scholarly journals Optimization for L1-Norm Error Fitting via Data Aggregation

2020 ◽  
Author(s):  
Young Woong Park
Keyword(s):  
Data Aggregation ◽  
State Of The Art ◽  
Subset Selection ◽  
Global Optimum ◽  
L1 Norm ◽  
Orthogonal Procrustes Problem ◽  
Monotonic Convergence ◽  
Procrustes Problem ◽  
Fitting Model ◽  
Norm Error

We propose a data aggregation-based algorithm with monotonic convergence to a global optimum for a generalized version of the L1-norm error fitting model with an assumption of the fitting function. The proposed algorithm generalizes the recent algorithm in the literature, aggregate and iterative disaggregate (AID), which selectively solves three specific L1-norm error fitting problems. With the proposed algorithm, any L1-norm error fitting model can be solved optimally if it follows the form of the L1-norm error fitting problem and if the fitting function satisfies the assumption. The proposed algorithm can also solve multidimensional fitting problems with arbitrary constraints on the fitting coefficients matrix. The generalized problem includes popular models, such as regression and the orthogonal Procrustes problem. The results of the computational experiment show that the proposed algorithms are faster than the state-of-the-art benchmarks for L1-norm regression subset selection and L1-norm regression over a sphere. Furthermore, the relative performance of the proposed algorithm improves as data size increases.

Solving Mono- and Multi-Objective Problems Using Hybrid Evolutionary Algorithms and Nelder-Mead Method

2021 ◽  
Vol 12 (4) ◽  
pp. 98-116
Author(s):  
Noureddine Boukhari ◽  
Fatima Debbat ◽  
Nicolas Monmarché ◽  
Mohamed Slimane
Keyword(s):  
Convergence Rate ◽  
Optimization Problem ◽  
Optimization Problems ◽  
State Of The Art ◽  
Hybrid Approach ◽  
Optimization Methods ◽  
Global Optimum ◽  
Stochastic Methods ◽  
Local Optima ◽  
Portfolio Optimization Problem

Evolution strategies (ES) are a family of strong stochastic methods for global optimization and have proved their capability in avoiding local optima more than other optimization methods. Many researchers have investigated different versions of the original evolution strategy with good results in a variety of optimization problems. However, the convergence rate of the algorithm to the global optimum stays asymptotic. In order to accelerate the convergence rate, a hybrid approach is proposed using the nonlinear simplex method (Nelder-Mead) and an adaptive scheme to control the local search application, and the authors demonstrate that such combination yields significantly better convergence. The new proposed method has been tested on 15 complex benchmark functions and applied to the bi-objective portfolio optimization problem and compared with other state-of-the-art techniques. Experimental results show that the performance is improved by this hybridization in terms of solution eminence and strong convergence.

Self-adaptively Commensal Learning-based Jaya Algorithm with Multi-populations and its Application

2021 ◽  
Author(s):  
Zuanjia Xie ◽  
Chunliang Zhang ◽  
Haibin Ouyang ◽  
Steven Li ◽  
Liqun Gao
Keyword(s):  
Learning Strategy ◽  
Optimization Problems ◽  
State Of The Art ◽  
Global Optimum ◽  
Benchmark Problems ◽  
Series System ◽  
Jaya Algorithm ◽  
Roulette Wheel Selection ◽  
Roulette Wheel ◽  
Distribution Scheme

Abstract Jaya algorithm is an advanced optimization algorithm, which has been applied to many real-world optimization problems. Jaya algorithm has better performance in some optimization field. However, Jaya algorithm exploration capability is not better. In order to enhance exploration capability of the Jaya algorithm, a self-adaptively commensal learning-based Jaya algorithm with multi-populations (Jaya-SCLMP) is presented in this paper. In Jaya-SCLMP, a commensal learning strategy is used to increase the probability of finding the global optimum, in which the person history best and worst information is used to explore new solution area. Moreover, a multi-populations strategy based on Gaussian distribution scheme and learning dictionary is utilized to enhance the exploration capability, meanwhile every sub-population employed three Gaussian distributions at each generation, roulette wheel selection is employed to choose a scheme based on learning dictionary. The performance of Jaya-SCLMP is evaluated based on 28 CEC 2013 unconstrained benchmark problems. In addition, three reliability problems, i.e. complex (bridge) system, series system and series-parallel system are selected. Compared with several Jaya variants and several state-of-the-art other algorithms, the experimental results reveal that Jaya-SCLMP is effective.

scholarly journals A Study on Scalable Representations for Evolutionary Optimization of Ground Structures

