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Register a new userData Driven VRP: A Neural Network Model to Learn Hidden Preferences for VRP
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Added by
Jayanta Mandi
Publication date
2021
fields
Informatics Engineering
and research's language is
English
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The traditional Capacitated Vehicle Routing Problem (CVRP) minimizes the total distance of the routes under the capacity constraints of the vehicles. But more often, the objective involves multiple criteria including not only the total distance of the tour but also other factors such as travel costs, travel time, and fuel consumption.Moreover, in reality, there are numerous implicit preferences ingrained in the minds of the route planners and the drivers. Drivers, for instance, have familiarity with certain neighborhoods and knowledge of the state of roads, and often consider the best places for rest and lunch breaks. This knowledge is difficult to formulate and balance when operational routing decisions have to be made. This motivates us to learn the implicit preferences from past solutions and to incorporate these learned preferences in the optimization process. These preferences are in the form of arc probabilities, i.e., the more preferred a route is, the higher is the joint probability. The novelty of this work is the use of a neural network model to estimate the arc probabilities, which allows for additional features and automatic parameter estimation. This first requires identifying suitable features, neural architectures and loss functions, taking into account that there is typically few data available. We investigate the difference with a prior weighted Markov counting approach, and study the applicability of neural networks in this setting.
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Data quality is a common problem in machine learning, especially in high-stakes settings such as healthcare. Missing data affects accuracy, calibration, and feature attribution in complex patterns. Developers often train models on carefully curated datasets to minimize missing data bias; however, this reduces the usability of such models in production environments, such as real-time healthcare records. Making machine learning models robust to missing data is therefore crucial for practical application. While some classifiers naturally handle missing data, others, such as deep neural networks, are not designed for unknown values. We propose a novel neural network modification to mitigate the impacts of missing data. The approach is inspired by neuromodulation that is performed by biological neural networks. Our proposal replaces the fixed weights of a fully-connected layer with a function of an additional input (reliability score) at each input, mimicking the ability of cortex to up- and down-weight inputs based on the presence of other data. The modulation function is jointly learned with the main task using a multi-layer perceptron. We tested our modulating fully connected layer on multiple classification, regression, and imputation problems, and it either improved performance or generated comparable performance to conventional neural network architectures concatenating reliability to the inputs. Models with modulating layers were more robust against degradation of data quality by introducing additional missingness at evaluation time. These results suggest that explicitly accounting for reduced information quality with a modulating fully connected layer can enable the deployment of artificial intelligence systems in real-time settings.
In recent years, the prosperity of deep learning has revolutionized the Artificial Neural Networks. However, the dependence of gradients and the offline training mechanism in the learning algorithms prevents the ANN for further improvement. In this study, a gradient-free training framework based on data assimilation is proposed to avoid the calculation of gradients. In data assimilation algorithms, the error covariance between the forecasts and observations is used to optimize the parameters. Feedforward Neural Networks (FNNs) are trained by gradient decent, data assimilation algorithms (Ensemble Kalman Filter (EnKF) and Ensemble Smoother with Multiple Data Assimilation (ESMDA)), respectively. ESMDA trains FNN with pre-defined iterations by updating the parameters using all the available observations which can be regard as offline learning. EnKF optimize FNN when new observation available by updating parameters which can be regard as online learning. Two synthetic cases with the regression of a Sine Function and a Mexican Hat function are assumed to validate the effectiveness of the proposed framework. The Root Mean Square Error (RMSE) and coefficient of determination (R2) are used as criteria to assess the performance of different methods. The results show that the proposed training framework performed better than the gradient decent method. The proposed framework provides alternatives for online/offline training the existing ANNs (e.g., Convolutional Neural Networks, Recurrent Neural Networks) without the dependence of gradients.
Recent years have seen the introduction of a range of methods for post-hoc explainability of image classifier predictions. However, these post-hoc explanations may not always align perfectly with classifier predictions, which poses a significant challenge when attempting to debug models based on such explanations. To this end, we seek a methodology that can improve alignment between model predictions and explanation method that is both agnostic to the model and explanation classes and which does not require ground truth explanations. We achieve this through a novel explanation-driven data augmentation (EDDA) method that augments the training data with occlusions of existing data stemming from model-explanations; this is based on the simple motivating principle that occluding salient regions for the model prediction should decrease the model confidence in the prediction, while occluding non-salient regions should not change the prediction -- if the model and explainer are aligned. To verify that this augmentation method improves model and explainer alignment, we evaluate the methodology on a variety of datasets, image classification models, and explanation methods. We verify in all cases that our explanation-driven data augmentation method improves alignment of the model and explanation in comparison to no data augmentation and non-explanation driven data augmentation methods. In conclusion, this approach provides a novel model- and explainer-agnostic methodology for improving alignment between model predictions and explanations, which we see as a critical step forward for practical deployment and debugging of image classification models.
Many available formal verification methods have been shown to be instances of a unified Branch-and-Bound (BaB) formulation. We propose a novel machine learning framework that can be used for designing an effective branching strategy as well as for computing better lower bounds. Specifically, we learn two graph neural networks (GNN) that both directly treat the network we want to verify as a graph input and perform forward-backward passes through the GNN layers. We use one GNN to simulate the strong branching heuristic behaviour and another to compute a feasible dual solution of the convex relaxation, thereby providing a valid lower bound. We provide a new verification dataset that is more challenging than those used in the literature, thereby providing an effective alternative for testing algorithmic improvements for verification. Whilst using just one of the GNNs leads to a reduction in verification time, we get optimal performance when combining the two GNN approaches. Our combined framework achieves a 50% reduction in both the number of branches and the time required for verification on various convolutional networks when compared to several state-of-the-art verification methods. In addition, we show that our GNN models generalize well to harder properties on larger unseen networks.
Algorithms often have tunable parameters that impact performance metrics such as runtime and solution quality. For many algorithms used in practice, no parameter settings admit meaningful worst-case bounds, so the parameters are made available for the user to tune. Alternatively, parameters may be tuned implicitly within the proof of a worst-case approximation ratio or runtime bound. Worst-case instances, however, may be rare or nonexistent in practice. A growing body of research has demonstrated that data-driven algorithm design can lead to significant improvements in performance. This approach uses a training set of problem instances sampled from an unknown, application-specific distribution and returns a parameter setting with strong average performance on the training set. We provide a broadly applicable theory for deriving generalization guarantees that bound the difference between the algorithms average performance over the training set and its expected performance. Our results apply no matter how the parameters are tuned, be it via an automated or manual approach. The challenge is that for many types of algorithms, performance is a volatile function of the parameters: slightly perturbing the parameters can cause large changes in behavior. Prior research has proved generalization bounds by employing case-by-case analyses of greedy algorithms, clustering algorithms, integer programming algorithms, and selling mechanisms. We uncover a unifying structure which we use to prove extremely general guarantees, yet we recover the bounds from prior research. Our guarantees apply whenever an algorithms performance is a piecewise-constant, -linear, or -- more generally -- piecewise-structured function of its parameters. Our theory also implies novel bounds for voting mechanisms and dynamic programming algorithms from computational biology.
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