Shape-constrained Symbolic Regression with NSGA-III

• URL: http://arxiv.org/abs/2209.13851v1
• Date: Wed, 28 Sep 2022 06:10:34 GMT
• Title: Shape-constrained Symbolic Regression with NSGA-III
• Authors: Christian Haider
• Abstract summary: Shape-constrained symbolic regression (SCSR) allows to include prior knowledge into data-based modeling. This paper presents a mutlicriterial approach to minimize the approximation error as well as the constraint violations. Explicitly the two algorithms NSGA-II and NSGA-III are implemented and compared against each other in terms of model quality and runtime.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Shape-constrained symbolic regression (SCSR) allows to include prior knowledge into data-based modeling. This inclusion allows to ensure that certain expected behavior is better reflected by the resulting models. The expected behavior is defined via constraints, which refer to the function form e.g. monotonicity, concavity, convexity or the models image boundaries. In addition to the advantage of obtaining more robust and reliable models due to defining constraints over the functions shape, the use of SCSR allows to find models which are more robust to noise and have a better extrapolation behavior. This paper presents a mutlicriterial approach to minimize the approximation error as well as the constraint violations. Explicitly the two algorithms NSGA-II and NSGA-III are implemented and compared against each other in terms of model quality and runtime. Both algorithms are capable of dealing with multiple objectives, whereas NSGA-II is a well established multi-objective approach performing well on instances with up-to 3 objectives. NSGA-III is an extension of the NSGA-II algorithm and was developed to handle problems with "many" objectives (more than 3 objectives). Both algorithms are executed on a selected set of benchmark instances from physics textbooks. The results indicate that both algorithms are able to find largely feasible solutions and NSGA-III provides slight improvements in terms of model quality. Moreover, an improvement in runtime can be observed using the many-objective approach.

Related papers

• Geometric Algebra Planes: Convex Implicit Neural Volumes [70.12234371845445]
  We show that GA-Planes is equivalent to a sparse low-rank factor plus low-resolution matrix. We also show that GA-Planes can be adapted for many existing representations.
  arXiv  Detail & Related papers  (2024-11-20T18:21:58Z)
• Multiobjective Vehicle Routing Optimization with Time Windows: A Hybrid Approach Using Deep Reinforcement Learning and NSGA-II [52.083337333478674]
  This paper proposes a weight-aware deep reinforcement learning (WADRL) approach designed to address the multiobjective vehicle routing problem with time windows (MOVRPTW) The Non-dominated sorting genetic algorithm-II (NSGA-II) method is then employed to optimize the outcomes produced by the WADRL.
  arXiv  Detail & Related papers  (2024-07-18T02:46:06Z)
• Runtime Analyses of NSGA-III on Many-Objective Problems [10.955844285189372]
  We present the first runtime analyses of NSGA-III on the popular many-objective benchmark problems mLOTZ, mOMM, and mCOCZ. We show how these parameters should be scaled with the problem dimension, the number of objectives and the fitness range. To our knowledge, these are the first runtime analyses for NSGA-III for more than 3 objectives.
  arXiv  Detail & Related papers  (2024-04-17T14:39:14Z)
• Probabilistic Reach-Avoid for Bayesian Neural Networks [71.67052234622781]
  We show that an optimal synthesis algorithm can provide more than a four-fold increase in the number of certifiable states. The algorithm is able to provide more than a three-fold increase in the average guaranteed reach-avoid probability.
  arXiv  Detail & Related papers  (2023-10-03T10:52:21Z)
• A Mathematical Runtime Analysis of the Non-dominated Sorting Genetic Algorithm III (NSGA-III) [9.853329403413701]
  The Non-dominated Sorting Genetic Algorithm II (NSGA-II) is the most prominent multi-objective evolutionary algorithm for real-world applications. We provide the first mathematical runtime analysis of the NSGA-III, a refinement of the NSGA-II aimed at better handling more than two objectives.
  arXiv  Detail & Related papers  (2022-11-15T15:10:36Z)
• Multi-objective Explanations of GNN Predictions [15.563499097282978]
  Graph Neural Network (GNN) has achieved state-of-the-art performance in various high-stake prediction tasks. Prior methods use simpler subgraphs to simulate the full model, or counterfactuals to identify the causes of a prediction.
  arXiv  Detail & Related papers  (2021-11-29T16:08:03Z)
• Using Shape Constraints for Improving Symbolic Regression Models [0.0]
  We describe and analyze algorithms for shape-constrained symbolic regression. We use a set of models from physics textbooks to test the algorithms. The results show that all algorithms are able to find models which conform to all shape constraints.
  arXiv  Detail & Related papers  (2021-07-20T12:53:28Z)
• Self-supervised Geometric Perception [96.89966337518854]
  Self-supervised geometric perception is a framework to learn a feature descriptor for correspondence matching without any ground-truth geometric model labels. We show that SGP achieves state-of-the-art performance that is on-par or superior to the supervised oracles trained using ground-truth labels.
  arXiv  Detail & Related papers  (2021-03-04T15:34:43Z)
• PC-RGNN: Point Cloud Completion and Graph Neural Network for 3D Object Detection [57.49788100647103]
  LiDAR-based 3D object detection is an important task for autonomous driving. Current approaches suffer from sparse and partial point clouds of distant and occluded objects. In this paper, we propose a novel two-stage approach, namely PC-RGNN, dealing with such challenges by two specific solutions.
  arXiv  Detail & Related papers  (2020-12-18T18:06:43Z)
• Hyperspectral Classification Based on Lightweight 3-D-CNN With Transfer Learning [67.40866334083941]
  We propose an end-to-end 3-D lightweight convolutional neural network (CNN) for limited samples-based HSI classification. Compared with conventional 3-D-CNN models, the proposed 3-D-LWNet has a deeper network structure, less parameters, and lower computation cost. Our model achieves competitive performance for HSI classification compared to several state-of-the-art methods.
  arXiv  Detail & Related papers  (2020-12-07T03:44:35Z)
• Evolutionary Multi Objective Optimization Algorithm for Community Detection in Complex Social Networks [10.855626765597005]
  We propose two variants of a three-objective formulation to find community structures in a network. Experiments are conducted on four benchmark network datasets.
  arXiv  Detail & Related papers  (2020-05-07T00:13:31Z)

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.