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.

Multi-Dimensional Optimization of Groove Parameters in Gas Film Seal

2011 ◽  
Vol 199-200 ◽  
pp. 1303-1307
Author(s):  
Gang Ma ◽  
Xiu Hua Li ◽  
Xin Min Shen
Keyword(s):  
Steady State ◽  
Objective Function ◽  
Optimization Design ◽  
Objective Function Value ◽  
Optimization Method ◽  
Geometric Features ◽  
One Dimensional ◽  
Particle Swarm Intelligence ◽  
Swarm Intelligence Algorithm ◽  
Dimensional Optimization

Groove parameters in gas film seal with grooved interface make an obvious impact on the performance of seal system. There are many parameters to describe the geometric features of the groove. In general, a big limitation exists in one-dimensional optimization of groove geometry. Based on particle swarm intelligence algorithm, this article proposed and carried out multi-dimensional optimization of groove geometry in gas film seal, regarded the groove geometry parameters as components of the particle, completed numerical solution of the objective function for the seal performance, and obtained better groove geometry parameters. The example showed that the effect that every geometry dimension plays on the steady-state characteristics of cylindrical gas film seal is not independent, and the multi-dimensional optimization method effectively improves the results of the objective function value. The proposed method can be used for the dimensional optimization design of groove geometry in both cylinder and face gas film seal.

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 Global Optimization for Sum of Linear Ratios Problem Using New Pruning Technique

2008 ◽  
Vol 2008 ◽  
pp. 1-13 ◽  
Author(s):  
Hongwei Jiao ◽  
Qigao Feng ◽  
Peiping Shen ◽  
Yunrui Guo
Keyword(s):  
Global Optimization ◽  
Optimization Algorithm ◽  
Global Minimum ◽  
Linearization Method ◽  
Linear Constraints ◽  
Feasible Region ◽  
Global Optimization Algorithm ◽  
Equivalent Problem ◽  
Successive Refinement ◽  
Pruning Technique

A global optimization algorithm is proposed for solving sum of general linear ratios problem (P) using new pruning technique. Firstly, an equivalent problem (P1) of the (P) is derived by exploiting the characteristics of linear constraints. Then, by utilizing linearization method the relaxation linear programming (RLP) of the (P1) can be constructed and the proposed algorithm is convergent to the global minimum of the (P) through the successive refinement of the linear relaxation of feasible region and solutions of a series of (RLP). Then, a new pruning technique is proposed, this technique offers a possibility to cut away a large part of the current investigated feasible region by the optimization algorithm, which can be utilized as an accelerating device for global optimization of problem (P). Finally, the numerical experiments are given to illustrate the feasibility of the proposed algorithm.

Global Optimization Using the Multistart Method

1993 ◽  
Vol 115 (4) ◽  
pp. 770-775 ◽  
Author(s):  
P. Jain ◽  
A. M. Agogino
Keyword(s):  
Global Optimization ◽  
Vector Quantization ◽  
Computation Time ◽  
Sphere Packing ◽  
Optimization Method ◽  
Global Optimum ◽  
Feasible Region ◽  
Test Problems ◽  
Highly Nonlinear ◽  
Nonlinear Mechanical

Multistart is a stochastic global optimization method for finding the global optimum of highly nonlinear mechanical problems. In this paper we introduce and develop a variant of the multistart method in which a fraction of the sample points in the feasible region with smallest function value are clustered using the Vector Quantization technique. The theories of lattices and sphere packing are used to define optimal lattices. These lattices are optimal with respect to quantization error and are used as code points for vector quantization. The implementation of these ideas has resulted in the VQ-multistart algorithm for finding the global optimum with substantial reductions in both the incore memory requirements and the computation time. We solve several mathematical test problems and a mechanical optimal design problem using the VQ-multistart algorithm.

Taboo evolutionary programming: a new method of global optimization

2006 ◽  
Vol 462 (2076) ◽  
pp. 3613-3627 ◽  
Author(s):  
Mingjun Ji ◽  
Jacek Klinowski
Keyword(s):  
Global Optimization ◽  
Global Minimum ◽  
Single Point ◽  
Evolutionary Programming ◽  
Optimization Method ◽  
Efficient Global Optimization ◽  
Benchmark Problems ◽  
Single Point Mutation ◽  
Central Idea ◽  
Real World Problems

We introduce taboo evolutionary programming, a very efficient global optimization method which combines features of single-point mutation evolutionary programming (SPMEP) and taboo search. As demonstrated by solving 18 benchmark problems, the algorithm is not trapped in local minima and quickly approaches the global minimum. The results are superior to those from SPMEP, fast evolutionary programming and generalized evolutionary programming. The method is easily applicable to real-world problems, and the central idea may be introduced into other algorithms.

Application of Genetic Algorithm to Minimize the Number of Objects Processed and Setup in a One-Dimensional Cutting Stock Problem

2013 ◽  
pp. 32-45
Author(s):  
Julliany Sales Brandão ◽  
Alessandra Martins Coelho ◽  
João Flávio V. Vasconcellos ◽  
Luiz Leduíno de Salles Neto ◽  
André Vieira Pinto
Keyword(s):  
Genetic Algorithm ◽  
Objective Function ◽  
Model Problem ◽  
Cutting Stock Problem ◽  
Cutting Stock ◽  
Computational Results ◽  
New Approach ◽  
One Dimensional ◽  
The One

This paper presents the application of the one new approach using Genetic Algorithm in solving One-Dimensional Cutting Stock Problems in order to minimize two objectives, usually conflicting, i.e., the number of processed objects and setup while simultaneously treating them as a single goal. The model problem, the objective function, the method denominated SingleGA10 and the steps used to solve the problem are also presented. The obtained results of the SingleGA10 are compared to the following methods: SHP, Kombi234, ANLCP300 and Symbio10, found in literature, verifying its capacity to find feasible and competitive solutions. The computational results show that the proposed method, which only uses a genetic algorithm to solve these two objectives inversely related, provides good results.

Reply by authors to discussion by M. Al‐Chalabi

Geophysics ◽  
1974 ◽  
Vol 39 (5) ◽  
pp. 693-694
Author(s):  
P. H. McGrath ◽  
P. J. Hood
Keyword(s):  
Objective Function ◽  
Parameter Space ◽  
Global Minimum ◽  
Optimization Methods ◽  
Optimization Method ◽  
Objective Functions

The success of any optimization method is primarily related to the smoothness and simplicity of the objective function in parameter space. Most optimization methods are successful when used with well‐behaved objective functions. As the complexity of the objective function in parameter space increases, much more sophisticated optimization strategies are required to assure convergence to an absolute (global) minimum.

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