Dynamic clustering and strong patterns recognition: new tools in automatic classification

1977 ◽  
Vol 14 (10) ◽  
pp. 2232-2245 ◽  
Author(s):  
Denis Lefebvre ◽  
Michel David
Keyword(s):  
A Priori ◽  
Major Elements ◽  
Local Optimum ◽  
Dynamic Clustering ◽  
Local Optima ◽  
Whole Process ◽  
Rock Types ◽  
Group Number ◽  
Stable Partition ◽  
Partitioning Problems

The dynamic clustering method (D.C.M.) developed by Diday is a nonhierarchical classification procedure which can help the geologist who is faced with the problem of forming groups among a multidimensional population of chemical analyses. Instead of computing the similarity between every possible pair of elements of a population, the D.C.M. suggests the use of a set of nuclei which will act as a template in the process of grouping elements together to form a partition of the population. By using the concept of similarity between an element and a group of elements, called a nucleus, the D.C.M. will assign a group number to every individual of the original population.When the first partition has been completed, the more representative elements of the groups are chosen and combined into an improved set of nuclei. This set will then be used to perform a second grouping and the whole process will be repeated over and over until no improvement can be achieved by an other iteration. The result is a local optimum, i.e. a stable partition into a given number of groups. The D.C.M. can be applied several times to the same set of data to generate different local optima (the starting set of nuclei being different). By grouping the elements which were classified together for every local optimum, a partition into an equal or greater number of groups can result. This is the concept of strong patterns.Three hundred and thirty-three rocks of the Monteregian Hills petrogenetic suite were classified on the basis of their content in ten major elements. Five major groups, corresponding to five different rock types could be easily recognized and discriminated without any a priori assumptions. It is suggested that the algorithms presented here could be used to achieve more subtle partitioning problems, efficiently and economically, on larger sets of data.

scholarly journals Sales Growth Rate Forecasting Using Improved PSO and SVM

2014 ◽  
Vol 2014 ◽  
pp. 1-13 ◽  
Author(s):  
Xibin Wang ◽  
Junhao Wen ◽  
Shafiq Alam ◽  
Xiang Gao ◽  
Zhuo Jiang ◽  
...  
Keyword(s):  
Growth Rate ◽  
Decisive Role ◽  
Convergence Speed ◽  
Classification Model ◽  
Support Vector ◽  
Local Optimum ◽  
Sales Growth ◽  
Local Optima ◽  
Proposed Model ◽  
Forecasting Performance

Accurate forecast of the sales growth rate plays a decisive role in determining the amount of advertising investment. In this study, we present a preclassification and later regression based method optimized by improved particle swarm optimization (IPSO) for sales growth rate forecasting. We use support vector machine (SVM) as a classification model. The nonlinear relationship in sales growth rate forecasting is efficiently represented by SVM, while IPSO is optimizing the training parameters of SVM. IPSO addresses issues of traditional PSO, such as relapsing into local optimum, slow convergence speed, and low convergence precision in the later evolution. We performed two experiments; firstly, three classic benchmark functions are used to verify the validity of the IPSO algorithm against PSO. Having shown IPSO outperform PSO in convergence speed, precision, and escaping local optima, in our second experiment, we apply IPSO to the proposed model. The sales growth rate forecasting cases are used to testify the forecasting performance of proposed model. According to the requirements and industry knowledge, the sample data was first classified to obtain types of the test samples. Next, the values of the test samples were forecast using the SVM regression algorithm. The experimental results demonstrate that the proposed model has good forecasting performance.

Local Best Particle Swarm Optimization Using Crown Jewel Defense Strategy

2018 ◽  
pp. 27-52 ◽  
Author(s):  
Jiarui Zhou ◽  
Junshan Yang ◽  
Ling Lin ◽  
Zexuan Zhu ◽  
Zhen Ji
Keyword(s):  
Particle Swarm Optimization ◽  
High Efficiency ◽  
Particle Swarm ◽  
Global Optimum ◽  
Population Diversity ◽  
Local Optimum ◽  
Swarm Optimization ◽  
Local Optima ◽  
Von Neumann ◽  
Swarm Intelligence Algorithm

Particle swarm optimization (PSO) is a swarm intelligence algorithm well known for its simplicity and high efficiency on various problems. Conventional PSO suffers from premature convergence due to the rapid convergence speed and lack of population diversity. It is easy to get trapped in local optima. For this reason, improvements are made to detect stagnation during the optimization and reactivate the swarm to search towards the global optimum. This chapter imposes the reflecting bound-handling scheme and von Neumann topology on PSO to increase the population diversity. A novel crown jewel defense (CJD) strategy is introduced to restart the swarm when it is trapped in a local optimum region. The resultant algorithm named LCJDPSO-rfl is tested on a group of unimodal and multimodal benchmark functions with rotation and shifting. Experimental results suggest that the LCJDPSO-rfl outperforms state-of-the-art PSO variants on most of the functions.

