Pitch Adjustment Rate Research Articles

Equilibrium optimizer-based harmony search algorithm with nonlinear dynamic domains and its application to real-world optimization problems

Harmony Search (HS) algorithm is a swarm intelligence algorithm inspired by musical improvisation. Although HS has been applied to various engineering problems, it faces challenges such as getting trapped in local optima, slow convergence speed, and low optimization accuracy when applied to complex problems. To address these issues, this paper proposes an improved version of HS called Equilibrium Optimization-based Harmony Search Algorithm with Nonlinear Dynamic Domains (EO-HS-NDD). EO-HS-NDD integrates multiple leadership-guided strategies from the Equilibrium Optimizer (EO) algorithm, using harmony memory considering disharmony and historical harmony memory, while leveraging the hidden guidance direction information from the Equilibrium Optimizer. Additionally, the algorithm designs a nonlinear dynamic convergence domain to adaptively adjust the search space size and accelerate convergence speed. Furthermore, to balance exploration and exploitation capabilities, appropriate adaptive adjustments are made to Harmony Memory Considering Rate (HMCR) and Pitch Adjustment Rate (PAR). Experimental validation on the CEC2017 test function set demonstrates that EO-HS-NDD outperforms HS and nine other HS variants in terms of robustness, convergence speed, and optimization accuracy. Comparisons with advanced versions of the Differential Evolution (DE) algorithm also indicate that EO-HS-NDD exhibits superior solving capabilities. Moreover, EO-HS-NDD is applied to solve 15 real-world optimization problems from CEC2020 and compared with advanced algorithms from the CEC2020 competition. The experimental results show that EO-HS-NDD performs well in solving real-world optimization problems.

A novel PID controller for BLDCM speed control using dual fuzzy logic systems with HSA optimization

In order to enhance the speed control performance of the brushless DC motor (BLDCM), a novel proportion integration differentiation (PID) is proposed in this paper by using dual fuzzy logic systems (FLSs) with harmony search algorithm (HSA) optimization, which is called DFPID-HSA. Firstly, the FLS1 in DFPID-HSA locks the three coefficients of the PID controller in an extensive range on the basis of the system error and error change rate. Then, the FLS2 is optimized by HSA (HSA-F2) to obtain the precise correction of the three coefficients. To get the optimal global harmony better, the improved dynamic adjustment mode is used for the pitch adjustment rate (PAR) and distance bandwidth (BW) in HSA, and the triple selection method is adopted in the composition harmony section to realize the global search. Finally, DFPID-HSA provides the optimal supply control signal to BLDCM so that it can control the speed effectively. Moreover, the stability of the system is analyzed by the pole, Lyapunov, and Nyquist determination methods. And the sensitivity analysis of DFPID-HSA is carried out under the condition of different motor’s mechanical parameters to check its robustness. In addition, the superiority of DFPID-HSA is verified by MATLAB simulation and experiment platform.

A Fully-Self-Adaptive Harmony Search GMDH-Type Neural Network Algorithm to Estimate Shear-Wave Velocity in Porous Media

Shear wave velocity (VS) is one of the most important parameters in deep and surface studies and the estimation of geotechnical design parameters. This parameter is widely utilized to determine permeability and porosity, lithology, rock mechanical parameters, and fracture assessment. However, measuring this important parameter is either impossible or difficult due to the challenges related to horizontal and deviation wells or the difficulty in reaching cores. Artificial Intelligence (AI) techniques, especially Machine Learning (ML), have emerged as efficient approaches for dealing with such challenges. Therefore, considering the advantage of the ML, the current research proposes a novel Fully-Self-Adaptive Harmony Search—Group Method of Data Handling (GMDH)-type neural network, named FSHS-GMDH, to estimate the VS parameter. In this way, the Harmony Memory Consideration Rate (HMCR) and Pitch Adjustment Rate (PAR) parameters are calculated automatically. A novel method is also introduced to adjust the value of the Bandwidth (BW) parameter based on the cosine wave and each decision variable values. In addition, a variable-size harmony memory is proposed to enhance both the diversification and intensification. Our proposed FSHS-GMDH algorithm quickly explores the problem space and exploits the best regions at the late iterations. This algorithm allows for the training of the prediction model based on the P-wave velocity (VP) and the bulk density of rock (RHOB). Applying the proposed algorithm to a carbonate petroleum reservoir in the Persian Gulf demonstrates that it is capable of accurately estimating the VS parameter better than state-of-the-art machine learning methods in terms of the coefficient of determination (R2), Mean Square Error (MSE), and Root Mean Square Error (RMSE).

