Learning to Accelerate Approximate Methods for Solving Integer Programming via Early Fixing

• URL: http://arxiv.org/abs/2207.02087v1
• Date: Tue, 5 Jul 2022 14:46:47 GMT
• Title: Learning to Accelerate Approximate Methods for Solving Integer Programming via Early Fixing
• Authors: Longkang Li, Baoyuan Wu
• Abstract summary: A large fraction of variables solved by some iterative approximate methods fluctuate around their final converged discrete states in very long iterations. Inspired by this observation, we aim to accelerate these approximate methods by early fixing these fluctuated variables to their converged states. We formulate the whole early fixing process as a Markov decision process, and train it using imitation learning.
• Score: 29.29673962163146
• License: http://creativecommons.org/licenses/by-nc-nd/4.0/
• Abstract: Integer programming (IP) is an important and challenging problem. Approximate methods have shown promising performance on both effectiveness and efficiency for solving the IP problem. However, we observed that a large fraction of variables solved by some iterative approximate methods fluctuate around their final converged discrete states in very long iterations. Inspired by this observation, we aim to accelerate these approximate methods by early fixing these fluctuated variables to their converged states while not significantly harming the solution accuracy. To this end, we propose an early fixing framework along with the approximate method. We formulate the whole early fixing process as a Markov decision process, and train it using imitation learning. A policy network will evaluate the posterior probability of each free variable concerning its discrete candidate states in each block of iterations. Specifically, we adopt the powerful multi-headed attention mechanism in the policy network. Extensive experiments on our proposed early fixing framework are conducted to three different IP applications: constrained linear programming, MRF energy minimization and sparse adversarial attack. The former one is linear IP problem, while the latter two are quadratic IP problems. We extend the problem scale from regular size to significantly large size. The extensive experiments reveal the competitiveness of our early fixing framework: the runtime speeds up significantly, while the solution quality does not degrade much, even in some cases it is available to obtain better solutions. Our proposed early fixing framework can be regarded as an acceleration extension of ADMM methods for solving integer programming. The source codes are available at \url{https://github.com/SCLBD/Accelerated-Lpbox-ADMM}.

Related papers

• Towards An Unsupervised Learning Scheme for Efficiently Solving Parameterized Mixed-Integer Programs [6.1860817947800655]
  We train an autoencoder for binary variables in an unsupervised learning fashion. We present a strategy to construct a class of cutting plane constraints from the decoder parameters of an offline-trained AE. Their integration into the primal MIP problem leads to a tightened MIP with the reduced feasible region.
  arXiv  Detail & Related papers  (2024-12-23T14:48:32Z)
• The Differentiable Feasibility Pump [49.55771920271201]
  This paper shows that the traditional feasibility pump and many of its follow-ups can be seen as gradient-descent algorithms with specific parameters. A central aspect of this reinterpretation is observing that the traditional algorithm differentiates the solution of the linear relaxation with respect to its cost.
  arXiv  Detail & Related papers  (2024-11-05T22:26:51Z)
• 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)
• Integer Programming Using A Single Atom [0.0]
  We develop an algorithm that maps and solves an IP problem in its original form to any quantum system. The optimal solution is found within a few microseconds for IP problems with up to eight variables and four constraints.
  arXiv  Detail & Related papers  (2024-02-26T12:59:20Z)
• Fast, Scalable, Warm-Start Semidefinite Programming with Spectral Bundling and Sketching [53.91395791840179]
  We present Unified Spectral Bundling with Sketching (USBS), a provably correct, fast and scalable algorithm for solving massive SDPs. USBS provides a 500x speed-up over the state-of-the-art scalable SDP solver on an instance with over 2 billion decision variables.
  arXiv  Detail & Related papers  (2023-12-19T02:27:22Z)
• Learning to Optimize Permutation Flow Shop Scheduling via Graph-based Imitation Learning [70.65666982566655]
  Permutation flow shop scheduling (PFSS) is widely used in manufacturing systems. We propose to train the model via expert-driven imitation learning, which accelerates convergence more stably and accurately. Our model's network parameters are reduced to only 37% of theirs, and the solution gap of our model towards the expert solutions decreases from 6.8% to 1.3% on average.
  arXiv  Detail & Related papers  (2022-10-31T09:46:26Z)
• Minimizing Entropy to Discover Good Solutions to Recurrent Mixed Integer Programs [0.0]
  Current solvers for mixed-integer programming (MIP) problems are designed to perform well on a wide range of problems. Recent works have shown that machine learning (ML) can be integrated with an MIP solver to inject domain knowledge and efficiently close the optimality gap. This paper proposes an online solver that uses the notion of entropy to efficiently build a model with minimal training data and tuning.
  arXiv  Detail & Related papers  (2022-02-07T18:52:56Z)
• Finite-Time Complexity of Online Primal-Dual Natural Actor-Critic Algorithm for Constrained Markov Decision Processes [13.908826484332282]
  We study an online primal-dual actor-critic method to solve a discounted cost constrained Markov decision process problem. This paper is the first to study the finite-time complexity of an online primal-dual actor-critic method for solving a CMDP problem.
  arXiv  Detail & Related papers  (2021-10-21T18:05:40Z)
• Learning Pseudo-Backdoors for Mixed Integer Programs [48.36587539004464]
  We propose a machine learning approach for solving Mixed Programs (MIP) by learning to prioritize a set of decision variables, which we call pseudo-backdoors, for branching that results in faster solution times. Our approach takes inspiration from the concept of strong backdoors, which corresponds to a small set of variables such that only branching on these variables yields an optimal integral solution and a proof of optimality. A key advantage of pseudo-backdoors over strong backdoors is that they are much amenable to data-driven identification or prediction.
  arXiv  Detail & Related papers  (2021-06-09T13:59:53Z)
• Learning to Schedule Heuristics in Branch-and-Bound [25.79025327341732]
  Real-world applications typically require finding good solutions early in the search to enable fast decision-making. We propose the first data-driven framework for schedulings in an exact MIP solver. Compared to the default settings of a state-of-the-art academic MIP solver, we are able to reduce the average primal integral by up to 49% on a class of challenging instances.
  arXiv  Detail & Related papers  (2021-03-18T14:49:52Z)
• Combining Deep Learning and Optimization for Security-Constrained Optimal Power Flow [94.24763814458686]
  Security-constrained optimal power flow (SCOPF) is fundamental in power systems. Modeling of APR within the SCOPF problem results in complex large-scale mixed-integer programs. This paper proposes a novel approach that combines deep learning and robust optimization techniques.
  arXiv  Detail & Related papers  (2020-07-14T12:38:21Z)

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.