A Sequential Deep Learning Algorithm for Sampled Mixed-integer Optimisation Problems

• URL: http://arxiv.org/abs/2301.10703v1
• Date: Wed, 25 Jan 2023 17:10:52 GMT
• Title: A Sequential Deep Learning Algorithm for Sampled Mixed-integer Optimisation Problems
• Authors: Mohammadreza Chamanbaz, Roland Bouffanais
• Abstract summary: We introduce and analyse two efficient algorithms for mixed-integer optimisation problems. We show that both algorithms exhibit finite-time convergence towards the optimal solution. We establish quantitatively the efficacy of these algorithms by means of three numerical tests.
• Score: 0.3867363075280544
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Mixed-integer optimisation problems can be computationally challenging. Here, we introduce and analyse two efficient algorithms with a specific sequential design that are aimed at dealing with sampled problems within this class. At each iteration step of both algorithms, we first test the feasibility of a given test solution for each and every constraint associated with the sampled optimisation at hand, while also identifying those constraints that are violated. Subsequently, an optimisation problem is constructed with a constraint set consisting of the current basis -- namely the smallest set of constraints that fully specifies the current test solution -- as well as constraints related to a limited number of the identified violating samples. We show that both algorithms exhibit finite-time convergence towards the optimal solution. Algorithm 2 features a neural network classifier that notably improves the computational performance compared to Algorithm 1. We establish quantitatively the efficacy of these algorithms by means of three numerical tests: robust optimal power flow, robust unit commitment, and robust random mixed-integer linear program.

Related papers

• Accelerating Cutting-Plane Algorithms via Reinforcement Learning Surrogates [49.84541884653309]
  A current standard approach to solving convex discrete optimization problems is the use of cutting-plane algorithms. Despite the existence of a number of general-purpose cut-generating algorithms, large-scale discrete optimization problems continue to suffer from intractability. We propose a method for accelerating cutting-plane algorithms via reinforcement learning.
  arXiv  Detail & Related papers  (2023-07-17T20:11:56Z)
• Accelerated First-Order Optimization under Nonlinear Constraints [73.2273449996098]
  We exploit between first-order algorithms for constrained optimization and non-smooth systems to design a new class of accelerated first-order algorithms. An important property of these algorithms is that constraints are expressed in terms of velocities instead of sparse variables.
  arXiv  Detail & Related papers  (2023-02-01T08:50:48Z)
• First-Order Algorithms for Nonlinear Generalized Nash Equilibrium Problems [88.58409977434269]
  We consider the problem of computing an equilibrium in a class of nonlinear generalized Nash equilibrium problems (NGNEPs) Our contribution is to provide two simple first-order algorithmic frameworks based on the quadratic penalty method and the augmented Lagrangian method. We provide nonasymptotic theoretical guarantees for these algorithms.
  arXiv  Detail & Related papers  (2022-04-07T00:11:05Z)
• Combining K-means type algorithms with Hill Climbing for Joint Stratification and Sample Allocation Designs [0.0]
  This is a sample problem in which we search for the optimal stratification from the set of all possible stratifications of basic strata. evaluating the cost of each solution is expensive. We compare the above multi-stage combination of algorithms with three recent algorithms and report the solution costs, evaluation times and training times.
  arXiv  Detail & Related papers  (2021-08-18T08:41:58Z)
• Zeroth and First Order Stochastic Frank-Wolfe Algorithms for Constrained Optimization [13.170519806372075]
  Problems of convex optimization with two sets of constraints arise frequently in the context of semidefinite programming. Since projection onto the first set of constraints is difficult, it becomes necessary to explore projection-free algorithms. The efficacy of the proposed algorithms is tested on relevant applications of sparse matrix estimation, clustering via semidefinite relaxation, and uniform sparsest cut problem.
  arXiv  Detail & Related papers  (2021-07-14T08:01:30Z)
• Adaptive Sampling for Best Policy Identification in Markov Decision Processes [79.4957965474334]
  We investigate the problem of best-policy identification in discounted Markov Decision (MDPs) when the learner has access to a generative model. The advantages of state-of-the-art algorithms are discussed and illustrated.
  arXiv  Detail & Related papers  (2020-09-28T15:22:24Z)
• Optimal and Practical Algorithms for Smooth and Strongly Convex Decentralized Optimization [21.555331273873175]
  We consider the task of decentralized minimization of the sum of smooth strongly convex functions stored across the nodes of a network. We propose two new algorithms for this decentralized optimization problem and equip them with complexity guarantees.
  arXiv  Detail & Related papers  (2020-06-21T11:23:20Z)
• Beyond Worst-Case Analysis in Stochastic Approximation: Moment Estimation Improves Instance Complexity [58.70807593332932]
  We study oracle complexity of gradient based methods for approximation problems. We focus on instance-dependent complexity instead of worst case complexity. Our proposed algorithm and its analysis provide a theoretical justification for the success of moment estimation.
  arXiv  Detail & Related papers  (2020-06-08T09:25:47Z)
• Extreme Algorithm Selection With Dyadic Feature Representation [78.13985819417974]
  We propose the setting of extreme algorithm selection (XAS) where we consider fixed sets of thousands of candidate algorithms. We assess the applicability of state-of-the-art AS techniques to the XAS setting and propose approaches leveraging a dyadic feature representation.
  arXiv  Detail & Related papers  (2020-01-29T09:40:58Z)

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.