Parameters Optimization of Taguchi Method Integrated Hybrid Harmony Search Algorithm for Engineering Design Problems

Performance of convergence to the optimum value is not completely a known process due to characteristics of the considered design problem and floating values of optimization algorithm control parameters. However, increasing robustness and effectiveness of an optimization algorithm may be possible statistically by estimating proper algorithm parameters values. Not only the algorithm which utilizes these estimated-proper algorithm parameter values may enable to find the best fitness in a shorter time, but also it may supply the optimum searching process with a pragmatical manner. This study focuses on the statistical investigation of the optimum values for the control parameters of the harmony search algorithm and their effects on the best solution. For this purpose, the Taguchi method integrated hybrid harmony search algorithm has been presented as an alternative method for optimization analyses instead of sensitivity analyses which are generally used for the investigation of the proper algorithm parameters. The harmony memory size, the harmony memory considering rate, the pitch adjustment rate, the maximum iteration number, and the independent run number of entire iterations have been debated as the algorithm control parameters of the harmony search algorithm. To observe the effects of design problem characteristics on control parameters, the new hybrid method has been applied to different engineering optimization problems including several engineering-optimization examples and a real-size engineering optimization design. End of extensive optimization and statistical analyses to achieve optimum values of control parameters providing rapid convergence to optimum fitness value and handling constraints have been estimated with reasonable relative errors. Employing the Taguchi method integrated hybrid harmony search algorithm in parameter optimization has been demonstrated as it is a reliable and efficient manner to obtain the optimum results with fewer numbers of run and iteration.

A Novel Multi-Objective Harmony Search Algorithm with Pitch Adjustment by Genotype

In this work, a new version of the Harmony Search algorithm for solving multi-objective optimization problems is proposed, MOHSg, with pitch adjustment using genotype. The main contribution consists of adjusting the pitch using the crowding distance by genotype; that is, the distancing in the search space. This adjustment automatically regulates the exploration–exploitation balance of the algorithm, based on the distribution of the harmonies in the search space during the formation of Pareto fronts. Therefore, MOHSg only requires the presetting of the harmony memory accepting rate and pitch adjustment rate for its operation, avoiding the use of a static bandwidth or dynamic parameters. MOHSg was tested through the execution of diverse test functions, and it was able to produce results similar or better than those generated by algorithms that constitute search variants of harmonies, representative of the state-of-the-art in multi-objective optimization with HS.

Hybrid of the fuzzy logic controller with the harmony search algorithm to PWR in-core fuel management optimization

One of the important parts of the in-core fuel management is loading pattern optimization (LPO). The loading pattern optimization as a reasonable design of the in-core fuel management can improve both economic and safe aspects of the nuclear reactor. This work proposes the hybrid of fuzzy logic controller with harmony search algorithm (HS) for loading pattern optimization in a pressurized water reactor. The music improvisation process to find a pleasing harmony is inspiring the harmony search algorithm. In this work, the adjustment of the harmony search algorithm parameters such as the bandwidth and the pitch adjustment rate are increasing performance of the proposed algorithm which is done through a fuzzy logic controller. Hence, membership functions and fuzzy rules are designed to improve the performance of the HS algorithm and achieve optimal results. The objective of the method is finding an optimum core arrangement according to safety and economic aspects such as reduction of power peaking factor (PPF) and increase of effective multiplication factor (Keff). The proposed approach effectiveness has been tried in two cases, Michalewicz's bivariate function problem and NEACRP LWR core. The results show that by using fuzzy harmony search algorithm the value of the fitness function is improved by 15.35%. Finally, with regard to the new solutions proposed in this research it could be used as a trustworthy method for other optimization issues of engineering field.

