scholarly journals A global optimization paradigm based on change of measures

2015 ◽  
Vol 2 (7) ◽  
pp. 150123 ◽  
Author(s):  
Saikat Sarkar ◽  
Debasish Roy ◽  
Ram Mohan Vasu
Keyword(s):  
Global Optimization ◽  
Random Perturbation ◽  
Evolutionary Optimization ◽  
Global Optimum ◽  
Global Search ◽  
Design Variables ◽  
Change Of Measures ◽  
Basic Ideas ◽  
Set Up ◽  
Optimization Schemes

A global optimization framework, COMBEO (Change Of Measure Based Evolutionary Optimization), is proposed. An important aspect in the development is a set of derivative-free additive directional terms, obtainable through a change of measures en route to the imposition of any stipulated conditions aimed at driving the realized design variables (particles) to the global optimum. The generalized setting offered by the new approach also enables several basic ideas, used with other global search methods such as the particle swarm or the differential evolution, to be rationally incorporated in the proposed set-up via a change of measures. The global search may be further aided by imparting to the directional update terms additional layers of random perturbations such as ‘scrambling’ and ‘selection’. Depending on the precise choice of the optimality conditions and the extent of random perturbation, the search can be readily rendered either greedy or more exploratory. As numerically demonstrated, the new proposal appears to provide for a more rational, more accurate and, in some cases, a faster alternative to many available evolutionary optimization schemes.

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 An Algorithm for Global Optimization Inspired by Collective Animal Behavior

2012 ◽  
Vol 2012 ◽  
pp. 1-24 ◽  
Author(s):  
Erik Cuevas ◽  
Mauricio González ◽  
Daniel Zaldivar ◽  
Marco Pérez-Cisneros ◽  
Guillermo García
Keyword(s):  
Global Optimization ◽  
Animal Behavior ◽  
Food Source ◽  
Collective Motion ◽  
Global Optimum ◽  
Migration Routes ◽  
Collective Behaviors ◽  
Biological Laws ◽  
Harvesting Efficiency ◽  
Collective Animal Behavior

A metaheuristic algorithm for global optimization called the collective animal behavior (CAB) is introduced. Animal groups, such as schools of fish, flocks of birds, swarms of locusts, and herds of wildebeest, exhibit a variety of behaviors including swarming about a food source, milling around a central locations, or migrating over large distances in aligned groups. These collective behaviors are often advantageous to groups, allowing them to increase their harvesting efficiency, to follow better migration routes, to improve their aerodynamic, and to avoid predation. In the proposed algorithm, the searcher agents emulate a group of animals which interact with each other based on the biological laws of collective motion. The proposed method has been compared to other well-known optimization algorithms. The results show good performance of the proposed method when searching for a global optimum of several benchmark functions.

scholarly journals Modeling, Simulation and Uncertain Optimization of the Gun Engraving System

Mathematics ◽  
2021 ◽  
Vol 9 (4) ◽  
pp. 398
Author(s):  
Tong Xin ◽  
Guolai Yang ◽  
Fengjie Xu ◽  
Quanzhao Sun ◽  
Alexandi Minak
Keyword(s):  
Performance Evaluation ◽  
Optimal Design ◽  
Resistance Force ◽  
Gas Temperature ◽  
Evaluation Indexes ◽  
Uncertain Optimization ◽  
Design Variables ◽  
Set Up ◽  
Rotating Band ◽  
Percent Decrease

The system designed to accomplish the engraving process of a rotating band projectile is called the gun engraving system. To obtain higher performance, the optimal design of the size parameters of the gun engraving system was carried out. First, a fluid–solid coupling computational model of the gun engraving system was built and validated by the gun launch experiment. Subsequently, three mathematic variable values, like performance evaluation indexes, were obtained. Second, a sensitivity analysis was performed, and four high-influence size parameters were selected as design variables. Finally, an optimization model based on the affine arithmetic was set up and solved, and then the optimized intervals of performance evaluation indexes were obtained. After the optimal design, the percent decrease of the maximum engraving resistance force ranged from 6.34% to 18.24%; the percent decrease of the maximum propellant gas temperature ranged from 1.91% to 7.45%; the percent increase of minimum pressure wave of the propellant gas ranged from 0.12% to 0.36%.

