# Harmony Search Algorithm and Fuzzy Logic Theory: An Extensive Review from Theory to Applications

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## Abstract

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## 1. Introduction

- (1)
- Generation. Complex natural or social processes replicate traditional metaheuristic methods. The computational modeling of partially known behaviors and non-characterized operations, while often still undefined, requires such a replication. It is also especially difficult to accurately model even basic metaphors. However, FL offers a simple and well-known framework for designing structures by using human intelligence [37].
- (2)
- Transparency. Metaphors used by metaheuristic methods contribute to algorithms that are difficult to understand from an optimization viewpoint. However, the metaphor should not be translated specifically as a clear search technique. On the other hand, fuzzy reasoning produces entirely interpretable models whose content reflects the quest technique as human beings would execute it [38].
- (3)
- Improvement. Metaheuristic methods were configured to preserve the same protocol for the generation of candidate solutions.

## 2. Harmony Search Algorithm

_{1}, x

_{2}, x

_{3}, …, x

_{HMS}), as many as HMS, and save them in the HM matrix.

- Select a value from the HM: ${x}_{i}^{\prime}\leftarrow {x}_{i}^{\mathrm{integer}\left(rand[0.1]\times HMS\right)+1}$ with probability HMCR (Harmony Memory Considering Rate), 0 ≤ HMCR ≤ 1;
- Perform the uniform random search between lower and upper bounds with probability (1-HMCR).

- Slightly modify ${x}_{i}^{\prime}$: ${x}_{i}^{\prime}\leftarrow {x}_{i}^{\prime}+BW\times (2\times rand-1)$ with a probability of PAR, 0 ≤ PAR ≤ 1, where rand denotes an evenly generated random value in interval span zero and one and BW is the maximum variation in the pitch adjusting phase;
- Do not change anything with probability (1-PAR).

Algorithm 1 Pseudo-code of the HS. |

Choose the HS user parameters: HMS, HMCR, PAR, BW, and Max_Improvisation. |

Create randomly the (HM considering the upper and lower bounds. |

Calculate the objective function of the HM individual. |

while (t ≤ Max_Improvisation) or (Any Stopping Condition) |

for each i ϵ [1, n] do |

if rand (0,1) ≤ HMCR |

${x}_{i}^{\prime}={x}_{i}^{j}$ where j ~ U (1, …, HMS). |

if rand (0,1) ≤ PAR |

${x}_{i}^{\prime}={x}_{i}^{\prime}+(2\times rand-1)\times BW$ |

end if |

else |

${x}_{i}^{\prime}={x}_{i}{}^{Lower}+rand\times ({x}_{i}{}^{Upper}-{x}_{i}{}^{Lower})$ |

