local minima
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Author(s):  
Hoang V. Nguyen ◽  
Niels G. Waller
Keyword(s):  

2022 ◽  
pp. 227-241
Author(s):  
Kuruge Darshana Abeyrathna ◽  
Chawalit Jeenanunta

This research proposes a new training algorithm for artificial neural networks (ANNs) to improve the short-term load forecasting (STLF) performance. The proposed algorithm overcomes the so-called training issue in ANNs, where it traps in local minima, by applying genetic algorithm operations in particle swarm optimization when it converges to local minima. The training ability of the hybridized training algorithm is evaluated using load data gathered by Electricity Generating Authority of Thailand. The ANN is trained using the new training algorithm with one-year data to forecast equal 48 periods of each day in 2013. During the testing phase, a mean absolute percentage error (MAPE) is used to evaluate performance of the hybridized training algorithm and compare them with MAPEs from Backpropagation, GA, and PSO. Yearly average MAPE and the average MAPEs for weekdays, Mondays, weekends, Holidays, and Bridging holidays show that PSO+GA algorithm outperforms other training algorithms for STLF.


2021 ◽  
Author(s):  
H. Tran-Ngoc ◽  
S Khatir ◽  
T. Le-Xuan ◽  
H. Tran - Viet ◽  
G. De Roeck ◽  
...  

Abstract Artificial neural network (ANN) is the study of computer algorithms that can learn from experience to improve performance. ANN employs backpropagation (BP) algorithms using gradient descent (GD)-based learning methods to reduce the discrepancies between predicted and real targets. Even though these differences are considerably decreased after each iteration, the network may still face major risks of being entrapped in local minima if complex error surfaces contain too numerous the best local solutions. To overcome those drawbacks of ANN, numerous researchers have come up with solutions to local minimum prevention by choosing a beneficial starting position that relies on the global search capability of other algorithms. This strategy possibly assists the network in avoiding the first local minima. However, a network often has many local bests widely distributed. Hence, the solution of choosing good starting points may no further be beneficial because the particles are probably entrapped in other local optimal solutions throughout the process of looking for the global best. Therefore, in this work, a novel ANN working parallel with the stochastic search capacity of evolutionary algorithms, is proposed. Additionally, to increase the efficiency of the global search capacity, a hybrid of particle swarm optimization and genetic algorithm (PSOGA) is applied during the process of seeking the best solution, which effectively guarantees to assist the network of ANN in escaping from local minima. This strategy gains both benefits of GD techniques as well as the global search capacity of PSOGA that possibly solves the local minima issues thoroughly. The effectiveness of ANNPSOGA is assessed using both numerical models consisting of various damage cases (single and multiple damages) and a free-free steel beam with different damage levels calibrated in the laboratory. The results demonstrate that ANNPSOGA provides higher accuracy than traditional ANN, PSO, and other hybrid ANNs (even a higher level of noise is employed) and also considerably decreases calculational cost compared with PSO.


Author(s):  
Alexander Zemliak

Purpose In this paper, the previously developed idea of generalized optimization of circuits for deterministic methods has been extended to genetic algorithm (GA) to demonstrate new possibilities for solving an optimization problem that enhance accuracy and significantly reduce computing time. Design/methodology/approach The disadvantages of GAs are premature convergence to local minima and an increase in the computer operation time when setting a sufficiently high accuracy for obtaining the minimum. The idea of generalized optimization of circuits, previously developed for the methods of deterministic optimization, is built into the GA and allows one to implement various optimization strategies based on GA. The shape of the fitness function, as well as the length and structure of the chromosomes, is determined by a control vector artificially introduced within the framework of generalized optimization. This study found that changing the control vector that determines the method for calculating the fitness function makes it possible to bypass local minima and find the global minimum with high accuracy and a significant reduction in central processing unit (CPU) time. Findings The structure of the control vector is found, which makes it possible to reduce the CPU time by several orders of magnitude and increase the accuracy of the optimization process compared with the traditional approach for GAs. Originality/value It was demonstrated that incorporating the idea of generalized optimization into the body of a stochastic optimization method leads to qualitatively new properties of the optimization process, increasing the accuracy and minimizing the CPU time.


2021 ◽  
Vol 118 (49) ◽  
pp. e2106230118
Author(s):  
Jianyuan Yin ◽  
Kai Jiang ◽  
An-Chang Shi ◽  
Pingwen Zhang ◽  
Lei Zhang

Due to structural incommensurability, the emergence of a quasicrystal from a crystalline phase represents a challenge to computational physics. Here, the nucleation of quasicrystals is investigated by using an efficient computational method applied to a Landau free-energy functional. Specifically, transition pathways connecting different local minima of the Lifshitz–Petrich model are obtained by using the high-index saddle dynamics. Saddle points on these paths are identified as the critical nuclei of the 6-fold crystals and 12-fold quasicrystals. The results reveal that phase transitions between the crystalline and quasicrystalline phases could follow two possible pathways, corresponding to a one-stage phase transition and a two-stage phase transition involving a metastable lamellar quasicrystalline state, respectively.


Photonics ◽  
2021 ◽  
Vol 8 (12) ◽  
pp. 541
Author(s):  
Yicheng Zhang ◽  
Mingjie Sun

Phase retrieval utilizing Fourier amplitudes plays a significant role in image recovery. Iterative phase retrieval algorithms have been developed to retrieve phase information that cannot be recorded by detectors directly. However, iterative algorithms face the problem of being trapped in local minima due to the nonconvexity of phase retrieval, and most existing works addressed this by optimizing in multiple runs parallelly to improve the possibility that one of these could reach the global minimum. Alternatively, we propose in this work to increase the probability of reaching the global minimum with one arbitrary initial distribution by adapting simulated annealing in the standard hybrid input-output (HIO) algorithm. Numerical and experimental results demonstrate that the proposed method reconstructs images with mean square errors 50.12% smaller than those reconstructed by HIO. More importantly, the proposed method can be applied to any HIO-based algorithm with multiple runs to further improve the performance.


2021 ◽  
Vol 28 ◽  
Author(s):  
Suryanarayana Seera ◽  
Hampapathalu A. Nagarajaram

Background: It is well known that disease-causing missense mutations (DCMMs) reduce the structural stability/integrity of the proteins with well-defined 3D structures, thereby impacting their molecular functions. However, it is not known in what way DCMMs affect the intrinsically disordered proteins (IDPs) that do not adopt well defined stable 3D structures. Methods: In order to investigate how DCMMs may impact intrinsically disordered regions (IDRs) in proteins, we undertook Molecular Dynamics (MD) based studies on three different examples of functionally important IDRs with known DCMMs. Our studies revealed that the functional impact of DCMMs is in reducing the conformational heterogeneity of IDRs, which is intrinsic and quintessential for their multi-faceted cellular roles. Results: These results are reinforced by energy landscapes of the wildtype and mutant IDRs where the former is characterized by many local minima separated by low barriers, whereas the latter are characterized by one global minimum and several local minima separated by high energy barriers. Our MD based studies also indicate that DCMMs stabilize very few structural possibilities of IDRs either by the newly formed interactions induced by the substituted side chains or by means of restricted or increased flexibilities of the backbone conformations at the mutation sites. Conclusion: Furthermore, the structural possibilities stabilized by DCMMs do not support the native functional roles of the IDRs, thereby leading to disease conditions.


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