Machine Learning for K-adaptability in Two-stage Robust Optimization

• URL: http://arxiv.org/abs/2210.11152v3
• Date: Tue, 15 Oct 2024 15:59:22 GMT
• Title: Machine Learning for K-adaptability in Two-stage Robust Optimization
• Authors: Esther Julien, Krzysztof Postek, Ş. İlker Birbil,
• Abstract summary: Two-stage robust optimization problems constitute one of the hardest optimization problem classes. One of the solution approaches to this class of problems is K-adaptability. We propose a machine learning-based node selection strategy.
• Score: 0.40964539027092906
• License:
• Abstract: Two-stage robust optimization problems constitute one of the hardest optimization problem classes. One of the solution approaches to this class of problems is K-adaptability. This approach simultaneously seeks the best partitioning of the uncertainty set of scenarios into K subsets, and optimizes decisions corresponding to each of these subsets. In general case, it is solved using the K-adaptability branch-and-bound algorithm, which requires exploration of exponentially-growing solution trees. To accelerate finding high-quality solutions in such trees, we propose a machine learning-based node selection strategy. In particular, we construct a feature engineering scheme based on general two-stage robust optimization insights that allows us to train our machine learning tool on a database of resolved B&B trees, and to apply it as-is to problems of different sizes and/or types. We experimentally show that using our learned node selection strategy outperforms a vanilla, random node selection strategy when tested on problems of the same type as the training problems, also in case the K-value or the problem size differs from the training ones.

Related papers

• Learning Multiple Initial Solutions to Optimization Problems [52.9380464408756]
  Sequentially solving similar optimization problems under strict runtime constraints is essential for many applications. We propose learning to predict emphmultiple diverse initial solutions given parameters that define the problem instance. We find significant and consistent improvement with our method across all evaluation settings and demonstrate that it efficiently scales with the number of initial solutions required.
  arXiv  Detail & Related papers  (2024-11-04T15:17:19Z)
• Learning Joint Models of Prediction and Optimization [56.04498536842065]
  Predict-Then-Then framework uses machine learning models to predict unknown parameters of an optimization problem from features before solving. This paper proposes an alternative method, in which optimal solutions are learned directly from the observable features by joint predictive models.
  arXiv  Detail & Related papers  (2024-09-07T19:52:14Z)
• Decision-focused Graph Neural Networks for Combinatorial Optimization [62.34623670845006]
  An emerging strategy to tackle optimization problems involves the adoption of graph neural networks (GNNs) as an alternative to traditional algorithms. Despite the growing popularity of GNNs and traditional algorithm solvers in the realm of CO, there is limited research on their integrated use and the correlation between them within an end-to-end framework. We introduce a decision-focused framework that utilizes GNNs to address CO problems with auxiliary support.
  arXiv  Detail & Related papers  (2024-06-05T22:52:27Z)
• A Machine Learning Approach to Two-Stage Adaptive Robust Optimization [6.943816076962257]
  We propose an approach based on machine learning to solve two-stage linear adaptive robust optimization problems. We encode the optimal here-and-now decisions, the worst-case scenarios associated with the optimal here-and-now decisions, and the optimal wait-and-see decisions. We train a machine learning model that predicts high-quality strategies for the here-and-now decisions, the worst-case scenarios associated with the optimal here-and-now decisions, and the wait-and-see decisions.
  arXiv  Detail & Related papers  (2023-07-23T19:23:06Z)
• Let the Flows Tell: Solving Graph Combinatorial Optimization Problems with GFlowNets [86.43523688236077]
  Combinatorial optimization (CO) problems are often NP-hard and out of reach for exact algorithms. GFlowNets have emerged as a powerful machinery to efficiently sample from composite unnormalized densities sequentially. In this paper, we design Markov decision processes (MDPs) for different problems and propose to train conditional GFlowNets to sample from the solution space.
  arXiv  Detail & Related papers  (2023-05-26T15:13:09Z)
• A machine learning framework for neighbor generation in metaheuristic search [4.521119623956821]
  We propose a general machine learning framework for neighbor generation in metaheuristic search. We validate our methodology on two metaheuristic applications.
  arXiv  Detail & Related papers  (2022-12-22T01:58:04Z)
• A Study of Scalarisation Techniques for Multi-Objective QUBO Solving [0.0]
  Quantum and quantum-inspired optimisation algorithms have shown promising performance when applied to academic benchmarks as well as real-world problems. However, QUBO solvers are single objective solvers. To make them more efficient at solving problems with multiple objectives, a decision on how to convert such multi-objective problems to single-objective problems need to be made.
  arXiv  Detail & Related papers  (2022-10-20T14:54:37Z)
• Quant-BnB: A Scalable Branch-and-Bound Method for Optimal Decision Trees with Continuous Features [5.663538370244174]
  We present a new discrete optimization method based on branch-and-bound (BnB) to obtain optimal decision trees. Our proposed algorithm Quant-BnB shows significant speedups compared to existing approaches for shallow optimal trees on various real datasets.
  arXiv  Detail & Related papers  (2022-06-23T17:19:29Z)
• Learning Primal Heuristics for Mixed Integer Programs [5.766851255770718]
  We investigate whether effective primals can be automatically learned via machine learning. We propose a new method to represent an optimization problem as a graph, and train a Graph Conal Network on solved problem instances with known optimal solutions. The prediction of variable solutions is then leveraged by a novel configuration of the B&B method, Probabilistic Branching with guided Depth-first Search.
  arXiv  Detail & Related papers  (2021-07-02T06:46:23Z)
• Generalized and Scalable Optimal Sparse Decision Trees [56.35541305670828]
  We present techniques that produce optimal decision trees over a variety of objectives. We also introduce a scalable algorithm that produces provably optimal results in the presence of continuous variables.
  arXiv  Detail & Related papers  (2020-06-15T19:00:11Z)
• Optimizing Wireless Systems Using Unsupervised and Reinforced-Unsupervised Deep Learning [96.01176486957226]
  Resource allocation and transceivers in wireless networks are usually designed by solving optimization problems. In this article, we introduce unsupervised and reinforced-unsupervised learning frameworks for solving both variable and functional optimization problems.
  arXiv  Detail & Related papers  (2020-01-03T11:01:52Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.