scholarly journals A bat optimization algorithm with moderate orientation and perturbation of trend

2021 ◽  
Vol 15 ◽  
pp. 174830262110084
Author(s):  
Jingsen Liu ◽  
Hongyuan Ji ◽  
Qingqing Liu ◽  
Yu Li
Keyword(s):  
Local Search ◽  
Optimization Algorithm ◽  
Random Perturbation ◽  
Bat Algorithm ◽  
Local Extremum ◽  
Global Search ◽  
Deep Mining ◽  
Nonlinear Variation ◽  
Optimal Value ◽  
Search Stage

In order to improve the convergence speed and optimization accuracy of the bat algorithm, a bat optimization algorithm with moderate optimal orientation and random perturbation of trend is proposed. The algorithm introduces the nonlinear variation factor into the velocity update formula of the global search stage to maintain a high diversity of bat populations, thereby enhanced the global exploration ability of the algorithm. At the same time, in the local search stage, the position update equation is changed, and a strategy that towards optimal value modestly is used to improve the ability of the algorithm to local search for deep mining. Finally, the adaptive decreasing random perturbation is performed on each bat individual that have been updated in position at each generation, which can improve the ability of the algorithm to jump out of the local extremum, and to balance the early global search extensiveness and the later local search accuracy. The simulating results show that the improved algorithm has a faster optimization speed and higher optimization accuracy.

Global Optimization of Atomic Cluster Structures Using Parallel Genetic Algorithms

2005 ◽  
Vol 894 ◽  
Author(s):  
Ofelia Oña ◽  
Victor E. Bazterra ◽  
María C. Caputo ◽  
Marta B. Ferraro ◽  
Julio Facelli
Keyword(s):  
Global Optimization ◽  
Density Functional ◽  
Atomic Clusters ◽  
Medium Size ◽  
Atomic Cluster ◽  
Approximate Methods ◽  
Functional Theory ◽  
Parallel Genetic Algorithms ◽  
Applied Technology ◽  
Optimization Schemes

AbstractThe study of the structure and physical properties of atomic clusters is an extremely active area of research due to their importance, both in fundamental science and in applied technology. For medium size atomic clusters most of the structures reported today have been obtained by local optimizations of plausible structures using DFT (Density Functional Theory) methods and/or by global optimizations in which much more approximate methods are used to calculate the cluster’s energetics. Our previous work shows that these approaches can not be reliably used to study atomic cluster structures and that approaches based on global optimization schemes are needed. In this paper, we report the implementation and application of a parallel Genetic Algorithm (GA) to predict the structure of medium size atomic clusters.

scholarly journals REALISTIC MODELING OF STRONGLY CORRELATED ELECTRON SYSTEMS: AN INTRODUCTION TO THE LDA+DMFT APPROACH

2001 ◽  
Vol 15 (19n20) ◽  
pp. 2611-2625 ◽  
Author(s):  
K. HELD ◽  
I. A. NEKRASOV ◽  
N. BLÜMER ◽  
V. I. ANISIMOV ◽  
D. VOLLHARDT
Keyword(s):  
Quantum Monte Carlo ◽  
Local Density ◽  
Mean Field Theory ◽  
Mean Field ◽  
Structure Theory ◽  
Strongly Correlated Electron ◽  
Correlated Electron Systems ◽  
Correlated Electron ◽  
Basic Ideas ◽  
Set Up

The LDA+DMFT approach merges conventional band structure theory in the local density approximation (LDA) with a state-of-the-art many-body technique, the dynamical mean-field theory (DMFT). This new computational scheme has recently become a powerful tool for ab initio investigations of real materials with strong electronic correlations. In this paper an introduction to the basic ideas and the set-up of the LDA+DMFT approach is given. Results for the photoemission spectra of the transition metal oxide La 1-x Sr x TiO 3, obtained by solving the DMFT equations by quantum Monte Carlo (QMC) simulations, are presented and are found to be in very good agreement with experiment. The numerically exact DMFT(QMC) solution is compared with results obtained by two approximative solutions, i.e. the iterative perturbation theory and the non-crossing approximation.

