of wind turbines, with ii) a novel optimization model that transforms these predictions into profit-optimal maintenance and operational decisions for wind farms. To date, most applications of predictive analytics focus on single turbine systems. In contrast, this paper provides a seamless integration of the predictive analytics with decision making for a fleet of wind turbines. Operational decisions identify the dispatch profiles. Maintenance decisions consider the tradeoff between sensor-driven optimal maintenance schedule, and the significant cost reductions arising from grouping the wind turbine maintenances together-a concept called opportunistic maintenance. We focus on two types of wind turbines. For the operational wind turbines, we find an optimal fleet-level condition-based maintenance schedule driven by the sensor data. For the failed wind turbines, we identify the optimal time to conduct corrective maintenance to start producing electricity. The economic and stochastic dependence between operations and maintenance decisions are also considered. Experiments conducted on i) a 100-turbine wind farm case, and ii) a 200-turbine multiple wind farms case demonstrate the advantages of our proposal over traditional policies.
•The optimal sizing and allocation problem of DG’s is formulated as a MINLP mixed integer nonlinear programming.•The stability index is calculated based on Thevenin.•The DGs are considered with ...different power factor to show the effect of reactive power capability of DGs on optimal allocation and sizing problem.•Comparative results show that proposed is better than the other methods.
The applications of Distributed Generation (DG) play a significant role to provide the benefit to conventional distribution systems. However, the sizing and location of these DG units should be taken into consideration to get maximum gain and benefit. If DGs are not located and sized properly, the distribution system can be adversely affected. So, optimal allocation and sizing are needed to avoid instability problems and more costs to increase the efficiency and quality of energy in distribution systems. This paper addresses the optimal sizing and allocation of DGs for power losses, voltage profile and stability improvement, introducing a proposed stability index based on Thevenin impedance in a distribution network. The stability index is calculated by the proposed approach based on Thevenin. Thevenin is obtained based on a two-bus system by reduction of more than two bus systems. The optimal sizing and location of DGs are also obtained by operating DGs under different power factors. The reactive capability of DGs is also shown by simulations with DGs operated under different power factors. The problem of optimal sizing and location of DGs, which is a nonlinear optimization problem with discrete and continuous variables, is solved based on the mixed integer Genetic Algorithm (GA). Also, the proposed approach is verified by using Grey Wolf Optimization (GWO) method. The problem contains multi-objectives with three objective functions: system power losses, voltage deviation and the Thevenin based stability index. The proposed approach has been tested on the IEEE-69 and 118-bus test system to demonstrate its effectiveness. The comparison with some other methods shows that the proposed approach gives better results than other methods while reducing the power losses and improving voltage and system stability in all suggested scenarios by finding the optimal placement and sizing of DG units. It is also shown that the reduction in power loss, voltage and stability improvements are increased more by using the reactive power capability of DGs. The results show that optimum located and sized DGs not only decreases the power loss, but also improve the voltage profile and stability of the system.
In this article, sparse nonnegative matrix factorization (SNMF) is formulated as a mixed-integer bicriteria optimization problem for minimizing matrix factorization errors and maximizing factorized ...matrix sparsity based on an exact binary representation of <inline-formula> <tex-math notation="LaTeX">l_{0} </tex-math></inline-formula> matrix norm. The binary constraints of the problem are then equivalently replaced with bilinear constraints to convert the problem to a biconvex problem. The reformulated biconvex problem is finally solved by using a two-timescale duplex neurodynamic approach consisting of two recurrent neural networks (RNNs) operating collaboratively at two timescales. A Gaussian score (GS) is defined as to integrate the bicriteria of factorization errors and sparsity of resulting matrices. The performance of the proposed neurodynamic approach is substantiated in terms of low factorization errors, high sparsity, and high GS on four benchmark datasets.
•Discusses dearth of efficient multiyear optimization approaches in literature.•Uses historic and forecasted data to show need for multiyear optimization approach.•Introduces novel and fast multiyear ...optimization approach.•Compares with standard literature approaches, showcasing significant time savings.•Discusses impact of forecasting error on the approaches.
With energy systems, the problem of economic planning is decisive in the design of a low carbon and resilient future grid. Although several tools to solve the problem already exist in literature and industry, most tools only consider a single “typical year” while providing investment decisions that last around a quarter of a century. In this paper, we introduce why such an approach is limited and derive two approaches to correct this. The first approach, the Forward-Looking model, assumes perfect knowledge and makes investment decisions based on the full planning horizon. The second novel approach, the Adaptive method, solves the optimization problem in single year iterations, making incremental investment decisions that are dependant on previous years, with only knowledge of the current year. Comparing the two approaches on a realistic microgrid, we find little difference in investment decisions (maximum 21% difference in total cost over 20 years), but large differences in optimization time (up to 12000% time difference). We close the paper by discussing implications of forecasting errors on the microgrid planning process, concluding that the Adaptive approach is a suitable choice.
Today’s automotive factories are essentially assembly plants that receive parts from a vast network of suppliers around the world. Transporting thousands of part types over very long distances is a ...major logistic problem whose solution is a critical factor in the factory management. In this study we have developed a statistical and optimization methodology implemented in a software tool to help the decision makers select the most appropriate container for each part. A key element is to determine the number of parts that fit in a given container. Two optimization procedures have been developed, depending on the type of part, and used to calculate costs of each container. These costs include not only transporting parts from supplier to factory, but also the costs of handling parts within the factory and returning the empty containers to the supplier.
•Selection of optimal container for parts transport from suppliers to assembly plant.•A new method estimates the number of parts in a container when loaded in bulk.•An algorithm optimizes parts in a container via strategic placement, not bulk loading.•Software integrates databases, geometry, optimization, learning and economic analysis.•The software, validated in the real world, is used by a major vehicle manufacturer.
We address the European natural gas supply chain with several tiers, including producers, mid-streamers, and consumers, where natural gas and Liquefied Natural Gas (LNG) could be traded via long-term ...contracts or spot markets. This network problem is formulated as a non-linear mixed-integer programming model which provides the optimal production and export decisions of producers, import and storage decisions of mid-streamers, and infrastructure investment decisions of European Union (EU) countries with respect to new pipelines and LNG regasification terminals that maximize the total social welfare in the EU natural gas market over a five-year horizon. We conduct several case studies to examine this network under different conditions. We first compare the actual and optimal decisions to provide insights. Then, we examine the effect of infrastructure decisions on social welfare. Our results reveal that new infrastructure investments increase the total social welfare by nearly three billion. In addition, we examine its sensitivity to the exclusion of Russian gas supply from the market with and without the infrastructure decisions. Results suggest that if Russian gas supply is excluded from the market, then the social welfare and cumulative natural gas consumption of 26 EU countries decrease by 10% and 15%, respectively and that considering infrastructure investments on LNG terminals and pipelines would reduce supply risk of consumer countries.
•This paper addresses the European natural gas supply chain with several tiers.•An optimization model is proposed to obtain investment and transportation decisions.•Optimal decisions increase the social welfare by nearly three billion.•Excluding Russia decreases the social welfare by 10% for the next five years.
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