scholarly journals Experimental Design for Optimization of Orthogonal Projection Pursuit Models

2020 ◽  
Vol 34 (06) ◽  
pp. 10235-10242
Author(s):  
Mojmir Mutny ◽  
Johannes Kirschner ◽  
Andreas Krause
Keyword(s):  
Experimental Design ◽  
Orthogonal Projection ◽  
Optimization Problems ◽  
Additive Model ◽  
Projection Pursuit ◽  
Parameter Tuning ◽  
Additive Models ◽  
Function Optimization ◽  
Bayesian Optimization ◽  
Additive Structure

Bayesian optimization and kernelized bandit algorithms are widely used techniques for sequential black box function optimization with applications in parameter tuning, control, robotics among many others. To be effective in high dimensional settings, previous approaches make additional assumptions, for example on low-dimensional subspaces or an additive structure. In this work, we go beyond the additivity assumption and use an orthogonal projection pursuit regression model, which strictly generalizes additive models. We present a two-stage algorithm motivated by experimental design to first decorrelate the additive components. Subsequently, the bandit optimization benefits from the statistically efficient additive model. Our method provably decorrelates the fully additive model and achieves optimal sublinear simple regret in terms of the number of function evaluations. To prove the rotation recovery, we derive novel concentration inequalities for linear regression on subspaces. In addition, we specifically address the issue of acquisition function optimization and present two domain dependent efficient algorithms. We validate the algorithm numerically on synthetic as well as real-world optimization problems.

scholarly journals A Survey on Flower pollination algorithm

2021 ◽  
pp. 05-11
Author(s):  
Safaa .. ◽  
◽  
◽  
Ibrahim Elhenawy
Keyword(s):  
Optimization Problems ◽  
Parameter Tuning ◽  
Function Optimization ◽  
Flower Pollination Algorithm ◽  
Complex Nature ◽  
Computer Gaming ◽  
Flower Pollination ◽  
Reproduction Strategy ◽  
Power And Energy ◽  
Energy Signal

Flower pollination algorithm (FPA) is a metaheuristic algorithm that proceeds its representation from flowers' proliferation role in plants. The optimal plant reproduction strategy involves the survival of the fittest as well as the optimal reproduction of plants in terms of numbers. These factors represent the fundamentals of the FPA and are optimization-oriented. Yang developed the FPA in 2012, which has since shown superiority to other metaheuristic algorithms in solving various real-world problems, such as power and energy, signal and image processing, communications, structural design, clustering and feature selection, global function optimization, computer gaming, and wireless sensor networking. Recently, many variants of FPA have been developed by modification, hybridization, and parameter-tuning to cope with the complex nature of optimization problems this paper provides a survey of FPA and its applications.

scholarly journals Predicting Malaria Transmission Dynamics in Dangassa, Mali: A Novel Approach Using Functional Generalized Additive Models

2020 ◽  
Vol 17 (17) ◽  
pp. 6339
Author(s):  
François Freddy Ateba ◽  
Manuel Febrero-Bande ◽  
Issaka Sagara ◽  
Nafomon Sogoba ◽  
Mahamoudou Touré ◽  
...  
Keyword(s):  
Wind Speed ◽  
Malaria Incidence ◽  
Generalized Additive Models ◽  
Community Health Center ◽  
Additive Model ◽  
Additive Models ◽  
Functional Regression ◽  
Novel Approach ◽  
Malaria Incidence Rate ◽  
Mean Wind Speed

Mali aims to reach the pre-elimination stage of malaria by the next decade. This study used functional regression models to predict the incidence of malaria as a function of past meteorological patterns to better prevent and to act proactively against impending malaria outbreaks. All data were collected over a five-year period (2012–2017) from 1400 persons who sought treatment at Dangassa’s community health center. Rainfall, temperature, humidity, and wind speed variables were collected. Functional Generalized Spectral Additive Model (FGSAM), Functional Generalized Linear Model (FGLM), and Functional Generalized Kernel Additive Model (FGKAM) were used to predict malaria incidence as a function of the pattern of meteorological indicators over a continuum of the 18 weeks preceding the week of interest. Their respective outcomes were compared in terms of predictive abilities. The results showed that (1) the highest malaria incidence rate occurred in the village 10 to 12 weeks after we observed a pattern of air humidity levels >65%, combined with two or more consecutive rain episodes and a mean wind speed <1.8 m/s; (2) among the three models, the FGLM obtained the best results in terms of prediction; and (3) FGSAM was shown to be a good compromise between FGLM and FGKAM in terms of flexibility and simplicity. The models showed that some meteorological conditions may provide a basis for detection of future outbreaks of malaria. The models developed in this paper are useful for implementing preventive strategies using past meteorological and past malaria incidence.