High-Speed Interval Type-2 Fuzzy Systems for Dynamic Parameter Adaptation in Harmony Search for Optimal Design of Fuzzy Controllers

Fuzzy systems have become a good solution to the problem of fixed parameters in metaheuristic algorithms, proving their efficiency when performing dynamic parameter adaptations using type-1 and type-2 fuzzy logic. However, the computational cost of type-2 fuzzy systems when using the continuous enhanced Karnik–Mendel (CKM) algorithm for type-reduction, when applied to control and optimization, is too high. Therefore, it is proposed to use an approximation to the CKM algorithm in the type-2 fuzzy system for adjusting the pitch adjustment rate (PArate) parameter in the original harmony search algorithm (HS). The main contribution of this article is to verify that the implementation of the proposed methodology achieves results that are equivalent to the interval type-2 fuzzy system with the CKM algorithm, but in less computing time and also allowing an efficient dynamic parameter adaptation. It is noteworthy that this method is relatively new in the area of metaheuristics algorithms so there is a current interest to work with this methodology. The proposed method was used in optimizing the antecedents and consequents for an interval type-2 fuzzy controller of direct current motor. Experimental results without noise and then with uniform random noise numbers (Gaussian noise) in the controller were obtained to verify that the implementation is efficient when compared to conventional and other existing methods.

Energy Optimization in Multi-Hop Wireless Sensor Networks based on Proposed Harmony Search Routing Algorithm

Spread application of wireless sensor networks (WSNs), has led many researchers aiming at energy optimization in these networks. The Proposed Energy Efficient Harmony Search Routing Algorithm (PEEHSRA) in accordance with a novel energy model is stated in this study to minimize the amount of energy consumption in WSNs. We first proposed an energy model on the basis of modulation scheme parameters for multi-hop transmission. Then, in order to develop a harmony search routing algorithm, pitch adjustment rate in the harmony memory was introduced based on both, the proposed energy model, and the node’s distance. Also, an energy-efficient fitness function was determined, which results in the most energy-efficient route for the network. At the end, four modulations including MQAM, MQPSK, OQPSK and MFSK were applied and the most energy-efficient one with corresponding parameters was specified. By comparing the results of the proposed method to the state-of-the-art studies, the improvements in extending the lifetime of the network was proved. These findings seem quite useful in designing an energy-efficient multi-hop WSN and pave the way for enhancement of the widespread applications in these networks.

Combination of BESO and harmony search for topology optimization of microstructures for materials

This paper introduces a metaheuristic algorithm for topology optimization of microstructures for cellular materials. It combines the harmony search (HS) algorithm with bi-directional evolutionary structural optimization (BESO) features. It is assumed that the cellular material comprises periodic base cells. Bulk and shear moduli are selected as the objectives of topology optimization with a volume constraint on the material solid phase. Each element in the base cell ground structure is treated as a discrete design variable and sensitivity numbers are calculated using homogenization theory. Through an iterative process, new sets of design variables are selected and the volume constraint is imposed using the BESO principals. Algorithm parameters such as filter radius, harmony memory considering rate (HMCR) and pitch adjusting rate (PAR) are selected experimentally. Numerical examples show the capability of the algorithm in designing microstructures of 2D and 3D materials with a high convergence speed. The proposed algorithm can also be easily extended to design of materials with other functional properties.

