Search for Global Maxima in Multimodal Functions by Applying Numerical Optimization Algorithms: A Comparison between Golden Section and Simulated Annealing

Guillot, Jordan; Restrepo-Leal, Diego; Robles-Algarín, Carlos; Oliveros, Ingrid

doi:10.3390/computation7030043

Cited by 11 publications

(11 citation statements)

References 28 publications

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“…Recently, some improved search trees have also been used to solve extrema in multi-modal or other optimization fields [15], [16], [25], [26]. These search trees, such as Binary Search [13], Golden-Section Search [14], and Golden-Section SINE Search [26] complete complex tasks by combining with population [27] or other strategies [15].…”

Section: B Search Methodsmentioning

confidence: 99%

“…Interestingly, certain classical search methods have attracted our attention. Some global search methods, like Binary Search [13] and Golden-Section Search [14], are not merely of use in finding extreme values in uni-modal functions, but have also shown promise when used in other fields [15], [16]. The search processes of the above global search method are similar to the reverse process of tree-based searching [17].…”

Section: Introductionmentioning

confidence: 99%

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Evolving Neural Networks through a Reverse Encoding Tree

Zhang,

Yang,

Zenil

et al. 2020

Preprint

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NeuroEvolution is one of the most competitive evolutionary learning strategies for designing novel neural networks for use in specific tasks, such as logic circuit design and digital gaming. However, the application of benchmark methods such as the NeuroEvolution of Augmenting Topologies (NEAT) remains a challenge, in terms of their computational cost and search time inefficiency. This paper advances a method which incorporates a type of topological edge coding, named Reverse Encoding Tree (RET), for evolving scalable neural networks efficiently. Using RET, two types of approaches -NEAT with Binary search encoding (Bi-NEAT) and NEAT with Golden-Section search encoding (GS-NEAT) -have been designed to solve problems in benchmark continuous learning environments such as logic gates, Cartpole, and Lunar Lander, and tested against classical NEAT and FS-NEAT as baselines. Additionally, we conduct a robustness test to evaluate the resilience of the proposed NEAT approaches. The results show that the two proposed approaches deliver an improved performance, characterized by (1) a higher accumulated reward within a finite number of time steps; (2) using fewer episodes to solve problems in targeted environments, and (3) maintaining adaptive robustness under noisy perturbations, which outperform the baselines in all tested cases. Our analysis also demonstrates that RET expends potential future research directions in dynamic environments. Code is available from https://github.com/HaolingZHANG/ReverseEncodingTree.

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Section: B Search Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Evolving Neural Networks through a Reverse Encoding Tree

Zhang,

Yang,

Zenil

et al. 2020

Preprint

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“…When evaluating multimodal functions with optimization algorithms, individual contributions of PV modules can be detected [1]. For this reason, the algorithm is not able to optimize the entire function.…”

Section: Experimental Design Materials and Methodsmentioning

confidence: 99%

Data from multimodal functions based on an array of photovoltaic modules and an approximation with artificial neural networks as a scenario for testing optimization algorithms

2019

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This paper presents the data of multimodal functions that emulate the performance of an array of five photovoltaic modules under partial shading conditions. These functions were obtained through mathematical modeling and represent the P–V curves of a photovoltaic module with several local maximums and a global maximum. In addition, data from a feedforward neural network are shown, which represent an approximation of the multimodal functions that were obtained with mathematical modeling. The modeling of multimodal functions, the architecture of the neural network and the use of the data were discussed in our previous work entitled “Search for Global Maxima in Multimodal Functions by Applying Numerical Optimization Algorithms: A Comparison Between Golden Section and Simulated Annealing” [1]. Data were obtained through simulations in a C code, which were exported to DAT files and subsequently organized into four Excel tables. Each table shows the voltage and power data for the five modules of the photovoltaic array, for multimodal functions and for the approximation of the multimodal functions implemented by the artificial neural network. In this way, a dataset that can be used to evaluate the performance of optimization algorithms and system identification techniques applied in multimodal functions was obtained.

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“…dtn is consistently lager than −ΦIP H , so the curve is monotonously increasing with no extreme point. Observing the possible cases, we employ an efficient golden section search (GSS) to find the extreme points [39]. In GSS, we limit the hovering time t n ≤t n to ensure that the total service duration does not exceed T max , wheret n is a maximal time limitation for cluster n. Intuitively, the clusters with more demands need more transmission frames.…”

Section: B Hovering Time Allocationmentioning

confidence: 99%