Enhancing Hyper-To-Real Space Projections Through Euclidean Norm Meta-Heuristic Optimization

• URL: http://arxiv.org/abs/2301.13671v1
• Date: Tue, 31 Jan 2023 14:40:49 GMT
• Title: Enhancing Hyper-To-Real Space Projections Through Euclidean Norm Meta-Heuristic Optimization
• Authors: Luiz C. F. Ribeiro, Mateus Roder, Gustavo H. de Rosa, Leandro A. Passos, Jo\~ao P. Papa
• Abstract summary: We show that meta-heuristic optimization can provide robust approximate solutions to different kinds of problems with a small computational burden. Previous works addressed this issue by employing a hypercomplex representation of the search space, like quaternions, where the landscape becomes smoother and supposedly easier to optimize. We have found that after the optimization procedure has finished, it is usually possible to obtain even better solutions by employing the Minkowski $p$-norm instead.
• Score: 0.39146761527401425
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: The continuous computational power growth in the last decades has made solving several optimization problems significant to humankind a tractable task; however, tackling some of them remains a challenge due to the overwhelming amount of candidate solutions to be evaluated, even by using sophisticated algorithms. In such a context, a set of nature-inspired stochastic methods, called meta-heuristic optimization, can provide robust approximate solutions to different kinds of problems with a small computational burden, such as derivative-free real function optimization. Nevertheless, these methods may converge to inadequate solutions if the function landscape is too harsh, e.g., enclosing too many local optima. Previous works addressed this issue by employing a hypercomplex representation of the search space, like quaternions, where the landscape becomes smoother and supposedly easier to optimize. Under this approach, meta-heuristic computations happen in the hypercomplex space, whereas variables are mapped back to the real domain before function evaluation. Despite this latter operation being performed by the Euclidean norm, we have found that after the optimization procedure has finished, it is usually possible to obtain even better solutions by employing the Minkowski $p$-norm instead and fine-tuning $p$ through an auxiliary sub-problem with neglecting additional cost and no hyperparameters. Such behavior was observed in eight well-established benchmarking functions, thus fostering a new research direction for hypercomplex meta-heuristic optimization.

Related papers

• Gradient-free neural topology optimization [0.0]
  gradient-free algorithms require many more iterations to converge when compared to gradient-based algorithms. This has made them unviable for topology optimization due to the high computational cost per iteration and high dimensionality of these problems. We propose a pre-trained neural reparameterization strategy that leads to at least one order of magnitude decrease in iteration count when optimizing the designs in latent space.
  arXiv  Detail & Related papers  (2024-03-07T23:00:49Z)
• 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)
• ProGO: Probabilistic Global Optimizer [9.772380490791635]
  In this paper we develop an algorithm that converges to the global optima under some mild conditions. We show that the proposed algorithm outperforms, by order of magnitude, many existing state-of-the-art methods.
  arXiv  Detail & Related papers  (2023-10-04T22:23:40Z)
• An Empirical Evaluation of Zeroth-Order Optimization Methods on AI-driven Molecule Optimization [78.36413169647408]
  We study the effectiveness of various ZO optimization methods for optimizing molecular objectives. We show the advantages of ZO sign-based gradient descent (ZO-signGD) We demonstrate the potential effectiveness of ZO optimization methods on widely used benchmark tasks from the Guacamol suite.
  arXiv  Detail & Related papers  (2022-10-27T01:58:10Z)
• 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)
• Learning Proximal Operators to Discover Multiple Optima [66.98045013486794]
  We present an end-to-end method to learn the proximal operator across non-family problems. We show that for weakly-ized objectives and under mild conditions, the method converges globally.
  arXiv  Detail & Related papers  (2022-01-28T05:53:28Z)
• Faster Algorithm and Sharper Analysis for Constrained Markov Decision Process [56.55075925645864]
  The problem of constrained decision process (CMDP) is investigated, where an agent aims to maximize the expected accumulated discounted reward subject to multiple constraints. A new utilities-dual convex approach is proposed with novel integration of three ingredients: regularized policy, dual regularizer, and Nesterov's gradient descent dual. This is the first demonstration that nonconcave CMDP problems can attain the lower bound of $mathcal O (1/epsilon)$ for all complexity optimization subject to convex constraints.
  arXiv  Detail & Related papers  (2021-10-20T02:57:21Z)
• Population-Based Methods: PARTICLE SWARM OPTIMIZATION -- Development of a General-Purpose Optimizer and Applications [0.0]
  This thesis is concerned with continuous, static, and single-objective optimization problems subject to inequality constraints. The particle swarm optimization paradigm was inspired by previous simulations of the cooperative behaviour observed in social beings.
  arXiv  Detail & Related papers  (2021-01-25T09:36:25Z)
• Learning to Optimize Under Constraints with Unsupervised Deep Neural Networks [0.0]
  We propose a machine learning (ML) method to learn how to solve a generic constrained continuous optimization problem. In this paper, we propose an unsupervised deep learning (DL) solution for solving constrained optimization problems in real-time.
  arXiv  Detail & Related papers  (2021-01-04T02:58:37Z)
• Divide and Learn: A Divide and Conquer Approach for Predict+Optimize [50.03608569227359]
  The predict+optimize problem combines machine learning ofproblem coefficients with a optimization prob-lem that uses the predicted coefficients. We show how to directlyexpress the loss of the optimization problem in terms of thepredicted coefficients as a piece-wise linear function. We propose a novel divide and algorithm to tackle optimization problems without this restriction and predict itscoefficients using the optimization loss.
  arXiv  Detail & Related papers  (2020-12-04T00:26:56Z)
• 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.