On bayes approach to univariate global optimization

2012 ◽  
Author(s):  
Leonidas Sakalauskas ◽  
Jurgis Susinskas
Keyword(s):  
Computer Simulation ◽  
Global Optimization ◽  
Objective Function ◽  
Optimization Method ◽  
Continuous Functions ◽  
Likelihood Method ◽  
Uhlenbeck Process ◽  
Ornstein Uhlenbeck Process ◽  
Learning Set ◽  
The Bayesian Approach

In this paper the Bayesian approach to global optimization of univariate continuous functions is developed, when the objective function is modelled by Ornstein-Uhlenbeck process. The parameters of model of function to be optimised are calibrated by maximal likelihood method using the learning set. The resulting optimization algorithm is rather simple and consists of reselection of values of expected step utility function, which maximizes at each step the expected increment of minimal observed value of the objective function. The convergence of method developed is studied by theoretical and experimental way. Efficiency of the Bayes optimization method created is studied by computer simulation, too.

Differential Evolution with Self-Adaptation

2011 ◽  
pp. 488-493 ◽  
Author(s):  
Janez Brest
Keyword(s):  
Global Optimization ◽  
Differential Evolution ◽  
Objective Function ◽  
Optimization Method ◽  
Control Parameters ◽  
Research Areas ◽  
De Algorithm ◽  
Practical Engineering ◽  
Self Adaptation ◽  
Self Adaptive

Many practical engineering applications can be formulated as a global optimization problem, in which objective function has many local minima, and derivatives of the objective function are unavailable. Differential Evolution (DE) is a floating-point encoding evolutionary algorithm for global optimization over continuous spaces (Storn & Price, 1997) (Liu & Lampinen, 2005) (Price, Storn & Lampinen, 2005) (Feoktistov, 2006). Nowadays it is used as a powerful global optimization method within a wide range of research areas. Recent researches indicate that self-adaptive DE algorithms are considerably better than the original DE algorithm. The necessity of changing control parameters during the optimization process is also confirmed based on the experiments in (Brest, Greiner, Boškovic, Mernik, Žumer, 2006a). DE with self-adaptive control parameters has already been presented in (Brest et al., 2006a). This chapter presents self-adaptive approaches that were recently proposed for control parameters in DE algorithm.

scholarly journals A GLOBAL OPTIMIZATION METHOD BASED ON THE REDUCED SIMPLICIAL STATISTICAL MODEL

2011 ◽  
Vol 16 (3) ◽  
pp. 451-460 ◽  
Author(s):  
Antanas Žilinskas ◽  
Julius Žilinskas
Keyword(s):  
Global Optimization ◽  
Statistical Model ◽  
Objective Function ◽  
Global Minimum ◽  
Objective Function Value ◽  
Optimization Method ◽  
Feasible Region ◽  
Multidimensional Space ◽  
One Dimensional ◽  
The One

A simplicial statistical model of multimodal functions is used to construct a global optimization algorithm. The search for the global minimum in the multidimensional space is reduced to the search over the edges of simplices covering the feasible region combined with the refinement of the cover. The refinement is performed by subdivision of selected simplices taking into account the point where the objective function value has been computed at the current iteration. For the search over the edges the one-dimensional P-algorithm based on the statistical smooth function model is adapted. Differently from the recently proposed algorithm here the statistical model is used for modelling the behaviour of the objective function not over the whole simplex but only over its edges. Testing results of the proposed algorithm are included.

scholarly journals Optimal Placement and Sizing of D-STATCOM in Radial and Meshed Distribution Networks Using a Discrete-Continuous Version of the Genetic Algorithm

Electronics ◽  
2021 ◽  
Vol 10 (12) ◽  
pp. 1452
Author(s):  
Cristian Mateo Castiblanco-Pérez ◽  
David Esteban Toro-Rodríguez ◽  
Oscar Danilo Montoya ◽  
Diego Armando Giral-Ramírez
Keyword(s):  
Genetic Algorithm ◽  
Objective Function ◽  
Programming Model ◽  
Distribution Networks ◽  
Optimization Method ◽  
Optimal Placement ◽  
Mixed Integer ◽  
Power Balance ◽  
Continuous Version ◽  
Discrete Part