Hybrid Harmony Search-Simulated Annealing Algorithm for Location-Inventory-Routing Problem in Supply Chain Network Design with Defect and Non-Defect Items

This paper considers a location-inventory-routing problem (LIRP) that integrates the strategic, tactical, and operational decision planning in supply chain network design. Both defect and non-defect items of returned products are considered in the cost of reverse logistics based on the economic production quantity model. The objective of the LIRP is to minimize the total cost of location-allocation of established depots, the cost of inventory, including production setup and holding cost, as well as the cost of travelled distance by the vehicles between the open depots and assigned customers. A Hybrid Harmony Search-Simulated Annealing (HS-SA) algorithm is proposed in this paper. This algorithm incorporates the dynamic values of harmony memory considering rate and pitch adjustment rate with the local optimization techniques to hybridize with the idea of probabilistic acceptance rule from simulated annealing, to avoid the local extreme points. Computational experiments on popular benchmark data sets show that the proposed hybrid HS-SA algorithm outperforms a standard HS and an improved HS for all cases.

Hybrid Harmony Search Algorithm With Grey Wolf Optimizer and Modified Opposition-Based Learning

Most metaheuristic algorithms, including harmony search (HS), suffer from parameter selection. Many variants have been developed to cope with this problem and improve algorithm performance. In this paper, a hybrid algorithm of HS with grey wolf optimizer (GWO) has been developed to solve the problem of HS parameter selection. Then, a modified version of opposition-based learning technique has been applied to the hybrid algorithm to improve the HS exploration because HS easily gets trapped into local optima. Two HS parameters were automatically updated using GWO, namely, pitch adjustment rate and bandwidth. The proposed hybrid algorithm for global optimization problems is called GWO-HS. The GWO-HS was evaluated using 24 classical benchmark functions with 30 state-of-the-art benchmark functions from CEC2014. Then, the GWO-HS has been compared with recent HS variants and other well-known metaheuristic algorithms. The results show that the GWO-HS is superior over the old HS variants and other well-known metaheuristics in terms of accuracy and speed process.

ADAPTIVE HARMONY SEARCH FOR OPTIMIZING CONSTRAINED RESOURCE ALLOCATION PROBLEM

Resource Allocation problem is finding the optimal assignment of finite available resources to tasks or users. Resource allocation problems refer to a wide range of applications such as production, supply chain management, transportation, ICT technologies, etc. Resource allocation problems are NP-hard in nature where the objective is to find the optimal allocations satisfying given constraints. Harmony search (HS) algorithm is a meta-heuristic population based algorithm found good for solving different optimization problems. This paper presents adaptive harmony search (AHS) for solving one-dimensional bin packing problem (BPP) and multi-objective virtual machine placement problem (VMP). The proposed real coded solution representation supports partial constraint satisfaction. Adaptive pitch adjustment rate (PAR) based on population diversity improves the performance of harmony search algorithm. Results show that proposed HS gives optimal solution for 50 BPP instances with 100 % success rate. The performance reduced for large instances of BPP. The proposed weighted AHS for multi objective VMP problem gives better results than genetic algorithm.

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.

Stability assessment and optimal state-feedback system design for PQ-Vf coordination in a PV/DFIG/DSG based microgrid

In this paper an improved comprehensive stability region is presented towards optimal feedback solution for multiple distributed generators (DGs) based microgrid. Overall optimal control design challenges for DGs undergoing grid integrated/islanded operation (i.e. variable stability regions) are addressed for photovoltaic (PV), wind generation system (WGS) as these are considered for multi-DGs dynamics in the present microgrid. Second order phase locked loop (PLL) based PV side voltage source converter (VSC) control, and doubly fed induction generator's (DFIG's), grid side converter (GSC) control are considered for proposed overall gain optimization. To enhance the stability margin global/overall optimal feedback path is targeted here instead of local optimal solutions (individual DG consideration). To achieve optimal stability margin out of multiple individual optimality an Improved Firefly Algorithm IFA) with increased diversity of population and enhanced population density (by harmony search algorithm) is proposed in this paper. The efficacy for global solution is achieved with incorporation of linear incremental pitch adjustment rate (PAR) and exponential decaying bandwidth to obtain fast convergence and to incorporate less randomization for proposed IFA. The overall DG optimization enhances the dynamic stability limits of respective controllers by minimizing low frequency network behavior. The efficacy of proposed stability assessment in terms of power oscillation damping and improved stability limits are verified in MATLAB script, Simulink platforms and validated in TMS320 C6713 DSP test-bench simulation.