end if |

Calculate the objective function (fitness/cost function) of a new harmony. |

If cost (new harmony) < cost (worst harmony in HM) |

Replace the worst harmony in HM with the new harmony |

end if |

end while |

Post process and visualization |

## 3. Fuzzy Logic Theory

#### 3.1. Fuzzy Sets

#### 3.2. Type-1 Fuzzy Logic System

#### 3.3. Type-2 Fuzzy Logic System

## 4. Harmony Search Algorithm and Fuzzy Logic Theory

#### 4.1. Hybrid HS Algorithm and Fuzzy Logic Theory

#### 4.2. Fuzzy Harmony Search Algorithm

#### 4.3. Harmony Search Algorithm and Fuzzy Controllers

#### 4.4. Harmony Search Algorithm and Fuzzy Clustering

#### 4.5. Harmony Search to Optimize Fuzzy Logic Systems

## 5. Discussion

#### 5.1. Variants of HS Algorithm

#### 5.2. Fuzzy Logic Models

#### 5.3. Combinations of HS and Fuzzy Logic Theory

#### 5.4. Applications of HS and Fuzzy Logic in Different Fields

## 6. Conclusions and Future Research

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## Nomenclature

Symbol | Description |

ABHS | Adaptive binary harmony search |

ABHSAFC | Adaptive binary harmony search algorithm fuzzy control |

ACO | Ant colony optimization |

AHS | Advanced harmony search |

ANFI | Adaptive neuro-fuzzy inference |

APP | Aggregate production planning |

ARIMA | Autoregressive integrated moving average |

BA | Bat algorithm |

BAP | Buffer allocation problem |

BCO | Bee colony optimization |

BTS | Base transceiver station |

CS | Cuckoo search |

CSA | Clone selection algorithm |

DCHS | Dynamic clustering technique based on the harmony search |

DE | Differential evolution |

DG | Distributed generation |

DHS | Discrete harmony search |

DHS | Differential harmony search |

EEG | Electroencephalogram |

EFSs | Evolutionary fuzzy systems |

FC | Fuzzy control |

FCC | Fuzzy c-means clustering |

FCM | Fuzzy c-means |

FCMAC | Fuzzy cerebellar articulation controller |

FCMAC | Fuzzy cerebellar model articulation controller |

FCMACNN | Fuzzy cerebellar model articulation controller neural networks |

FDE | Fuzzy differential evolution |

FDHS | Fuzzy discrete harmony search |

FHS | Fuzzy harmony search |

FHSC | Fuzzy harmony search clustering |

FHS-FT | Fuzzy harmony search-fourier transform |

FJSP | Flexible workshop scheduling |

FL | Fuzzy logic |

FLC | Fuzzy logic controller |

FLIHSBC | Fuzzy logic and improved harmony search-based clustering |

FLR | Fuzzy linear regression |

FLS | Fuzzy logic system |

FNS | Fuzzy neural system |

FO | Fuzzy optimization |

FPSS | Fuzzy logic power system stabilizer |

FRS | Fuzzy rough set |

FT | Fourier transform |

FTS | Fuzzy time series |

GAs | Genetic algorithms |

GHSA | Global harmony search algorithm |

GT2FHS | Generalized type-2 fuzzy harmony search |

GT2-FIS | General type-2 fuzzy inference system |

GWO | Gray wolf optimization |

HFISA | Harmony fuzzy image segmentation algorithm |

HHS | Hybridizations of harmony search |

HHS-FL | Hybrid harmony search and fuzzy logic |

HM | Harmony memory |

HMS | Harmony memory size |

HS | Harmony search |

HSBA | Harmony search -based approach |

HSCS | Harmony search with cuckoo search |

HSPS | HS optimized partitioning strategy |

ICA | Imperial competitive algorithm |

IHPS | Isolated hybrid power system |

IHS | Improved harmony search |

IT2-FIS | Interval type-2 fuzzy inference systems |

IT2-FLS | Interval type2- fuzzy logic system |

IT2-FLS-EGARCH | Interval type2- fuzzy logic system exponential generalized autoregressive conditional heteroscedastic |

IT2-CE-EGARCH | Interval type2-computationally efficient- exponential generalized autoregressive conditional heteroscedastic |

JADE | Adaptive differential evolution |

LFC | Load frequency control |

LNF | Local neuro-fuzzy |

LSBA | Logic strategy-based approach |

LSSVMs | Least square support vector machines |

LTE | Long-term 4G |

MF | Membership function |

MOHSA | Multi-objective harmony search algorithm |

NGHSA | Novel global best harmony search algorithm |

OPF | Optimal power flow |

PAR | Pitch adjusting rate |

PV | Photovoltaic |

PID | Proportional-integral-derivative |

PSO | Particle swarm optimization |

QOBL | Quasi-opposition-based learning principle |

QOHS | Quasi-oppositional harmony search |

REWFTS-IHS | Refined exponentially weighted fuzzy time series improved harmony search |

SAMOHSFC | Self-adapting multi-objective harmony search fuzzy clustering |

SERNFIS | Self-evolving, recursive neuro-fuzzy inference system |

SGHS | Self-adjusting global best harmony search |

SHS | Standard harmony search |

ST2-FIS | Shadowed type-2 fuzzy inference scheme |

T1-FIS | Type-1 fuzzy inference systems |

T1-FLS | Type-1 fuzzy logic system |

T2-FLHS | Type-2 fuzzy logic harmony search |

T2-FLS | Type-2 fuzzy logic scheme |

TS | Tabu search |

TSK | Takagi sugeno kang |

VHSA | Variable neighborhood search combined with harmony search algorithm |

WCA | Water cycle algorithm |

WDN | Water distribution network |

WSN | Wireless sensor network |

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**Figure 5.**REWFTS–IHS algorithm [66].

