The Differentiable Feasibility Pump

• URL: http://arxiv.org/abs/2411.03535v1
• Date: Tue, 05 Nov 2024 22:26:51 GMT
• Title: The Differentiable Feasibility Pump
• Authors: Matteo Cacciola, Alexandre Forel, Antonio Frangioni, Andrea Lodi,
• Abstract summary: 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.
• Score: 49.55771920271201
• License:
• Abstract: Although nearly 20 years have passed since its conception, the feasibility pump algorithm remains a widely used heuristic to find feasible primal solutions to mixed-integer linear problems. Many extensions of the initial algorithm have been proposed. Yet, its core algorithm remains centered around two key steps: solving the linear relaxation of the original problem to obtain a solution that respects the constraints, and rounding it to obtain an integer solution. 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. This reinterpretation opens many opportunities for improving the performance of the original algorithm. We study how to modify the gradient-update step as well as extending its loss function. We perform extensive experiments on MIPLIB instances and show that these modifications can substantially reduce the number of iterations needed to find a solution.

Related papers

• Analysis of the Non-variational Quantum Walk-based Optimisation Algorithm [0.0]
  This paper introduces in detail a non-variational quantum algorithm designed to solve a wide range of optimisation problems. The algorithm returns optimal and near-optimal solutions from repeated preparation and measurement of an amplified state.
  arXiv  Detail & Related papers  (2024-07-29T13:54:28Z)
• Discretize Relaxed Solution of Spectral Clustering via a Non-Heuristic Algorithm [77.53604156112144]
  We develop a first-order term to bridge the original problem and discretization algorithm. Since the non-heuristic method is aware of the original graph cut problem, the final discrete solution is more reliable.
  arXiv  Detail & Related papers  (2023-10-19T13:57:38Z)
• Beyond the Golden Ratio for Variational Inequality Algorithms [12.470097382737933]
  We improve the understanding of the $textitgolden ratio algorithm$, which solves monotone variational inequalities (VI) and convex-concave min-max problems. We introduce a new analysis that allows to use larger step sizes, to complete the bridge between the golden ratio algorithm and the existing algorithms in the literature.
  arXiv  Detail & Related papers  (2022-12-28T16:58:48Z)
• A Single-Loop Gradient Descent and Perturbed Ascent Algorithm for Nonconvex Functional Constrained Optimization [27.07082875330508]
  Non constrained inequality problems can be used to model a number machine learning problems, such as multi-class Neyman oracle. Under such a mild condition of regularity it is difficult to balance reduction alternating value loss and reduction constraint violation. In this paper, we propose a novel primal-dual inequality constrained problems algorithm.
  arXiv  Detail & Related papers  (2022-07-12T16:30:34Z)
• A framework for bilevel optimization that enables stochastic and global variance reduction algorithms [17.12280360174073]
  Bilevel optimization is a problem of minimizing a value function which involves the arg-minimum of another function. We introduce a novel framework, in which the solution of the inner problem, the solution of the linear system, and the main variable evolve at the same time. We demonstrate that SABA, an adaptation of the celebrated SAGA algorithm in our framework, has $O(frac1T)$ convergence rate, and that it achieves linear convergence under Polyak-Lojasciewicz assumption.
  arXiv  Detail & Related papers  (2022-01-31T18:17:25Z)
• Quadratic Unconstrained Binary Optimisation via Quantum-Inspired Annealing [58.720142291102135]
  We present a classical algorithm to find approximate solutions to instances of quadratic unconstrained binary optimisation. We benchmark our approach for large scale problem instances with tuneable hardness and planted solutions.
  arXiv  Detail & Related papers  (2021-08-18T09:26:17Z)
• A Hybrid Quantum-Classical Heuristic to solve large-scale Integer Linear Programs [0.4925222726301578]
  We present a method that integrates any quantum algorithm capable of finding solutions to integer linear programs into the Branch-and-Price algorithm. The role of the quantum algorithm is to find integer solutions to subproblems appearing in Branch-and-Price.
  arXiv  Detail & Related papers  (2021-03-29T08:59:26Z)
• Boosting Data Reduction for the Maximum Weight Independent Set Problem Using Increasing Transformations [59.84561168501493]
  We introduce new generalized data reduction and transformation rules for the maximum weight independent set problem. Surprisingly, these so-called increasing transformations can simplify the problem and also open up the reduction space to yield even smaller irreducible graphs later in the algorithm. Our algorithm computes significantly smaller irreducible graphs on all except one instance, solves more instances to optimality than previously possible, is up to two orders of magnitude faster than the best state-of-the-art solver, and finds higher-quality solutions than solvers DynWVC and HILS.
  arXiv  Detail & Related papers  (2020-08-12T08:52:50Z)
• 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)
• Conditional gradient methods for stochastically constrained convex minimization [54.53786593679331]
  We propose two novel conditional gradient-based methods for solving structured convex optimization problems. The most important feature of our framework is that only a subset of the constraints is processed at each iteration. Our algorithms rely on variance reduction and smoothing used in conjunction with conditional gradient steps, and are accompanied by rigorous convergence guarantees.
  arXiv  Detail & Related papers  (2020-07-07T21:26:35Z)

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.