In this paper, we propose a new discrete-continuous codification of the Chu–Beasley genetic algorithm to address the optimal placement and sizing problem of the distribution static compensators (D-STATCOM) in electrical distribution grids. The discrete part of the codification determines the nodes where D-STATCOM will be installed. The continuous part of the codification regulates their sizes. The objective function considered in this study is the minimization of the annual operative costs regarding energy losses and installation investments in D-STATCOM. This objective function is subject to the classical power balance constraints and devices’ capabilities. The proposed discrete-continuous version of the genetic algorithm solves the mixed-integer non-linear programming model that the classical power balance generates. Numerical validations in the 33 test feeder with radial and meshed configurations show that the proposed approach effectively minimizes the annual operating costs of the grid. In addition, the GAMS software compares the results of the proposed optimization method, which allows demonstrating its efficiency and robustness.

scholarly journals Global optimization based on active preference learning with radial basis functions

2020 ◽  
Author(s):  
Alberto Bemporad ◽  
Dario Piga
Keyword(s):  
Global Optimization ◽  
Objective Function ◽  
Decision Maker ◽  
Optimization Problems ◽  
Global Optimum ◽  
Bayesian Optimization ◽  
Preference Learning ◽  
Global Optimizer ◽  
Radial Basis ◽  
Decision Vector

AbstractThis paper proposes a method for solving optimization problems in which the decision-maker cannot evaluate the objective function, but rather can only express a preference such as “this is better than that” between two candidate decision vectors. The algorithm described in this paper aims at reaching the global optimizer by iteratively proposing the decision maker a new comparison to make, based on actively learning a surrogate of the latent (unknown and perhaps unquantifiable) objective function from past sampled decision vectors and pairwise preferences. A radial-basis function surrogate is fit via linear or quadratic programming, satisfying if possible the preferences expressed by the decision maker on existing samples. The surrogate is used to propose a new sample of the decision vector for comparison with the current best candidate based on two possible criteria: minimize a combination of the surrogate and an inverse weighting distance function to balance between exploitation of the surrogate and exploration of the decision space, or maximize a function related to the probability that the new candidate will be preferred. Compared to active preference learning based on Bayesian optimization, we show that our approach is competitive in that, within the same number of comparisons, it usually approaches the global optimum more closely and is computationally lighter. Applications of the proposed algorithm to solve a set of benchmark global optimization problems, for multi-objective optimization, and for optimal tuning of a cost-sensitive neural network classifier for object recognition from images are described in the paper. MATLAB and a Python implementations of the algorithms described in the paper are available at http://cse.lab.imtlucca.it/~bemporad/glis.

scholarly journals Topology Optimization of Hard-Coating Thin Plate for Maximizing Modal Loss Factors

Coatings ◽  
2021 ◽  
Vol 11 (7) ◽  
pp. 774
Author(s):  
Haitao Luo ◽  
Rong Chen ◽  
Siwei Guo ◽  
Jia Fu
Keyword(s):  
Topology Optimization ◽  
Objective Function ◽  
Composite Plates ◽  
Optimization Method ◽  
Hard Coating ◽  
Design Variables ◽  
Coating Composite ◽  
Damping Materials ◽  
Topology Optimization Method ◽  
Loss Factors

At present, hard coating structures are widely studied as a new passive damping method. Generally, the hard coating material is completely covered on the surface of the thin-walled structure, but the local coverage cannot only achieve better vibration reduction effect, but also save the material and processing costs. In this paper, a topology optimization method for hard coated composite plates is proposed to maximize the modal loss factors. The finite element dynamic model of hard coating composite plate is established. The topology optimization model is established with the energy ratio of hard coating layer to base layer as the objective function and the amount of damping material as the constraint condition. The sensitivity expression of the objective function to the design variables is derived, and the iteration of the design variables is realized by the Method of Moving Asymptote (MMA). Several numerical examples are provided to demonstrate that this method can obtain the optimal layout of damping materials for hard coating composite plates. The results show that the damping materials are mainly distributed in the area where the stored modal strain energy is large, which is consistent with the traditional design method. Finally, based on the numerical results, the experimental study of local hard coating composites plate is carried out. The results show that the topology optimization method can significantly reduce the frequency response amplitude while reducing the amount of damping materials, which shows the feasibility and effectiveness of the method.

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