**Figure 6.**Distribution per year of submitted publications applicable to the HS and FL (2007~22 August 2020).

**Figure 7.**Distribution per annum of presented papers applicable to the HS and FL (2007~22 August 2020).

**Figure 8.**Variants distribution of HS algorithm equipped with FL in the reviewed papers (2007~22 August 2020).

**Figure 10.**Distribution of reported articles according to the combination type of HS and FL (2007~22 August 2020).

**Figure 11.**Percentage of the reported articles that used HS and FL in various research fields (2012~22 August 2020).

**Figure 12.**Number of HS-based and fuzzy-related articles published by various research repositories (2012~22 August 2020).

Reference | Problems/Applications | Results | Year | Fuzzy Model/Technique | Variants of HS |
---|---|---|---|---|---|

[60] | Buffer allocation problems | The proposed algorithm has capable of generating better solutions | 2020 | FO | SHS |

[64] | Machining system | The efficiency of the proposed model | 2019 | FO | SHS |

[68] | High–order fuzzy time series forecasting model | The superiority of the proposed model over the other models | 2019 | FTS | SHS |

[58] | Optimization of a benchmark set of functions | Efficacy of the algorithm in most of the reference functions | 2018 | FO | SHS |

[70] | LFC | Good performance of the proposed method | 2018 | FNS | SHS |

[54] | Unit commitment problem | The efficiency of the proposed model is | 2018 | FO | SHS |

[55] | Optimization of a Benchmark Set of Functions | Finding global minima of complex functions. | 2018 | FO | SHS |

[61] | Food transportation problem | Effectiveness of the algorithm | 2017 | FO | IHS |

[45] | Congestion management problem in an electricity market | The results demonstrate that the proposed technique is better and superior to CPSO, PSO-TVAC, and PSOTVIW methods. | 2016 | FO | SHS |

[48] | OPF | Finding the optimal solution | 2016 | FO | SHS |

[49] | Optimization problems | Effectiveness and efficiency of the proposed approach. | 2016 | FO | SHS |

[67] | Electric load forecasting | The efficiency of the proposed method | 2016 | FTS | IHS |

[69] | Efficient stock price prediction | The effectiveness of the proposed model | 2016 | FNS | IHS |

[63] | Multi-objective optimization in the drilling of CFRP (polyester) composites | Effectiveness of the proposed HS | 2016 | FO | SHS |

[46] | Flexible job shop scheduling problem | The results and comparisons show the effectiveness and efficiency of DHS | 2015 | FO | IHS |

[51] | Placement of DG units in electrical distribution systems | Finding the optimal solution | 2015 | FO | SHS |

[53] | Multi-objective optimization of water distribution networks | founding a Pareto set of solutions | 2015 | FO | SHS |

[57] | Placement and sizing of passive and active power filters | Finding the optimal solution | 2015 | FO | IHS |

[47] | Dynamic reconfiguration of distribution network | Effectiveness of the proposed method | 2014 | FO | IHS |

[52] | Simultaneous reconfiguration and capacitor placement | Finding the optimal solution | 2014 | FO | SHS |

[59] | Image thresholding method | Good search stability of the HS | 2014 | FO | SHS |

[66] | Short-term load forecasting | Effectiveness of the proposed method | 2014 | FTS | IHS |

[71] | Short-term wind power forecasting | Good performance of the proposed model | 2014 | FNS | SHS |

[56] | Multi-objective optimal location of SSSC and STATCOM | Finding the optimal solution | 2013 | FO | SHS |

[65] | Benchmarks problems | The efficiency of the hybrid method | 2012 | FO | SHS |

[62] | Aggregate production planning | VHSA can find better solutions | 2011 | FO | HHS |

[50] | Image segmentation | The efficiency of the proposed algorithm | 2009 | FO | SHS |

Reference | Problems/Applications | Results | Year | Fuzzy Model/Technique | Variants of HS Algorithm |
---|---|---|---|---|---|