Effective Algorithms for Scheduling Workflow Tasks on Mobile Clouds

2020 ◽  
Vol 29 (16) ◽  
pp. 2050255
Author(s):  
Heng Li ◽  
Yaoqin Zhu ◽  
Meng Zhou ◽  
Yun Dong
Keyword(s):  
Mobile Devices ◽  
Solution Space ◽  
Iterated Local Search ◽  
Mobile Cloud ◽  
Local Optimum ◽  
Perturbation Operator ◽  
Evolutionary Mechanisms ◽  
Local Optima ◽  
Np Hard Problem ◽  
Workflow Tasks

In mobile cloud computing, the computing resources of mobile devices can be integrated to execute complicated applications, in order to tackle the problem of insufficient resources of mobile devices. Such applications are, in general, characterized as workflows. Scheduling workflow tasks on a mobile cloud system consisting of heterogeneous mobile devices is a NP-hard problem. In this paper, intelligent algorithms, e.g., particle swarm optimization (PSO) and simulated annealing (SA), are widely used to solve this problem. However, both PSO and SA suffer from the limitation of easily being trapped into local optima. Since these methods rely on their evolutionary mechanisms to explore new solutions in solution space, the search procedure converges once getting stuck in local optima. To address this limitation, in this paper, we propose two effective metaheuristic algorithms that incorporate the iterated local search (ILS) strategy into PSO and SA algorithms, respectively. In case that the intelligent algorithm converges to a local optimum, the proposed algorithms use a perturbation operator to explore new solutions and use the newly explored solutions to start a new round of evolution in the solution space. This procedure is iterated until no better solutions can be explored. Experimental results show that by incorporating the ILS strategy, our proposed algorithms outperform PSO and SA in reducing workflow makespans. In addition, the perturbation operator is beneficial for improving the effectiveness of scheduling algorithms in exploring high-quality scheduling solutions.

scholarly journals Zur Rolle der Ökonometrie in der wissenschaftlichen Politikberatung

2013 ◽  
Vol 14 (1-2) ◽  
pp. 3-30 ◽  
Author(s):  
Gebhard Kirchgässner
Keyword(s):  
Political Institutions ◽  
A Priori ◽  
Policy Advice ◽  
Scientific Policy ◽  
Conflicts Of Interests ◽  
Whole Process ◽  
Open Discussion ◽  
Econometric Analyses ◽  
Scientific Policy Advice ◽  
Empirical Analyses

AbstractBecause economic theory alone does in many situations not provide unambiguous policy advice, most of the time empirical analyses are needed in addition. Thus, today econometric analyses are often parts of reports for political institutions or courts. However, it is not unusual that reports with contradicting evidence are presented by different groups or parties. Using the relation between government size and economic growth as an example, it is shown how such contradicting results are possible even if all scientists involved behave sincerely and adhere to the rules of scientific research. Our second example, studies investigating whether the death penalty serves as a deterrent to homicide, shows that the results of empirical analyses might to a large extent depend on a priori convictions of the scientists. Thus, the process of scientific policy advice has to be organised in a way so that - similar to the genuinely scientific discourse - open discussion and criticisms of methods and results are possible. In order to disclose possible conflicts of interests, this demand transparency of the whole process and, in particular for empirical analyses, that data and programmes are made available for re-estimations.

