On the role of orthonormality of sensitivity functions in parameter optimization problems

Automatica ◽  
1969 ◽  
Vol 5 (4) ◽  
pp. 513-517 ◽  
Author(s):  
S.P. Bingulac
2021 ◽  
Author(s):  
Leila Zahedi ◽  
Farid Ghareh Mohammadi ◽  
M. Hadi Amini

Machine learning techniques lend themselves as promising decision-making and analytic tools in a wide range of applications. Different ML algorithms have various hyper-parameters. In order to tailor an ML model towards a specific application, a large number of hyper-parameters should be tuned. Tuning the hyper-parameters directly affects the performance (accuracy and run-time). However, for large-scale search spaces, efficiently exploring the ample number of combinations of hyper-parameters is computationally challenging. Existing automated hyper-parameter tuning techniques suffer from high time complexity. In this paper, we propose HyP-ABC, an automatic innovative hybrid hyper-parameter optimization algorithm using the modified artificial bee colony approach, to measure the classification accuracy of three ML algorithms, namely random forest, extreme gradient boosting, and support vector machine. Compared to the state-of-the-art techniques, HyP-ABC is more efficient and has a limited number of parameters to be tuned, making it worthwhile for real-world hyper-parameter optimization problems. We further compare our proposed HyP-ABC algorithm with state-of-the-art techniques. In order to ensure the robustness of the proposed method, the algorithm takes a wide range of feasible hyper-parameter values, and is tested using a real-world educational dataset.


2001 ◽  
Vol 7 (2) ◽  
pp. 106-114
Author(s):  
Ela Chraptovič ◽  
Juozas Atkočiūnas

The theory of mathematical programming widely spread as a method of a solution of extreme problems. It accompanies the study of plastic theory problem from its posing up to final solution. However, here again from our point of view not all possibilities are realized. Unfortunately, the use of mathematical programming as an instrument of a numerical solution for structural analysis frequently is also restricted by that. The possibilities of mechanical interpretation of optimality criteria of applied algorithms are not uncovered. The global solution of the problem of mathematical programming exists, if Kuhn-Tucker conditions are satisfied. These conditions do not depend on the applied algorithm of a problem solution. The identity of Kuhn-Tucker conditions with a optimality criteria of Rosen algorithm is finding out in this research. The role of a design matrix for the creating of strain compatibility equations is clarified. The Kuhn-Tucker conditions mean the residual strain compatibility equations in analysis of elastic-plastic systems. It is proved in the article that for problems of limiting equilibrium the Kuhn-Tucker conditions include the dependences of the associated law of plastic flow. The Kuhn-Tucker conditions together with limitations of a source problem of account represent a complete set of dependences of the theory of shakedown. The correct mathematical and mechanical interpretation of the Kuhn-Tucker conditions allows to refuse a direct solution of a dual problem of mathematical programming. It makes easier the solution of optimization problems of structures at shakedown.


2019 ◽  
Vol 184 (3) ◽  
pp. 762-780 ◽  
Author(s):  
Jae Youn Ahn ◽  
Sebastian Fuchs

AbstractIn the present paper, we study extreme negative dependence focussing on the concordance order for copulas. With the absence of a least element for dimensions $$d\ge 3$$d≥3, the set of all minimal elements in the collection of all copulas turns out to be a natural and quite important extreme negative dependence concept. We investigate several sufficient conditions, and we provide a necessary condition for a copula to be minimal. The sufficient conditions are related to the extreme negative dependence concept of d-countermonotonicity and the necessary condition is related to the collection of all copulas minimizing multivariate Kendall’s tau. The concept of minimal copulas has already been proved to be useful in various continuous and concordance order preserving optimization problems including variance minimization and the detection of lower bounds for certain measures of concordance. We substantiate this key role of minimal copulas by showing that every continuous and concordance order preserving functional on copulas is minimized by some minimal copula, and, in the case the continuous functional is even strictly concordance order preserving, it is minimized by minimal copulas only. Applying the above results, we may conclude that every minimizer of Spearman’s rho is also a minimizer of Kendall’s tau.


1999 ◽  
Vol 7 (1) ◽  
pp. 19-44 ◽  
Author(s):  
Slawomir Koziel ◽  
Zbigniew Michalewicz

During the last five years, several methods have been proposed for handling nonlinear constraints using evolutionary algorithms (EAs) for numerical optimization problems. Recent survey papers classify these methods into four categories: preservation of feasibility, penalty functions, searching for feasibility, and other hybrids. In this paper we investigate a new approach for solving constrained numerical optimization problems which incorporates a homomorphous mapping between n-dimensional cube and a feasible search space. This approach constitutes an example of the fifth decoder-based category of constraint handling techniques. We demonstrate the power of this new approach on several test cases and discuss its further potential.


2002 ◽  
Vol 10 (4) ◽  
pp. 371-395 ◽  
Author(s):  
Kalyanmoy Deb ◽  
Ashish Anand ◽  
Dhiraj Joshi

Due to increasing interest in solving real-world optimization problems using evolutionary algorithms (EAs), researchers have recently developed a number of real-parameter genetic algorithms (GAs). In these studies, the main research effort is spent on developing an efficient recombination operator. Such recombination operators use probability distributions around the parent solutions to create an offspring. Some operators emphasize solutions at the center of mass of parents and some around the parents. In this paper, we propose a generic parent-centric recombination operator (PCX) and a steady-state, elite-preserving, scalable, and computationally fast population-alteration model (we call the G3 model). The performance of the G3 model with the PCX operator is investigated on three commonly used test problems and is compared with a number of evolutionary and classical optimization algorithms including other real-parameter GAs with the unimodal normal distribution crossover (UNDX) and the simplex crossover (SPX) operators, the correlated self-adaptive evolution strategy, the covariance matrix adaptation evolution strategy (CMA-ES), the differential evolution technique, and the quasi-Newton method. The proposed approach is found to consistently and reliably perform better than all other methods used in the study. A scale-up study with problem sizes up to 500 variables shows a polynomial computational complexity of the proposed approach. This extensive study clearly demonstrates the power of the proposed technique in tackling real-parameter optimization problems.


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