[88] | Optimization of PWR nuclear power plant | FHS better performance | 2019 | FLC | SHS |

[13] | Mathematical functions and controller optimization | Achieving good solutions for both algorithm | 2019 | ST2-FIS | IHS |

[94] | Benchmarks functions | Finding better solutions in comparison to a type-1 FHS | 2019 | T2-FLS | IHS |

[93] | Mathematical functions | Achieving the FHS better solutions than HS | 2018 | T1 and IT2-FLS | IHS |

[92] | Mathematical functions | Achieving the FHS better solutions than HS | 2018 | T1 and IT2-FLS | IHS |

[90] | Capacitor placement in distribution systems | Effectiveness of FDHS | 2016 | FL | IHS |

[91] | Benchmark mathematical functions | The proposed algorithm finds better solutions than a type-1 FHS | 2016 | T2-FLS | SHS |

[89] | Optimization of mathematical functions | Improving the performance of HS | 2015 | FLC | SHS |

[74] | Optimization problems | The proposed algorithm can find better solutions | 2015 | FLC | SHS |

Reference | Problems/Applications | Results | Year | Fuzzy Model/Technique | Variants of HS |
---|---|---|---|---|---|

[107] | Type-2 fuzzy logic controllers | Good performance presented model | 2020 | IT2-FLS | SHS |

[108] | Optimization problems | The FHS method efficiency | 2020 | FL | SHS |

[101] | Fuzzy controller | FDE algorithm outperforms the results of the FBCO and FHS algorithms in the optimization of fuzzy controllers | 2019 | T1-FLS | SHS |

[102] | FCMAC | Faster convergence speed and better accuracy | 2018 | FCMAC | IHS |

[97] | Design of a fuzzy PID controller for load frequency control | Robustness of the controller’s gains designed for the concerned power system | 2018 | FLC | SHS |

[113] | Optimization of the Ball and Beam Controller | Better results than other methods | 2018 | FL | SHS |

[112] | FCMACNN | High convergence speed | 2017 | FNS | IHS |

[114] | Benchmark control problems | Significant improvement in the three benchmark control problems | 2017 | T1 and T2-FLS | SHS |

[115] | Benchmark control problems | The efficiency of the proposed method | 2017 | FL | SHS |

[105] | Frequency and power control of an isolated hybrid power system (HPS) (IHPS) | Fractional order (FO) fuzzy PID (FO-F-PID) controller shows better performance over the integer order-PID and F-PID controller | 2017 | FLC | IHS |

[118] | Load Frequency Control | The effectiveness of the proposed method | 2016 | FLC | SHS |

[99] | Load frequency stabilization of an isolated hybrid power system | Obtaining the minimum frequency and power deviations | 2015 | FLC | IHS |

[98] | Frequency stabilization of an isolated hybrid power system | Obtaining the minimum frequency and power deviations | 2015 | FLC | IHS |

[100] | The design of fuzzy logic power system stabilizer (FPSS) | Less optimization time and speed. | 2015 | FLC | SHS |

[110] | Temperature control of air heater system | The efficiency of the proposed model | 2014 | Lyapunov-based adaptive fuzzy control | SHS |

[95] | Power plant control | The efficiency of the ABHSAFC | 2013 | Lyapunov-based adaptive fuzzy control | IHS |

[103] | Designing stable adaptive fuzzy controllers | The efficiency of the proposed method | 2013 | Lyapunov-based adaptive fuzzy control | IHS |

[104] | Improving the electronic throttle valve | Effective performance of the proposed controller. | 2013 | FLC | SHS |

[106] | Design of fuzzy power system stabilizer | The efficiency of the HS algorithm | 2013 | FLC | SHS |

[111] | Design of stable adaptive fuzzy tracking control strategy for vision-based navigation of autonomous mobile robots | The efficiency of the proposed model | 2013 | Lyapunov-based adaptive fuzzy control | IHS |

[109] | Stable fuzzy controller design | The superiority of the GrHSBA to GA and PSO methods | 2013 | FLC | IHS |

