Optimal Clustering

1986 ◽  
Vol 18 (11) ◽  
pp. 1463-1476 ◽  
Author(s):  
K E Rosing ◽  
C S ReVelle
Keyword(s):  
Cluster Analysis ◽  
Objective Function ◽  
Optimization Model ◽  
Total Flow ◽  
Clustering Problem ◽  
Integer Variables ◽  
Central Member ◽  
Realistic Formulation

Cluster analysis can be performed with several models. One method is to seek those clusters for which the total flow between all within-cluster members is a maximum. This model has, until now, been viewed as mathematically difficult because of the presence of products of integer variables in the objective function. In another optimization model of cluster analysis, the p-median, a central member is found for each cluster, so that relationships of cluster members with the various central members are maximized (or minimized). This problem, although mathematically tractable, is a less realistic formulation of the general clustering problem. The formulation of the maximum interflow problem is here transformed in stages into a linear analogue which is economically solvable. Computation experience with the several transformed stages is reported and a practical example of the analysis demonstrated.

COMPARISON OF TWO OPTIMIZATION MODELS FOR CONSTRUCTING PATTERNS IN THE METHOD OF LOGICAL ANALYSIS OF DATA

2020 ◽  
pp. 10-13
Author(s):  
Р.И. Кузьмич ◽  
А.А. Ступина ◽  
С.Н. Ежеманская ◽  
А.П. Шугалей
Keyword(s):  
Objective Function ◽  
Optimization Model ◽  
Logical Analysis ◽  
Optimization Models ◽  
Logical Analysis Of Data

Предлагаются две оптимизационные модели для построения информативных закономерностей. Приводится эмпирическое подтверждение целесообразности использования критерия бустинга в качестве целевой функции оптимизационной модели для получения информативных закономерностей. Информативность, закономерность, критерий бустинга, оптимизационная модель Comparison of two optimization models for constructing patterns in the method of logical analysis of data Two optimization models for constructing informative patterns are proposed. An empirical confirmation of the expediency of using the boosting criterion as an objective function of the optimization model for obtaining informative patterns is given.

Research on the Properties of Coaxality Error Objective Function

2009 ◽  
Vol 16-19 ◽  
pp. 1164-1168 ◽  
Author(s):  
Ping Liu ◽  
San Yang Liu
Keyword(s):  
Euclidean Space ◽  
Objective Function ◽  
Optimization Model ◽  
Dimensional Euclidean Space ◽  
Modern Theory ◽  
Minimal Point ◽  
Zone Method ◽  
Deviation Measurement ◽  
Minimum Zone ◽  
Theoretical Results

The unconstrained optimization model applying to radial deviation measurement is established for assessing coaxality errors by the positioned minimum zone method. The properties of the objective function in the optimization model are thoroughly researched. On the basis of the modern theory of convex functions, it is strictly proved that the objective function is a continuous and non-differentiable and convex function defined on the four-dimensional Euclidean space R4. Therefore, the global minimal value of the objective function is unique and any of its minimal point must be its global minimal point. Thus, any existing optimization algorithm, as long as it is convergent, can be used to solve the objective function to get the wanted values of coaxality errors by the positioned minimum zone assessment. An example is given to verify the theoretical results presented.

A multi-objective optimization model for logistic planning in the crisis response phase

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Mohammad Mahdi Ershadi ◽  
Hossein Shams Shemirani
Keyword(s):  
Objective Function ◽  
Optimization Model ◽  
Crisis Response ◽  
Multi Objective Optimization ◽  
Content Type ◽  
Multi Objective ◽  
Proposed Model ◽  
Different Types ◽  
Response Phase ◽  
Logistic Planning

PurposeProper planning for the response phase of humanitarian relief can significantly prevent many financial and human losses. To this aim, a multi-objective optimization model is proposed in this paper that considers different types of injured people, different vehicles with determining capacities and multi-period logistic planning. This model can be updated based on new information about resources and newly identified injured people.Design/methodology/approachThe main objective function of the proposed model in this paper is minimizing the unsatisfied prioritized injured people in the network. Besides, the total transportation activities of different types of vehicles are considered as another objective function. Therefore, these objectives are optimized hierarchically in the proposed model using the Lexicographic method. This method finds the best value for the first objective function. Then, it tries to optimize transportation activities as the second objective function while maintaining the optimality of the first objective function.FindingsThe performances of the proposed model were analyzed in different cases and its robust approach for different problems was shown within the framework of a case study. Besides, the sensitivity analysis of results shows the logical behavior of the proposed model against various factors.Practical implicationsThe proposed methodology can be applied to find the best response plan for all crises.Originality/valueIn this paper, we have tried to use a multi-objective optimization model to guide and correct response programs to deal with the occurred crisis. This is important because it can help emergency managers to improve their plans.

scholarly journals Cable Tension Analysis Oriented the Enhanced Stiffness of a 3-DOF Joint Module of a Modular Cable-Driven Human-Like Robotic Arm