The Use of Factorial Design to Improve a Harmony Search Algorithm to Synthesize Heat-Integrated Distillation Sequences

Optimization problems often involve a large number of design variables, and the exact influence of each of these variables upon the objective function can become rather complex; there may exist local optima for the objective function, but for the typical heat-integrated distillation sequence, the matter of interest is solely the global optimum. Therefore, it is necessary to create a stochastic algorithm method which can synthesize distillation systems with multiple components. The encoding process employs and integer number series which allows the system flow sheet structure to be portrayed and then managed. Within this portrayal, the broad synthesis problem takes the form of an implicit MILP (mixed-integer linear programming) problem. This study considers the attributes of six well-known optimization algorithms: Harmony Search algorithm (HS), Artificial Bee Colony (ABC), Bat Algorithm (BA), Crow Search Optimization (CSO), Grew Wolf Optimization (GWO) and Monarch Butterfly Optimization (MBO). The optimal variables which influence the harmony search algorithm can be determined through full factorial design analysis. These variables can then be employed in the search to discover the optimal heat-integrated distillation sequence. The study investigates the attributes of the optimal configuration solution, in terms of harmony size (HS), required number of iterations, harmony memory considering the rate (HMCR), and pitch adjustment rate (PAR). The study then adopts the HS algorithm which is duly improved in order to address the problem. In comparison with alternative techniques, HS is more effective and more robust than other approaches.

Heuristic nonlinear regression strategy for detecting phishing websites

In this paper, we propose a method of phishing website detection that utilizes a meta-heuristic-based nonlinear regression algorithm together with a feature selection approach. In order to validate the proposed method, we used a dataset comprised of 11055 phishing and legitimate webpages, and select 20 features to be extracted from the mentioned websites. This research utilizes two feature selection methods: decision tree and wrapper to select the best feature subset, while the latter incurred the detection accuracy rate as high as 96.32%. After the feature selection process, two meta-heuristic algorithms are successfully implemented to predict and detect the fraudulent websites: harmony search (HS) which was deployed based on nonlinear regression technique and support vector machine (SVM). The nonlinear regression approach was used to classify the websites, where the parameters of the proposed regression model were obtained using HS algorithm. The proposed HS algorithm uses dynamic pitch adjustment rate and generated new harmony. The nonlinear regression based on HS led to accuracy rates of 94.13 and 92.80% for train and test processes, respectively. As a result, the study finds that the nonlinear regression-based HS results in better performance compared to SVM.

Modified Parameters of Harmony Search Algorithm for Better Searching

The scheduling and rostering problems are deliberated as integrated due to they depend on each other whereby the input of rostering problems is a scheduling problems. In this research, the integrated scheduling and rostering bus driver problems are defined as maximising the balance of the assignment of tasks in term of distribution of shifts and routes. It is essential to achieve is fairer among driver because this can bring to increase in driver levels of satisfaction. The latest approaches still unable to address the fairness problem that has emerged, thus this research proposes a strategy to adopt an amendment of a harmony search algorithm in order to address the fairness issue and thus the level of fairness will be escalate. The harmony search algorithm is classified as a meta-heuristics algorithm that is capable of solving hard and combinatorial or discrete optimisation problems. In this respect, the three main operators in HS, namely the Harmony Memory Consideration Rate (HMCR), Pitch Adjustment Rate (PAR) and Bandwidth (BW) play a vital role in balancing local exploitation and global exploration. These parameters influence the overall performance of the HS algorithm, and therefore it is crucial to fine-tune them. The contributions to this research are the HMCR parameter using step function while the fret spacing concept on guitars that is associated with mathematical formulae is also applied in the BW parameter. The model of constant step function is introduced in the alteration of HMCR parameter. The experimental results revealed that our proposed approach is superior than parameter adaptive harmony search algorithm. In conclusion, this proposed approach managed to generate a fairer roster and was thus capable of maximising the balancing distribution of shifts and routes among drivers, which contributed to the lowering of illness, incidents, absenteeism and accidents.