[117] | Multi-stage fuzzy load frequency control | The robustness of the proposed strategy. | 2013 | FLC | MOHS |

[116] | Multi-area restructure problem | The robust performance of a proposed method | 2012 | FLC | MOHS |

[96] | Optimization of FLC | Good performance of a hybrid method | 2010 | Lyapunov-based adaptive fuzzy control | IHS |

Reference | Problems/Applications | Results | Year | Fuzzy Model/Technique | Variants of HS |
---|---|---|---|---|---|

[135] | Optimization of wireless sensor networks | Better performance of proposed method than other methods | 2020 | Fuzzy clustering | Hybridization of FL and HS |

[126] | FTS optimization | Robustness of the proposed model | 2019 | Fuzzy clustering (time series) | Hybridization of K-means and HS |

[134] | Enodeb position forecasting of LTE based on BTS existing | The efficiency of the proposed method. | 2019 | Fuzzy clustering | SHS |

[133] | Image segmentation | The SAMOHSFC has well self adaptiveness and strong robustness to noise. | 2018 | Fuzzy clustering | IHS |

[131] | Energy-efficient wireless sensor networks | Finding an optimal solution. | 2018 | Fuzzy clustering | SHS |

[127] | Wireless Sensor Networks | Better performance of the method in prolonging the lifetime of the sensor network. | 2017 | Fuzzy clustering | Hybridization of fuzzy suitable judgment method and HS |

[128] | Scheme Classification | Good performance of the presented method | 2017 | Fuzzy clustering | IHS |

[137] | Image Clustering method | The efficiency of the proposed model | 2016 | Fuzzy Clustering | IHS |

[138] | Fuzzy Classification Systems | The algorithm can classify the data with considerable classification accuracy. | 2014 | Fuzzy clustering | Hybridization of GA and HS |

[136] | EEG Signals Classification | Good performance of the proposed method | 2011 | Fuzzy clustering | SHS |

[123] | MRI brain segmentation | The efficiency of the proposed method | 2011 | Fuzzy clustering | IHS |

[132] | Simultaneous estimation of groundwater recharge rates, associated zone structures, and hydraulic conductivity values | The efficiency of the proposed solution | 2011 | Fuzzy clustering | SHS |

[50] | Fuzzy C-Means Segmentation of MR Images | The superiority of the algorithm over the randomly initialized FCM algorithm and improvement of the harmony search speed. | 2009 | Fuzzy clustering | SHS |

[122] | Sugeno fuzzy classification systems | The approach can achieve a better classification performance than that of the original CSA and HS method. | 2009 | Fuzzy clustering | Hybridization of CSA and HS |

[130] | Clustering to Image Segmentation | DCHS is able to find the appropriate number of clusters and locations of cluster centers and, solutions with the higher quality to other methods. | 2009 | Fuzzy clustering | IHS |

[120] | Web document clustering | The results show that the clusters produced by the proposed method have higher quality. | 2008 | Fuzzy clustering | IHS |

[121] | Clustering web documents | The hybrid algorithm can generate higher quality clusters than using either the HClust or the K-means alone. | 2008 | Fuzzy clustering | IHS |

[125] | Fuzzy Clustering | Finding an optimal solution with high convergence speed. | 2008 | Fuzzy clustering | IHS |

[124] | Simultaneous determination of aquifer parameters and zone structures | The effectiveness of the proposed solution algorithm | 2007 | Fuzzy clustering | SHS |

Reference | Problems/Applications | Results | Year | Fuzzy Model/Technique | Variants of HS Algorithm |
---|---|---|---|---|---|

[140] | Approximate normal parameter reduction of fuzzy soft | The efficiency of the proposed method | 2015 | Fuzzy soft set | SHS |

[141] | Fuzzy rough set reduct | The efficiency of the proposed method | 2015 | Fuzzy rough set | IHS |

[143] | Stock market volatility prediction | Significant improvements in forecasting performance | 2015 | IT2-FLS | IHS |

[144] | Fuzzy aggregate production planning | Obtaining good solutions | 2012 | Fuzzy programming model | HHS |

[142] | The design of FLR models | Good performance of the proposed method | 2011 | Fuzzy Regression | Hybridization of TS and HS |

