Self-adaptive global best harmony search algorithm for training neural networks

AbstractThis paper addresses the application of Self-adaptive Global Best Harmony Search (SGHS) algorithm for the supervised training of feed-forward neural networks (NNs). A structure suitable to data representation of NNs is adapted to SGHS algorithm. The technique is empirically tested and verified by training NNs on two classification benchmarking problems. Overall training time, sum of squared errors, training and testing accuracies of SGHS algorithm is compared with other harmony search algorithms and the standard back-propagation algorithm. The experiments presented that the proposed algorithm lends itself very well to training of NNs and it is also highly competitive with the compared methods

Solving systems of nonlinear equations by harmony search

In this paper, we aim to analyze the performance of some variants of the harmony search (HS) metaheuristic when solving systems of nonlinear equations through the global optimization of an appropriate merit function. The HS metaheuristic draws its inspiration from an artistic process, the improvisation process of musicians seeking a wonderful harmony. A new differential best HS algorithm, based on an improvisation operator that mimics the best harmony and uses a differential variation, is proposed. Computational experiments involving a well-known set of small-dimensional problems are presented.Fundação para a Ciência e a Tecnologia (FCT

Utilizing global-best harmony search to train a PID-like ANFIS controller

This paper presents a PID-like adaptive neuro-fuzzy inference system (ANFIS) controller that can be trained by the global-best harmony search (GHS) technique to control nonlinear systems. Instead of the hybrid learning methods that are widely used in the literature to train the ANFIS structure, the GHS technique alone is used to train the ANFIS as a feedback controller, and hence, the necessity for the teaching signal required by other techniques has been eliminated. Moreover, the input and output scaling factors for this controller are also determined by the GHS. To show the effectiveness of this controller and its learning method, two nonlinear plants, including the continuous stirred tank reactor (CSTR), were used to test its performance in terms of generalization ability and reference tracking. In addition, this controller robustness to output disturbances has been also tested and the results clearly indicate the remarkable performance of this controller

Cosine Harmony Search (CHS) for Static Optimization

Harmony Search (HS) is a behaviour imitation of a musician looking for the balance harmony. HS suffers to find the best parameter tuning especially for Pitch Adjustment Rate (PAR). PAR plays a crucial role in selecting historical solution and adjusting it using Bandwidth (BW) value. However, PAR in HS requires to be initialized with a constant value at the beginning step. On top of that, it also causes delay in convergence speed due to disproportion of global and local search capabilities. Even though, some HS variants claimed to overcome that shortcoming by introducing the self-modification of pitch adjustment rate, some of their justification were imprecise and required deeper and extensive experiments. Local Opposition-Based Learning Self-Adaptation Global Harmony Search (LHS) implements a heuristic factor, η for self-modification of PAR. It (η) manages the probability for selecting the adaptive step either as global or worst. If the value of η is large, the opportunity to select the global adaptive step is high, so the algorithm will further exploit for better harmony value. Otherwise, if η is small, the worst adaptive step is prone to be selected, therefore the algorithm will close to the global best solution. In this paper, regarding to the HS problem, we introduce a Cosine Harmony Search (CHS) by incorporating embedment of cosine and additional strategy rule with self-modification of pitch tuning to enlarge the exploitation capability of solution space. The additional strategy employs the η inspired by LHS and contains the cosine parameter. We test our proposed CHS on twelve standard static benchmark functions and compare it with basic HS and five state-of-the-art HS variants. Our proposed method and these state-of-the-art algorithms executed using 30 and 50 dimensions. The numerical results demonstrated that the CHS has outperformed with other state-of-the-art in accuracy and convergence speed evaluations

Self-Adaptive Global-Best Harmony Search Algorithm-Based Airflow Control of a Wells-Turbine-Based Oscillating-Water Column

The Harmony Search algorithm has attracted a lot of interest in the past years because of its simplicity and efficiency. This led many scientists to develop various variants for many applications. In this paper, four variants of the Harmony search algorithm were implemented and tested to optimize the control design of the Proportional-Integral-derivative (PID) controller in a proposed airflow control scheme. The airflow control strategy has been proposed to deal with the undesired stalling phenomenon of the Wells turbine in an Oscillating Water Column (OWC). To showcase the effectiveness of the Self-Adaptive Global Harmony Search (SGHS) algorithm over traditional tuning methods, a comparative study has been carried out between the optimized PID, the traditionally tuned PID and the uncontrolled OWC system. The results of optimization showed that the Self-Adaptive Global Harmony Search (SGHS) algorithm adapted the best to the problem of the airflow control within the wave energy converter. Moreover, the OWC performance is superior when using the SGHS-tuned PID.This work was supported in part by the Basque Government, through project IT1207-19 and by the MCIU/MINECO through RTI2018-094902-B-C21 / RTI2018-094902-B-C22 (MCIU/AEI/FEDER, UE)