2020 ◽  
Vol 10 (24) ◽  
pp. 8871
Author(s):  
Kaisheng Yang ◽  
Guilin Yang ◽  
Chi Zhang ◽  
Chinyin Chen ◽  
Tianjiang Zheng ◽  
...  
Keyword(s):  
Objective Function ◽  
Optimization Model ◽  
Human Robot Interaction ◽  
Robotic Arm ◽  
Robot Interaction ◽  
Cable Tension ◽  
Tension Distribution ◽  
Stiffness Model ◽  
Redundantly Actuated ◽  
Objective Function Values

Inspired by the structure of human arms, a modular cable-driven human-like robotic arm (CHRA) is developed for safe human–robot interaction. Due to the unilateral driving properties of the cables, the CHRA is redundantly actuated and its stiffness can be adjusted by regulating the cable tensions. Since the trajectory of the 3-DOF joint module (3DJM) of the CHRA is a curve on Lie group SO(3), an enhanced stiffness model of the 3DJM is established by the covariant derivative of the load to the displacement on SO(3). In this paper, we focus on analyzing the how cable tension distribution problem oriented the enhanced stiffness of the 3DJM of the CHRA for stiffness adjustment. Due to the complexity of the enhanced stiffness model, it is difficult to solve the cable tensions from the desired stiffness analytically. The problem of stiffness-oriented cable tension distribution (SCTD) is formulated as a nonlinear optimization model. The optimization model is simplified using the symmetry of the enhanced stiffness model, the rank of the Jacobian matrix and the equilibrium equation of the 3DJM. Since the objective function is too complicated to compute the gradient, a method based on the genetic algorithm is proposed for solving this optimization problem, which only utilizes the objective function values. A comprehensive simulation is carried out to validate the effectiveness of the proposed method.

An Integer Programming Optimization Model of Container Shipping of Sea-Carriage

2012 ◽  
Vol 220-223 ◽  
pp. 2678-2683
Author(s):  
Bin Wang ◽  
Tao Yang
Keyword(s):  
Integer Programming ◽  
Objective Function ◽  
Optimization Model ◽  
Container Shipping ◽  
Empty Container ◽  
Shipping Company ◽  
Shipping Cost ◽  
Total Profit ◽  
Empty Containers ◽  
The Cost

The paper dose research about the optimization of container shipping of sea –carriage for meeting the goods transport requirement by use of integer programming. Both laden and empty containers are combined into a system. In particular, the effect of special laden container shipping capacity on the shipping plan is investigated. In the model, the objective function is to maximize the total profit of container shipping. The profit caused by laden container shipping minus the cost caused by both laden and empty container shipping equal to the total profit. The constraints to the model include meeting the need of both laden and empty containers, shipping limit to both common and special laden containers , the number of empty container supported. Lingo9.0 is used to solve the model and shipping methods in varied parameters are shown by simulation. The aim of the paper is to provide a reasonable plan of container shipping of sea-carriage, so the container shipping cost of a shipping company can be reduced and the its profit made by container shipping are maximized.

scholarly journals A Bayesian Classifier Learning Algorithm Based on Optimization Model

2013 ◽  
Vol 2013 ◽  
pp. 1-9 ◽  
Author(s):  
Sanyang Liu ◽  
Mingmin Zhu ◽  
Youlong Yang
Keyword(s):  
Objective Function ◽  
Optimization Model ◽  
Learning Algorithm ◽  
Classification Performance ◽  
Bayesian Classifier ◽  
Bayes Classifier ◽  
Independence Assumption ◽  
Maximum Value ◽  
Chi Squared ◽  
Classifier Learning

Naive Bayes classifier is a simple and effective classification method, but its attribute independence assumption makes it unable to express the dependence among attributes and affects its classification performance. In this paper, we summarize the existing improved algorithms and propose a Bayesian classifier learning algorithm based on optimization model (BC-OM). BC-OM uses the chi-squared statistic to estimate the dependence coefficients among attributes, with which it constructs the objective function as an overall measure of the dependence for a classifier structure. Therefore, a problem of searching for an optimal classifier can be turned into finding the maximum value of the objective function in feasible fields. In addition, we have proved the existence and uniqueness of the numerical solution. BC-OM offers a new opinion for the research of extended Bayesian classifier. Theoretical and experimental results show that the new algorithm is correct and effective.