[139] | FLC parameters Optimization | Effectiveness of presented model | 2010 | FL | IHS |

Variants of HS Algorithm | Problems/Applications | Reference |
---|---|---|

SHS | Optimization of a benchmark set of functions | [58] |

Image thresholding method | [59] | |

Buffer allocation problems | [60] | |

Multi-objective optimization in the drilling of CFRP (polyester) composites | [63] | |

Machining system | [64] | |

Benchmarks problems | [65] | |

High–order FTS forecasting model | [68] | |

LFC | [70] | |

Short-term wind power forecasting | [71] | |

Optimization of PWR nuclear power plant | [88] | |

Optimization of mathematical functions | [89] | |

Optimization problems | [74] | |

Benchmark mathematical functions | [91] | |

Design of a fuzzy PID controller for load frequency control | [97] | |

The design of FPSS | [100] | |

Fuzzy controller | [101] | |

Improving the electronic throttle valve | [104] | |

Design of fuzzy power system stabilizer | [106] | |

Type-2 FL controllers | [108] | |

Optimization problems | [107] | |

Temperature control of air heater system | [110] | |

Optimization of the ball and beam controller | [113] | |

Benchmark control problems | [72] | |

Benchmark control problems | [73] | |

Load frequency control | [118] | |

Fuzzy c-means segmentation of MR images | [50] | |

Simultaneous determination of aquifer parameters and zone structures | [124] | |

Congestion management problem in an electricity market | [45] | |

OPF | [48] | |

Optimization problems | [49] | |

Image segmentation | [145] | |

Placement of dg units in electrical distribution systems | [51] | |

Simultaneous reconfiguration and capacitor placement | [52] | |

Multi-objective optimization of water distribution networks | [53] | |

Unit commitment problem | [54] | |

Optimization of a benchmark set of functions | [55] | |

Multi-objective optimal location of SSSC and STATCOM | [56] | |

Energy-efficient wireless sensor networks | [131] | |

Simultaneous estimation of groundwater recharge rates, associated zone structures, and hydraulic conductivity values | [132] | |

Enodeb position forecasting of LTE based on BTS existing | [134] | |

EEG signals classification | [136] | |

Approximate normal parameter reduction of fuzzy soft | [140] | |

Multi-area restructure problem | [116] | |

Multi-stage fuzzy load frequency control | [117] | |

IHS | Placement and sizing of passive and active power filters | [57] |

Flexible job shop scheduling problem | [46] | |

Dynamic reconfiguration of distribution network | [47] | |

Food transportation problem | [61] | |

Short-term load forecasting | [66] | |

Electric load forecasting | [67] | |

Efficient stock price prediction | [69] | |

Capacitor placement in distribution systems | [90] | |

Mathematical functions and controller optimization | [13] | |

Mathematical functions | [93] | |

Mathematical functions | [92] | |

Benchmarks functions | [94] | |

Power plant control | [95] | |

Optimization of FLC | [96] | |

Load frequency stabilization of an isolated hybrid power system | [99] | |

Frequency stabilization of an isolated hybrid power system | [98] | |

FCMAC | [102] | |

Designing stable adaptive fuzzy controllers | [103] | |

Frequency and power control of an IHPS | [105] | |

Design of stable adaptive fuzzy tracking control strategy for vision-based navigation of autonomous mobile robots | [111] | |