2012 ◽  
Vol 20 (3) ◽  
pp. 453-472 ◽  
Author(s):  
Alexandre Devert ◽  
Thomas Weise ◽  
Ke Tang
Keyword(s):  
State Of The Art ◽  
Computational Cost ◽  
Global Optimum ◽  
Design Parameters ◽  
Optimization Scheme ◽  
Design Problems ◽  
Truss Design ◽  
Objective Value ◽  
Ground Structures ◽  
2D Space

This paper presents a comparative study of two indirect solution representations, a generative and an ontogenic one, on a set of well-known 2D truss design problems. The generative representation encodes the parameters of a trusses design as a mapping from a 2D space. The ontogenic representation encodes truss design parameters as a local truss transformation iterated several times, starting from a trivial initial truss. Both representations are tested with a naive evolution strategy based optimization scheme, as well as the state of the art HyperNEAT approach. We focus both on the best objective value obtained and the computational cost to reach a given level of optimality. The study shows that the two solution representations behave very differently. For experimental settings with equal complexity, with the same optimization scheme and settings, the generative representation provides results which are far from optimal, whereas the ontogenic representation delivers near-optimal solutions. The ontogenic representation is also much less computationally expensive than a direct representation until very close to the global optimum. The study questions the scalability of the generative representations, while the results for the ontogenic representation display much better scalability.

Uncertainty characterization of the orthogonal Procrustes problem with arbitrary covariance matrices

2017 ◽  
Vol 61 ◽  
pp. 210-220 ◽  
Author(s):  
Pedro Lourenço ◽  
Bruno J. Guerreiro ◽  
Pedro Batista ◽  
Paulo Oliveira ◽  
Carlos Silvestre
Keyword(s):  
Covariance Matrices ◽  
Uncertainty Characterization ◽  
Orthogonal Procrustes Problem ◽  
Procrustes Problem

scholarly journals Self-Directed Online Machine Learning for Topology Optimization

2021 ◽  
Author(s):  
Changyu Deng ◽  
Yizhou Wang ◽  
Can Qin ◽  
Wei Lu
Keyword(s):  
Topology Optimization ◽  
Optimization Problems ◽  
State Of The Art ◽  
Computational Cost ◽  
Region Of Interest ◽  
Global Optimum ◽  
Training Data ◽  
Computational Time ◽  
Minimization Problems ◽  
Design Variables

Abstract Topology optimization by optimally distributing materials in a given domain requires gradient-free optimizers to solve highly complicated problems. However, with hundreds of design variables or more involved, solving such problems would require millions of Finite Element Method (FEM) calculations whose computational cost is huge and impractical. Here we report a Self-directed Online Learning Optimization (SOLO) which integrates Deep Neural Network (DNN) with FEM calculations. A DNN learns and substitutes the objective as a function of design variables. A small number of training data is generated dynamically based on the DNN's prediction of the global optimum. The DNN adapts to the new training data and gives better prediction in the region of interest until convergence. Our algorithm was tested by compliance minimization problems and fluid-structure optimization problems. It reduced the computational time by 2 ~ 5 orders of magnitude compared with directly using heuristic methods, and outperformed all state-of-the-art algorithms tested in our experiments. This approach enables solving large multi-dimensional optimization problems.

scholarly journals Near-Optimal Graph Signal Sampling by Pareto Optimization

Sensors ◽  
2021 ◽  
Vol 21 (4) ◽  
pp. 1415
Author(s):  
Dongqi Luo ◽  
Binqiang Si ◽  
Saite Zhang ◽  
Fan Yu ◽  
Jihong Zhu
Keyword(s):  
State Of The Art ◽  
Greedy Algorithms ◽  
Empirical Studies ◽  
Subset Selection ◽  
Reconstruction Error ◽  
Pareto Optimization ◽  
Signal Sampling ◽  
Approximation Bound ◽  
Sampling Problem ◽  
Optimal Graph

In this paper, we focus on the bandlimited graph signal sampling problem. To sample graph signals, we need to find small-sized subset of nodes with the minimal optimal reconstruction error. We formulate this problem as a subset selection problem, and propose an efficient Pareto Optimization for Graph Signal Sampling (POGSS) algorithm. Since the evaluation of the objective function is very time-consuming, a novel acceleration algorithm is proposed in this paper as well, which accelerates the evaluation of any solution. Theoretical analysis shows that POGSS finds the desired solution in quadratic time while guaranteeing nearly the best known approximation bound. Empirical studies on both Erdos-Renyi graphs and Gaussian graphs demonstrate that our method outperforms the state-of-the-art greedy algorithms.

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