Topology optimization based on the harmony search method

A new topology optimization scheme based on a Harmony search (HS) as a metaheuristic method was proposed and applied to static stiffness topology optimization problems. To apply the HS to topology optimization, the variables in HS were transformed to those in topology optimization. Compliance was used as an objective function, and harmony memory was defined as the set of the optimized topology. Also, a parametric study for Harmony memory considering rate (HMCR), Pitch adjusting rate (PAR), and Bandwidth (BW) was performed to find the appropriate range for topology optimization. Various techniques were employed such as a filtering scheme, simple average scheme and harmony rate. To provide a robust optimized topology, the concept of the harmony rate update rule was also implemented. Numerical examples are provided to verify the effectiveness of the HS by comparing the optimal layouts of the HS with those of Bidirectional evolutionary structural optimization (BESO) and Artificial bee colony algorithm (ABCA). The following conclusions could be made: (1) The proposed topology scheme is very effective for static stiffness topology optimization problems in terms of stability, robustness and convergence rate. (2) The suggested method provides a symmetric optimized topology despite the fact that the HS is a stochastic method like the ABCA. (3) The proposed scheme is applicable and practical in manufacturing since it produces a solid-void design of the optimized topology. (4) The suggested method appears to be very effective for large scale problems like topology optimization.

Stability improvement of PV‐BESS diesel generator‐based microgrid with a new modified harmony search‐based hybrid firefly algorithm

Using a new improved harmony search-based hybrid firefly algorithm (IHBFA), a comprehensive controller gain parameter estimation of all distributed resources-based microgrid is proposed. To ensure a fast convergence and to endeavour less randomisation to conventional firefly algorithm (FA), diversity of population is increased by an improved harmony search (HS) algorithm. To decrease local optima searching delay, a linear incremental pitch adjustment rate and exponential decaying bandwidth is considered for proposed HS-based hybrid FA. Photovoltaic (PV), an auxiliary battery energy storage system (BESS) with the second-order phase-locked loop control, is considered as a primary DG ( DG 1) for the proposed microgrid. Pade approximation delay-based governor control is used for the diesel generator unit, considered as a secondary DG ( DG 2). The overall gain optimisation improves the dynamic stability limits by minimising low-frequency network behaviour. The effectiveness of proposed IHBFA in terms of power oscillation damping and improved stability limits is clearly demonstrated for microgrid applications.

An improved harmony search-based functional link higher order ANN for nonlinear data classification

To obtain the optimal set of weights in any higher order artificial neural network, it is often laborious to adjust the set of weights by using appropriate learning algorithm. In this paper, an improved variant of harmony search (HS), called improved harmony search (IHS) along with gradient descent learning (GDL) is used with functional link artificial neural network (FLANN) for the task of classification in data mining. IHS performs better than HS by eliminating constant parameters [bandwidth (bw), pitch adjustment rate (PAR)] in HS algorithm and incorporating changes dynamically in PAR and bw with iteration. The searching capability of IHS to obtain optimal harmony is used along with GDL to discover optimal set of weights for FLANN model. The proposed IHS-GDL-FLANN is implemented in MATLAB and compared with other alternatives. In order to get statistical correctness of results, the proposed method is analysed by using various statistical analysis under null-hypothesis.