A microbial treatment population dynamics optimization approach

2021 ◽  
pp. 1-15
Author(s):  
Jinding Gao
Keyword(s):  
Population Dynamics ◽  
Information Exchange ◽  
Information Diffusion ◽  
Optimization Problems ◽  
Microbial Control ◽  
Function Optimization ◽  
Optimization Approach ◽  
Dynamics Model ◽  
Population Dynamics Model ◽  
Number Of Individuals

In order to solve some function optimization problems, Population Dynamics Optimization Algorithm under Microbial Control in Contaminated Environment (PDO-MCCE) is proposed by adopting a population dynamics model with microbial treatment in a polluted environment. In this algorithm, individuals are automatically divided into normal populations and mutant populations. The number of individuals in each category is automatically calculated and adjusted according to the population dynamics model, it solves the problem of artificially determining the number of individuals. There are 7 operators in the algorithm, they realize the information exchange between individuals the information exchange within and between populations, the information diffusion of strong individuals and the transmission of environmental information are realized to individuals, the number of individuals are increased or decreased to ensure that the algorithm has global convergence. The periodic increase of the number of individuals in the mutant population can greatly increase the probability of the search jumping out of the local optimal solution trap. In the iterative calculation, the algorithm only deals with 3/500∼1/10 of the number of individual features at a time, the time complexity is reduced greatly. In order to assess the scalability, efficiency and robustness of the proposed algorithm, the experiments have been carried out on realistic, synthetic and random benchmarks with different dimensions. The test case shows that the PDO-MCCE algorithm has better performance and is suitable for solving some optimization problems with higher dimensions.

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.

ADDITIVE-VETO MODELS FOR CHOICE AND RANKING MULTICRITERIA DECISION PROBLEMS

2013 ◽  
Vol 30 (06) ◽  
pp. 1350026 ◽  
Author(s):  
ADIEL TEIXEIRA DE ALMEIDA
Keyword(s):  
High Performance ◽  
Additive Model ◽  
Additive Models ◽  
Numerical Application ◽  
Multicriteria Decision ◽  
Decision Methods ◽  
Overall Evaluation ◽  
Low Performance ◽  
Ranking Problems ◽  
Multicriteria Decision Problems

Using additive models for aggregation of criteria is an important procedure in many multicriteria decision methods. This compensatory approach, which scores the alternatives straightforwardly, may have significant drawbacks. For instance, the Decision Maker (DM) may prefer not to select alternatives which have a very low performance in whatever criterion. In contrast, such an alternative may have the best overall evaluation, since the additive model may compensate this low performance in one of the criteria as a result of high performance in other criteria. Thus, additive-veto models are proposed with a view to considering the possibility of vetoing alternatives in such situations, particularly for choice and ranking problems. A numerical application illustrates the use of such models, with a detailed discussion related to real practical problems. Moreover, the results obtained from a numerical simulation show that it is not so rare for a veto of the best alternative to occur in the additive model. This is of considerable relevance depending on the DM's preference structure.

Improved Particle Swarm Optimization Algorithm and its Application Based on the Aggregation Degree

2013 ◽  
Vol 427-429 ◽  
pp. 1934-1938
Author(s):  
Zhong Rong Zhang ◽  
Jin Peng Liu ◽  
Ke De Fei ◽  
Zhao Shan Niu
Keyword(s):  
Particle Swarm Optimization ◽  
Optimization Algorithm ◽  
Particle Swarm Optimization Algorithm ◽  
Optimization Problems ◽  
Particle Swarm ◽  
Population Diversity ◽  
Function Optimization ◽  
Local Optimum ◽  
Swarm Optimization ◽  
Improved Particle Swarm Optimization

The aim is to improve the convergence of the algorithm, and increase the population diversity. Adaptively particles of groups fallen into local optimum is adjusted in order to realize global optimal. by judging groups spatial location of concentration and fitness variance. At the same time, the global factors are adjusted dynamically with the action of the current particle fitness. Four typical function optimization problems are drawn into simulation experiment. The results show that the improved particle swarm optimization algorithm is convergent, robust and accurate.

PSO and GA tuned conventional and fractional order PID controllers for quadrotor control

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Hasan Saribas ◽  
Sinem Kahvecioglu
Keyword(s):  
Fractional Order ◽  
Pid Controller ◽  
Controller Design ◽  
Optimization Problems ◽  
Parameter Tuning ◽  
Absolute Error ◽  
Cost Functions ◽  
Pid Controllers ◽  
Content Type ◽  
Quadrotor Control

Purpose This study aims to compare the performance of the conventional and fractional order proportional-integral-derivative (PID and FOPID) controllers tuned with a particle swarm optimization (PSO) and genetic algorithm (GA) for quadrotor control. Design/methodology/approach In this study, the gains of the controllers were tuned using PSO and GA, which are included in the heuristic optimization methods. The tuning processes of the controller’s gains were formulated as optimization problems. While generating the objective functions (cost functions), four different decision criteria were considered separately: integrated summation error (ISE), integrated absolute error, integrated time absolute error and integrated time summation error (ITSE). Findings According to the simulation results and comparison tables that were created, FOPID controllers tuned with PSO performed better performances than PID controllers. In addition, the ITSE criterion returned better results in control of all axes except for altitude control when compared to the other cost functions. In the control of altitude with the PID controller, the ISE criterion showed better performance. Originality/value While a conventional PID controller has three parameters (Kp, Ki, Kd) that need to be tuned, FOPID controllers have two additional parameters (µ). The inclusion of these two extra parameters means more flexibility in the controller design but much more complexity for parameter tuning. This study reveals the potential and effectiveness of PSO and GA in tuning the controller despite the increased number of parameters and complexity.

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