An Improved Differential Evolution Algorithm for Numerical Optimization Problems

2013 ◽  
Vol 415 ◽  
pp. 349-352
Author(s):  
Hong Wei Zhao ◽  
Hong Gang Xia
Keyword(s):  
Differential Evolution ◽  
Numerical Optimization ◽  
Optimization Problems ◽  
Differential Evolution Algorithm ◽  
Population Based ◽  
Local Optimum ◽  
Local Optima ◽  
De Algorithm ◽  
Evolution Algorithm ◽  
Improved Differential Evolution Algorithm

Differential evolution (DE) is a population-based stochastic function minimizer (or maximizer), whose simple yet powerful and straightforward features make it very attractive for numerical optimization. However, DE is easy to trapped into local optima. In this paper, an improved differential evolution algorithm (IDE) proposed to speed the convergence rate of DE and enhance the global search of DE. The IDE employed a new mutation operation and modified crossover operation. The former can rapidly enhance the convergence of the MDE, and the latter can prevent the MDE from being trapped into the local optimum effectively. Besides, we dynamic adjust the scaling factor (F) and the crossover rate (CR), which is aimed at further improving algorithm performance. Based on several benchmark experiment simulations, the IDE has demonstrated stronger convergence and stability than original differential (DE) algorithm and other algorithms (PSO and JADE) that reported in recent literature.

scholarly journals Spacecraft Multiple-Impulse Trajectory Optimization Using Differential Evolution Algorithm with Combined Mutation Strategies and Boundary-Handling Schemes

2015 ◽  
Vol 2015 ◽  
pp. 1-13 ◽  
Author(s):  
Yuehe Zhu ◽  
Hua Wang ◽  
Jin Zhang
Keyword(s):  
Differential Evolution ◽  
Trajectory Optimization ◽  
Optimization Problems ◽  
Differential Evolution Algorithm ◽  
Optimal Solution ◽  
Global Optimum ◽  
Local Optimum ◽  
Local Optima ◽  
Trial Vector ◽  
Mutation Strategies

Since most spacecraft multiple-impulse trajectory optimization problems are complex multimodal problems with boundary constraint, finding the global optimal solution based on the traditional differential evolution (DE) algorithms becomes so difficult due to the deception of many local optima and the probable existence of a bias towards suboptimal solution. In order to overcome this issue and enhance the global searching ability, an improved DE algorithm with combined mutation strategies and boundary-handling schemes is proposed. In the first stage, multiple mutation strategies are utilized, and each strategy creates a mutant vector. In the second stage, multiple boundary-handling schemes are used to simultaneously address the same infeasible trial vector. Two typical spacecraft multiple-impulse trajectory optimization problems are studied and optimized using the proposed DE method. The experimental results demonstrate that the proposed DE method efficiently overcomes the problem created by the convergence to a local optimum and obtains the global optimum with a higher reliability and convergence rate compared with some other popular evolutionary methods.

scholarly journals Ultimate Limits for Counterweight Balancing of Crank-Rocker Four-Bar Linkages

2006 ◽  
Vol 128 (6) ◽  
pp. 1272-1284 ◽  
Author(s):  
Bram Demeulenaere ◽  
Erwin Aertbeliën ◽  
Myriam Verschuure ◽  
Jan Swevers ◽  
Joris De Schutter
Keyword(s):  
Nonlinear Optimization ◽  
Optimization Problem ◽  
Design Procedure ◽  
Global Optimum ◽  
Convex Program ◽  
Local Optimum ◽  
Local Optima ◽  
Nonlinear Optimization Problem ◽  
Driving Torque ◽  
Shaking Moment

This paper focuses on reducing the dynamic reactions (shaking force, shaking moment, and driving torque) of planar crank-rocker four-bars through counterweight addition. Determining the counterweight mass parameters constitutes a nonlinear optimization problem, which suffers from local optima. This paper, however, proves that it can be reformulated as a convex program, that is, a nonlinear optimization problem of which any local optimum is also globally optimal. Because of this unique property, it is possible to investigate (and by virtue of the guaranteed global optimum, in fact prove) the ultimate limits of counterweight balancing. In a first example a design procedure is presented that is based on graphically representing the ultimate limits in design charts. A second example illustrates the versatility and power of the convex optimization framework by reformulating an earlier counterweight balancing method as a convex program and providing improved numerical results for it.

scholarly journals An Analysis of the Fitness Landscape of Travelling Salesman Problem

2016 ◽  
Vol 24 (2) ◽  
pp. 347-384 ◽  
Author(s):  
Mohammad-H. Tayarani-N. ◽  
Adam Prügel-Bennett
Keyword(s):  
Principal Component Analysis ◽  
Fitness Landscape ◽  
Travelling Salesman Problem ◽  
Principal Component ◽  
Component Analysis ◽  
Global Optimum ◽  
Local Optimum ◽  
Travelling Salesman ◽  
Local Optima ◽  
Expected Fitness

