Robust surface estimation in multi-response multistage statistical optimization problems

2017 ◽  
Vol 47 (3) ◽  
pp. 762-782 ◽  
Author(s):  
Amir Moslemi ◽  
Mirmehdi Seyyed-Esfahani ◽  
Seyed Taghi Akhavan Niaki
Keyword(s):  
Optimization Problems ◽  
Statistical Optimization ◽  
Surface Estimation

scholarly journals Mathematical relations for constructing an algorithm for estimating signal parameters under conditions of constraints

2021 ◽  
pp. 153-156
Author(s):  
Я.Я. Эглит ◽  
К.Я. Эглите ◽  
А.А. Ковтун ◽  
Д.А. Глушко
Keyword(s):  
Transport System ◽  
Optimization Problems ◽  
Inequality Constraint ◽  
Statistical Optimization ◽  
Computing Environment ◽  
Dummy Variables ◽  
Signal Parameters ◽  
Main Production ◽  
Mathematical Relationships ◽  
Mathematical Relations

Статья посвящена разработке математических соотношений для построения алгоритма оценивания параметров сигналов в условиях ограничений. При работе транспортной системы возникают довольно сложные проблемы, которые связаны с необходимостью проведения оценки принятых параметров с требованиями соблюдения имеющихся ограничений. Ограничения могут представлять собой как равенства, так и неравенства. Поскольку ограничения-неравенства могут быть сведены путём добавления фиктивных переменных к условиям, а также их можно проверить по шагам, переводя в состав равенства, в статье разработан алгоритм, позволяющий иметь ограничения-равенства. Данная задача относится к классу статистических проблем оптимизации. Для ее решения использованы стандартные функции из подкаталога "optimization" вычислительной среды MatLAB. Построение такого алгоритма даст возможность не только уменьшить складские расходы, но и сократить основное производственное время. The article is devoted to the development of mathematical relationships for constructing an algorithm for estimating signal parameters under constraints. During the operation of the transport system, rather complex problems arise, which are associated with the need to assess the adopted parameters with the requirements of compliance with the existing restrictions. Constraints can be either equality or inequality. Since the inequality constraint can be reduced by adding dummy variables to the equality conditions, and they can also be checked step by step, transforming them into equality, we will develop an algorithm that allows us to have equality constraints. This task belongs to the class of statistical optimization problems. To solve it, standard functions from the "optimization" subdirectory of the MatLAB computing environment will be used. The construction of such an algorithm will make it possible not only to reduce storage costs, but also to reduce the main production time.

scholarly journals Some Notes on Concordance between Optimization and Statistics

2019 ◽  
Vol 2019 ◽  
pp. 1-6
Author(s):  
Weiyan Mu ◽  
Qiuyue Wei ◽  
Shifeng Xiong
Keyword(s):  
Maximum Likelihood ◽  
General Framework ◽  
Optimization Problem ◽  
Theoretical Study ◽  
Optimization Problems ◽  
Likelihood Estimation ◽  
Statistical Optimization ◽  
Comparison Theorems ◽  
Engineering Problems ◽  
Statistical Sense

Many engineering problems require solutions to statistical optimization problems. When the global solution is hard to attain, engineers or statisticians always use the better solution because we intuitively believe a principle, called better solution principle (BSP) in this paper, that a better solution to a statistical optimization problem also has better statistical properties of interest. This principle displays some concordance between optimization and statistics and is expected to widely hold. Since theoretical study on BSP seems to be neglected by statisticians, this paper presents a primary discussion on BSP within a relatively general framework. We demonstrate two comparison theorems as the key results of this paper. Their applications to maximum likelihood estimation are presented. It can be seen that BSP for this problem holds under reasonable conditions; i.e., an estimator with greater likelihood is better in some statistical sense.

Comparison of Meta-heuristic Algorithms on Benchmark Functions

2019 ◽  
Vol 2 (3) ◽  
pp. 508-517
Author(s):  
FerdaNur Arıcı ◽  
Ersin Kaya
Keyword(s):  
Heuristic Algorithms ◽  
Optimization Problems ◽  
Search Algorithm ◽  
Optimization Algorithms ◽  
Gravitational Search Algorithm ◽  
Differential Evolution Algorithm ◽  
Population Based ◽  
Time Interval ◽  
Bee Colony ◽  
Different Characteristics

Optimization is a process to search the most suitable solution for a problem within an acceptable time interval. The algorithms that solve the optimization problems are called as optimization algorithms. In the literature, there are many optimization algorithms with different characteristics. The optimization algorithms can exhibit different behaviors depending on the size, characteristics and complexity of the optimization problem. In this study, six well-known population based optimization algorithms (artificial algae algorithm - AAA, artificial bee colony algorithm - ABC, differential evolution algorithm - DE, genetic algorithm - GA, gravitational search algorithm - GSA and particle swarm optimization - PSO) were used. These six algorithms were performed on the CEC’17 test functions. According to the experimental results, the algorithms were compared and performances of the algorithms were evaluated.

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