Implementing Business Intelligence in Electricity Markets

2010 ◽  
pp. 283-295
Author(s):  
José Ramón Cancelo ◽  
Antoni Espasa
Keyword(s):  
Electricity Markets ◽  
Business Intelligence ◽  
Explicit Knowledge ◽  
Time Series Data ◽  
Contextual Information ◽  
Electricity Consumption ◽  
Point Of View ◽  
Series Data ◽  
Basic Ideas ◽  
Set Up

The authors elaborate on three basic ideas that should guide the implementation of business intelligence tools. First, the authors advocate for closing the gap between structured information and contextual information. Second, they emphasize the need for adopting the point of view of the organization to assess the relevance of any proposal. In the third place, they remark that any new tool is expected to become a relevant instrument to enhance the learning of the organization and to generate explicit knowledge. To illustrate their point, they discuss how to set up a forecasting support system to predict electricity consumption that converts raw time series data into market intelligence, to meet the needs of a major organization operating at the Spanish electricity markets.

Global search in single-solution-based metaheuristics

2020 ◽  
Vol 54 (3) ◽  
pp. 275-296 ◽  
Author(s):  
Najmeh Sadat Jaddi ◽  
Salwani Abdullah
Keyword(s):  
Search Space ◽  
Population Based ◽  
Global Optimum ◽  
Global Search ◽  
Hill Climbing ◽  
Search Process ◽  
Local Optimum ◽  
Content Type ◽  
Solution Algorithms ◽  
Single Solution

PurposeMetaheuristic algorithms are classified into two categories namely: single-solution and population-based algorithms. Single-solution algorithms perform local search process by employing a single candidate solution trying to improve this solution in its neighborhood. In contrast, population-based algorithms guide the search process by maintaining multiple solutions located in different points of search space. However, the main drawback of single-solution algorithms is that the global optimum may not reach and it may get stuck in local optimum. On the other hand, population-based algorithms with several starting points that maintain the diversity of the solutions globally in the search space and results are of better exploration during the search process. In this paper more chance of finding global optimum is provided for single-solution-based algorithms by searching different regions of the search space.Design/methodology/approachIn this method, different starting points in initial step, searching locally in neighborhood of each solution, construct a global search in search space for the single-solution algorithm.FindingsThe proposed method was tested based on three single-solution algorithms involving hill-climbing (HC), simulated annealing (SA) and tabu search (TS) algorithms when they were applied on 25 benchmark test functions. The results of the basic version of these algorithms were then compared with the same algorithms integrated with the global search proposed in this paper. The statistical analysis of the results proves outperforming of the proposed method. Finally, 18 benchmark feature selection problems were used to test the algorithms and were compared with recent methods proposed in the literature.Originality/valueIn this paper more chance of finding global optimum is provided for single-solution-based algorithms by searching different regions of the search space.

THE KINEMATIC SYNTHESIS OF STEERING MECHANISMS

2000 ◽  
Vol 24 (3-4) ◽  
pp. 453-476 ◽  
Author(s):  
Jin Yao ◽  
Jorge Angeles
Keyword(s):  
Polynomial Equation ◽  
Global Optimum ◽  
Polynomial Equations ◽  
Kinematic Synthesis ◽  
Local Optima ◽  
Speed Reduction ◽  
Design Variables ◽  
Transmission Quality ◽  
Four Bar Linkage ◽  
Maximum Transmission

We propose a computational-kinematics approach based on elimination procedures to synthesize a steering four-bar linkage. In this regard, we aim at minimizing the root-mean square error of the synthesized linkage in meeting the steering condition over a number of linkage configurations within the linkage range of motion. A minimization problem is thus formulated, whose normality conditions lead to two polynomial equations in two unknown design variables. Upon eliminating one of these two variables, a monovariate polynomial equation is obtained, whose roots yield all locally-optimum linkages. From these roots, the global optimum, as well as unfeasible local optima, are readily identified. The global optimum, however, turns out to be impractical because of the large differences in its link lengths, which we refer to as dimensional unbalance. To cope with this drawback, we use a kinematically-equivalent focal mechanism, i.e., a six-bar linkage with an input-output function identical to that of the four-bar linkage. Given that the synthesized linkage requires a rotational input, as opposed to most existing steering linkages, which require a translational input, we propose a spherical four-bar linkage to drive the steering linkage. The spherical linkage is synthesized so as to yield a speed reduction as close as possible to 2:1 and to have a maximum transmission quality.

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