Decomposition of Difficulties in Complex Optimization Problems Using a Bilevel Approach

• URL: http://arxiv.org/abs/2407.03454v1
• Date: Wed, 3 Jul 2024 18:59:17 GMT
• Title: Decomposition of Difficulties in Complex Optimization Problems Using a Bilevel Approach
• Authors: Ankur Sinha, Dhaval Pujara, Hemant Kumar Singh,
• Abstract summary: Practical optimization problems may contain different kinds of difficulties that are often not tractable if one relies on a particular optimization method. We propose a decomposition strategy that allows us to apply two approaches at the same time on a complex optimization problem.
• Score: 0.30723404270319693
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Practical optimization problems may contain different kinds of difficulties that are often not tractable if one relies on a particular optimization method. Different optimization approaches offer different strengths that are good at tackling one or more difficulty in an optimization problem. For instance, evolutionary algorithms have a niche in handling complexities like discontinuity, non-differentiability, discreteness and non-convexity. However, evolutionary algorithms may get computationally expensive for mathematically well behaved problems with large number of variables for which classical mathematical programming approaches are better suited. In this paper, we demonstrate a decomposition strategy that allows us to synergistically apply two complementary approaches at the same time on a complex optimization problem. Evolutionary algorithms are useful in this context as their flexibility makes pairing with other solution approaches easy. The decomposition idea is a special case of bilevel optimization that separates the difficulties into two levels and assigns different approaches at each level that is better equipped at handling them. We demonstrate the benefits of the proposed decomposition idea on a wide range of test problems.

Related papers

• Smooth Tchebycheff Scalarization for Multi-Objective Optimization [15.047246588148495]
  Multi-objective optimization problems can be found in many real-world applications, where the objectives often conflict each other and cannot be optimized by a single solution. We propose a lightweight and efficient smooth Tchebycheff scalarization approach for gradient-based multi-objective optimization.
  arXiv  Detail & Related papers  (2024-02-29T12:03:05Z)
• Analyzing and Enhancing the Backward-Pass Convergence of Unrolled Optimization [50.38518771642365]
  The integration of constrained optimization models as components in deep networks has led to promising advances on many specialized learning tasks. A central challenge in this setting is backpropagation through the solution of an optimization problem, which often lacks a closed form. This paper provides theoretical insights into the backward pass of unrolled optimization, showing that it is equivalent to the solution of a linear system by a particular iterative method. A system called Folded Optimization is proposed to construct more efficient backpropagation rules from unrolled solver implementations.
  arXiv  Detail & Related papers  (2023-12-28T23:15:18Z)
• 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)
• Linearization Algorithms for Fully Composite Optimization [61.20539085730636]
  This paper studies first-order algorithms for solving fully composite optimization problems convex compact sets. We leverage the structure of the objective by handling differentiable and non-differentiable separately, linearizing only the smooth parts.
  arXiv  Detail & Related papers  (2023-02-24T18:41:48Z)
• Backpropagation of Unrolled Solvers with Folded Optimization [55.04219793298687]
  The integration of constrained optimization models as components in deep networks has led to promising advances on many specialized learning tasks. One typical strategy is algorithm unrolling, which relies on automatic differentiation through the operations of an iterative solver. This paper provides theoretical insights into the backward pass of unrolled optimization, leading to a system for generating efficiently solvable analytical models of backpropagation.
  arXiv  Detail & Related papers  (2023-01-28T01:50:42Z)
• Enhanced Opposition Differential Evolution Algorithm for Multimodal Optimization [0.2538209532048866]
  Most of the real-world problems are multimodal in nature that consists of multiple optimum values. Classical gradient-based methods fail for optimization problems in which the objective functions are either discontinuous or non-differentiable. We have proposed an algorithm known as Enhanced Opposition Differential Evolution (EODE) algorithm to solve the MMOPs.
  arXiv  Detail & Related papers  (2022-08-23T16:18:27Z)
• A Constrained Optimization Approach to Bilevel Optimization with Multiple Inner Minima [49.320758794766185]
  We propose a new approach, which convert the bilevel problem to an equivalent constrained optimization, and then the primal-dual algorithm can be used to solve the problem. Such an approach enjoys a few advantages including (a) addresses the multiple inner minima challenge; (b) fully first-order efficiency without Jacobian computations.
  arXiv  Detail & Related papers  (2022-03-01T18:20:01Z)
• Enhanced Bilevel Optimization via Bregman Distance [104.96004056928474]
  We propose a bilevel optimization method based on Bregman Bregman functions. We also propose an accelerated version of SBiO-BreD method (ASBiO-BreD) by using the variance-reduced technique.
  arXiv  Detail & Related papers  (2021-07-26T16:18:43Z)
• Learning Hard Optimization Problems: A Data Generation Perspective [44.4747903763245]
  This paper demonstrates the volatility of the training data to the ability to approximate it. It proposes a method for producing (exact or approximate) solutions to optimization problems that are amenable to supervised tasks.
  arXiv  Detail & Related papers  (2021-06-04T17:03:44Z)
• Quantum variational optimization: The role of entanglement and problem hardness [0.0]
  We study the role of entanglement, the structure of the variational quantum circuit, and the structure of the optimization problem. Our numerical results indicate an advantage in adapting the distribution of entangling gates to the problem's topology. We find evidence that applying conditional value at risk type cost functions improves the optimization, increasing the probability of overlap with the optimal solutions.
  arXiv  Detail & Related papers  (2021-03-26T14:06:54Z)
• Optimistic variants of single-objective bilevel optimization for evolutionary algorithms [6.788217433800101]
  A partial partial evolutionary approach has been proposed to solve the benchmark problems and have outstanding results. A new variant has also been proposed to the commonly used convergence approaches, i.e. optimistic and pessimistic. The experimental results demonstrate the algorithm converges differently to optimum solutions with the optimistic variants.
  arXiv  Detail & Related papers  (2020-08-22T23:12:07Z)

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.