Automatic Calibration for CE-QUAL-W2 Model Using Improved Global-Best Harmony Search Algorithm

CE-QUAL-W2 is widely used for simulating hydrodynamics and water quality of the aquatic environments. Currently, the model calibration is mainly based on trial and error, and therefore it is subject to the knowledge and experience of users. The Particle Swarm Optimization (PSO) algorithm has been tested for automatic calibration of CE-QUAL-W2, but it has an issue of prematurely converging to a local optimum. In this study, we proposed an Improved Global-Best Harmony Search (IGHS) algorithm to automatically calibrate the CE-QUAL-W2 model to overcome these shortcomings. We tested the performance of the IGHS calibration method by simulating water temperature of Devils Lake, North Dakota, which agreed with field observations with R2 = 0.98, and RMSE = 1.23 and 0.77 °C for calibration (2008–2011) and validation (2011–2016) periods, respectively. The same comparison, but with the PSO-calibrated CE-QUAL-W2 model, produced R2 = 0.98 and Root Mean Squared Error (RMSE) = 1.33 and 0.91 °C. Between the two calibration methods, the CE-QUAL-W2 model calibrated by the IGHS method could lower the RMSE in water temperature simulation by approximately 7–15%

FIR Digital Filter and Neural Network Design using Harmony Search Algorithm

Harmony Search (HS) is an emerging metaheuristic algorithm inspired by the improvisation process of jazz musicians. In the HS algorithm, each musician (= decision variable) plays (= generates) a note (= a value) for finding the best harmony (= global optimum) all together. This algorithm has been employed to cope with numerous tasks in the past decade. In this thesis, HS algorithm has been applied to design digital filters of orders 24 and 48 as well as the parameters of neural network problems. Both multiobjective and single objective optimization techniques were applied to design FIR digital filters. 2-dimensional digital filters can be used for image processing and neural networks can be used for medical image diagnosis. Digital filter design using Harmony Search Algorithm can achieve results close to Parks McClellan Algorithm which shows that the algorithm is capable of solving complex engineering problems. Harmony Search is able to optimize the parameter values of feedforward network problems and fuzzy inference neural networks. The performance of a designed neural network was tested by introducing various noise levels at the testing inputs and the output of the neural networks with noise was compared to that without noise. It was observed that, even if noise is being introduced to the testing input there was not much difference in the output. Design results were obtained within a reasonable amount of time using Harmony Search Algorithm

Finding multiple roots of systems of nonlinear equations by a hybrid harmony search-based multistart method

A multistart (MS) clustering technique to compute multiple roots of a system of nonlinear equations through the global optimization of an appropriate merit function is presented. The search procedure that is invoked to converge to a root, starting from a randomly generated point inside the search space, is a new variant of the harmony search (HS) metaheuristic. The HS draws its inspiration from an artistic process, the improvisation process of musicians seeking a wonderful harmony. The new hybrid HS algorithm is based on an improvisation operator that mimics the best harmony and uses the idea of a differential variation, borrowed from the differential evolution algorithm. Computational experiments involving a benchmark set of small and large dimensional problems with multiple roots are presented. The results show that the proposed hybrid HS-based MS algorithm is effective in locating multiple roots and competitive when compared with other metaheuristics.FCT - Fuel Cell Technologies Program(UID/EMS/0615/2016). The authors are grateful to the anonymous referees for their helpful suggestions to improve the paper. This research has been supported by CIDEM (Centre for Research & Development in Mechanical Engineering, Portugal), by COMPETE POCI-01-0145-FEDER-007043 and FCT (Foundation for Science and Technology, Portugal) within the projects UID/EMS/0615/2016 and UID/CEC/00319/2013

A Novel Discrete Global-Best Harmony Search Algorithm for Solving 0-1 Knapsack Problems

In order to better solve discrete 0-1 knapsack problems, a novel global-best harmony search algorithm with binary coding, called DGHS, is proposed. First, an initialization based on a greedy mechanism is employed to improve the initial solution quality in DGHS. Next, we present a novel improvisation process based on intuitive cognition of improvising a new harmony, in which the best harmony of harmony memory (HM) is used to guide the searching direction of evolution during the process of memory consideration, or else a harmony is randomly chosen from HM and then a discrete genetic mutation is done with some probability during the phase of pitch adjustment. Third, a two-phase repair operator is employed to repair an infeasible harmony vector and to further improve a feasible solution. Last, a new selection scheme is applied to decide whether or not a new randomly generated harmony is included into the HM. The proposed DGHS is evaluated on twenty knapsack problems with different scales and compared with other three metaheuristics from the literature. The experimental results indicate that DGHS is efficient, effective, and robust for solving difficult 0-1 knapsack problems