The fitness landscape of the travelling salesman problem is investigated for 11 different types of the problem. The types differ in how the distances between cities are generated. Many different properties of the landscape are studied. The properties chosen are all potentially relevant to choosing an appropriate search algorithm. The analysis includes a scaling study of the time to reach a local optimum, the number of local optima, the expected probability of reaching a local optimum as a function of its fitness, the expected fitness found by local search and the best fitness, the probability of reaching a global optimum, the distance between the local optima and the global optimum, the expected fitness as a function of the distance from an optimum, their basins of attraction and a principal component analysis of the local optima. The principal component analysis shows the correlation of the local optima in the component space. We show how the properties of the principal components of the local optima change from one problem type to another.

scholarly journals An Improved Moth-Flame Optimization Algorithm with Adaptation Mechanism to Solve Numerical and Mechanical Engineering Problems

Entropy ◽  
2021 ◽  
Vol 23 (12) ◽  
pp. 1637
Author(s):  
Mohammad H. Nadimi-Shahraki ◽  
Ali Fatahi ◽  
Hoda Zamani ◽  
Seyedali Mirjalili ◽  
Laith Abualigah
Keyword(s):  
Mechanical Engineering ◽  
Optimization Problems ◽  
Population Diversity ◽  
Local Optimum ◽  
Friedman Test ◽  
Exploration And Exploitation ◽  
Adaptation Mechanism ◽  
Local Optima ◽  
Engineering Problems ◽  
Moth Flame Optimization Algorithm

Moth-flame optimization (MFO) algorithm inspired by the transverse orientation of moths toward the light source is an effective approach to solve global optimization problems. However, the MFO algorithm suffers from issues such as premature convergence, low population diversity, local optima entrapment, and imbalance between exploration and exploitation. In this study, therefore, an improved moth-flame optimization (I-MFO) algorithm is proposed to cope with canonical MFO’s issues by locating trapped moths in local optimum via defining memory for each moth. The trapped moths tend to escape from the local optima by taking advantage of the adapted wandering around search (AWAS) strategy. The efficiency of the proposed I-MFO is evaluated by CEC 2018 benchmark functions and compared against other well-known metaheuristic algorithms. Moreover, the obtained results are statistically analyzed by the Friedman test on 30, 50, and 100 dimensions. Finally, the ability of the I-MFO algorithm to find the best optimal solutions for mechanical engineering problems is evaluated with three problems from the latest test-suite CEC 2020. The experimental and statistical results demonstrate that the proposed I-MFO is significantly superior to the contender algorithms and it successfully upgrades the shortcomings of the canonical MFO.

scholarly journals Multimodal Optimization with the Local Optimum Ranking 2 Algorithm

2022 ◽  
Author(s):  
Francisco Daniel Filip Duarte
Keyword(s):  
Structural Design ◽  
Local Population ◽  
Computation Time ◽  
Efficient Solutions ◽  
Local Optimum ◽  
Local Optima ◽  
Single Output ◽  
Niching Methods ◽  
Objective Value ◽  
Niching Method

Abstract In optimization tasks, it is interesting to achieve a set of efficient solutions instead of one single output, in the case the best solution is not suitable. Many niching methods offer a diversified response, yet some important problems are common: (1) The most interesting solutions of each local optimum are not identified. Thus, the output is the overall population of solutions, which increases the work of the designer in verifying which solution is the most interesting. (2) Existing niching algorithms tend to distribute the solutions on the most promising regions, over-populating some local optima and sub-populating others, which leads to poor optimization.To solve these challenges, a novel niching method is presented, named local optimum ranking 2 (LOR2). This sorting methodology favors the exploration of a defined number of local optima and ranks each local population by objective value within each local optimum. Thus, is performed a multi-focus exploration, with an equalized number of solutions on each local optimum, while identifying which solutions are the local apices. To exemplify its application, the LOR2 algorithm is applied in the design optimization of a metallic cantilever beam. It achieves a set of efficient and diverse design configurations, offering both performance and diversity for structural design challenges.In addition, a second experiment describes how the algorithm can be applied to segment the domain of any function, into a mesh of similar sized or custom-sized elements. Thus, it can significantly simplify metamodels and reduce their computation time.

Sign in / Sign up

Export Citation Format

Share Document