Application of the Structural Topological Optimization in the Column Stability Design

2010 ◽  
Vol 37-38 ◽  
pp. 190-193
Author(s):  
Bing Chuan Bian ◽  
Guan Ming Peng ◽  
Yun Kang Sui
Keyword(s):  
Topology Optimization ◽  
Objective Function ◽  
Optimization Model ◽  
Continuous Mapping ◽  
Rayleigh Quotient ◽  
Mapping Method ◽  
Topological Optimization ◽  
Topological Structures ◽  
Topology Optimization Problem ◽  
Dual Programming

In this paper, according to the ICM (Independent Continuous Mapping) method, the topology optimization problem of continuum structures is solved. The topology optimization model for the continuum structure is constructed, which minimized weight as the objective function and was subjected to the buckling constraints. Based on the Taylor expansion, the filtering function and the Rayleigh quotient, the objective function and the buckling constraint are approximately expressed as the explicit function. The optimization model is translated into a dual programming and solved by the sequence second-order programming. Finally, the compressed bar examples are presented. They verified the length coefficient which is converted into stability bar hinged at both ends, identified the location of bottlenecks in topological structures. According to the results, more reasonable topological structures were given.

scholarly journals Statistical approach to normalization of feature vectors and clustering of mixed datasets

2012 ◽  
Vol 468 (2145) ◽  
pp. 2630-2651 ◽  
Author(s):  
Maria M. Suarez-Alvarez ◽  
Duc-Truong Pham ◽  
Mikhail Y. Prostov ◽  
Yuriy I. Prostov
Keyword(s):  
Data Mining ◽  
Cluster Analysis ◽  
Objective Function ◽  
Categorical Data ◽  
Statistical Approach ◽  
Objective Functions ◽  
Feature Vectors ◽  
Benchmark Datasets ◽  
Categorical Attributes

Normalization of feature vectors of datasets is widely used in a number of fields of data mining, in particular in cluster analysis, where it is used to prevent features with large numerical values from dominating in distance-based objective functions. In this study, a unified statistical approach to normalization of all attributes of mixed databases, when different metrics are used for numerical and categorical data, is proposed. After the proposed normalization, the contributions of both numerical and categorical attributes to a specified objective function are statistically the same. Formulae for the statistically normalized Minkowski mixed p -metrics are given in an explicit way. It is shown that the classic z -score standardization and the min–max normalization are particular cases of the statistical normalization, when the objective function is, respectively, based on the Euclidean or the Tchebycheff (Chebyshev) metrics. Finally, clustering of several benchmark datasets is performed with non-normalized and introduced normalized mixed metrics using either the k -prototypes (for p =2) or another algorithm (for p ≠2).

Logistics Network Optimization of Import Crude Oil in China Based on Genetic Algorithm

2014 ◽  
Vol 945-949 ◽  
pp. 3126-3129 ◽  
Author(s):  
Jie Chen
Keyword(s):  
Genetic Algorithm ◽  
Crude Oil ◽  
Objective Function ◽  
Network Optimization ◽  
Optimization Model ◽  
Transportation Network ◽  
Original Data ◽  
Coastal Areas ◽  
Logistics Network ◽  
Oil Transportation

The primary goal of this paper is to save logistics cost and reach optimizing configuration of import crude oil transportation network. An optimization model is put forward with an objective function of minimum logistics expense. It is carried out by Genetic Algorithm (GA) and MATLAB with original data of 2012 and predicted data of 2017. Results indicate that large VLCC of 260000-320000 tons is the main tanker type in import crude oil transportation network. And crude oil logistics bases will be formed which are represented by Qingdao, Dalian, Tianjin, Ningbo-Zhoushan, Zhanjiang and Huizhou in coastal areas.

Operation Optimization of DC Distribution Network with BSS Based on GA-WDO Hybrid Algorithm

2020 ◽  
Vol 13 (7) ◽  
pp. 1087-1096
Author(s):  
Yang Wang ◽  
Fengyun Chen ◽  
Wen Xiao ◽  
Zhengming Li
Keyword(s):  
Power Generation ◽  
Objective Function ◽  
Optimization Model ◽  
Distribution System ◽  
Distribution Network ◽  
Minimum Variance ◽  
Utilization Rate ◽  
Solar Absorption ◽  
Dc Distribution ◽  
Operation Cost

Background: The high permeability of Distributed Generation (DG) and the development of DC load represented by electric vehicle Battery Swapping Station (BSS) pose new challenges to the reliable and economic operation of DC distribution system. Methods: In order to improve the wind and solar absorption rate and the reliable operation of DC distribution network and coordinate the interests and demands of BSS and DC distribution company, the upper level takes the abandonment rate and the minimum variance of BSS charging and discharging net load as two objective functions, and the lower level takes the minimum operation cost of DC distribution network and BSS as the objective function. Secondly, this paper proposes a method that combines Genetic Algorithm (GA) with Wind-Driven Optimization algorithm (WDO). CPLEX and hybrid GA-WDO are used to solve the upper and lower models, respectively. Results: Finally, an example shows that the proposed optimization model can reduce the operation cost of DC distribution network with BSS and improve the utilization rate of wind and light, which shows the rationality and effectiveness of the optimization model. Conclusion: In this paper, considering the randomness and uncertainty of wind power generation and photovoltaic power generation, this paper establishes the upper objective function with the minimum abandonment rate and load variance and the lower objective function with the minimum operation cost of DC distribution network and BSS operators.

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