Stable fuzzy controller design | [109] | |

FCMACNN | [112] | |

Web document clustering | [120] | |

Clustering web documents | [121] | |

MRI brain segmentation | [123] | |

Fuzzy clustering | [125] | |

Scheme classification | [128] | |

Image segmentation | [133] | |

Clustering to image segmentation | [130] | |

Image clustering method | [137] | |

FLC parameters optimization | [139] | |

Fuzzy rough set reduct | [141] | |

Stock market volatility prediction | [143] | |

HHS | Aggregate production planning | [62] |

FTS optimization | [126] | |

Wireless sensor networks | [127] | |

Sugeno fuzzy classification systems | [122] | |

Optimization of wireless sensor networks | [135] | |

Fuzzy classification systems | [138] | |

The design of FLR models | [142] | |

Fuzzy aggregate production planning | [144] |

Fuzzy Model/Technique | Problems/Applications | Reference |
---|---|---|

FO | Congestion management problem in an electricity market | [45] |

Flexible job shop scheduling problem | [46] | |

Dynamic reconfiguration of distribution network | [47] | |

OPF | [48] | |

Optimization problems | [49] | |

Image segmentation | [145] | |

Placement of dg units in electrical distribution systems | [51] | |

Simultaneous reconfiguration and capacitor placement | [52] | |

Multi-objective optimization of water distribution networks | [53] | |

Unit commitment problem | [54] | |

Optimization of a benchmark set of functions | [55] | |

Multi-objective optimal location of SSSC and STATCOM | [56] | |

Placement and sizing of passive and active power filters | [57] | |

Optimization of a benchmark set of functions | [58] | |

Image thresholding method | [59] | |

Buffer allocation problems | [60] | |

Food transportation problem | [61] | |

Multi-objective optimization in the drilling of CFRP (polyester) composites | [63] | |

Aggregate production planning | [62] | |

Machining system | [64] | |

Benchmarks problems | [65] | |

Optimization problems | [107] | |

Benchmark control problems | [73] | |

Optimization of the ball and beam controller | [113] | |

FLC parameters optimization | [139] | |

Capacitor placement in distribution systems | [90] | |

FTS | Short-term load forecasting | [66] |

Electric load forecasting | [67] | |

High–order FTS forecasting model | [68] | |

FNS | Efficient stock price prediction | [69] |

LFC | [70] | |

Short-term wind power forecasting | [71] | |

FCMACNN | [112] | |

FLC | Optimization of PWR nuclear power plant | [88] |

Optimization of mathematical functions | [89] | |

Optimization problems | [74] | |

Design of a fuzzy PID controller for load frequency control | [97] | |

Load frequency stabilization of an isolated hybrid power system | [99] | |

Frequency stabilization of an isolated hybrid power system | [98] | |

The design of FL power system stabilizer (FPSS) | [100] | |

Improving the electronic throttle valve | [104] | |

Frequency and power control of an isolated hybrid power system (IHPS) | [105] | |

Design of fuzzy power system stabilizer | [106] | |

Multi-area restructure problem | [116] | |

Multi-stage fuzzy load frequency control | [117] | |

Load frequency control | [118] | |

Stable fuzzy controller design | [109] | |

Power plant control | [95] | |

Optimization of FLC | [96] | |

FCMAC | [102] | |

Designing stable adaptive fuzzy controllers | [103] | |

Type-2 FL controllers | [108] | |

Temperature control of air heater system | [110] | |

Design of stable adaptive fuzzy tracking control strategy for vision-based navigation of autonomous mobile robots | [111] | |

Fuzzy controller | [101] | |

T2-FLS | Benchmark mathematical functions | [91] |

Mathematical functions and controller optimization | [13] | |

Mathematical functions | [93] | |

Mathematical functions | [92] | |

Benchmarks functions | [94] | |

Stock market volatility prediction | [143] | |

Benchmark control problems | [72] | |

Fuzzy Clustering | Web document clustering | [120] |

Clustering web documents | [121] | |

Fuzzy c-means segmentation of MR images | [50] | |

MRI brain segmentation | [123] | |

Simultaneous determination of aquifer parameters and zone structures | [124] | |

Fuzzy clustering | [125] | |

FTS (FTS) optimization | [126] | |

Wireless sensor networks | [127] | |

Scheme classification | [128] | |

Energy-efficient wireless sensor networks | [131] | |

Simultaneous estimation of groundwater recharge rates, associated zone structures, and hydraulic conductivity values | [132] | |

Image segmentation | [133] | |

Enodeb position forecasting of LTE based on BTS existing | [134] | |

Sugeno fuzzy classification systems | [122] | |

Clustering to image segmentation | [130] | |

Optimization of wireless sensor networks | [135] | |

EEG signals classification | [136] | |

Image clustering method | [137] | |

Fuzzy classification systems | [138] | |

Fuzzy Soft Sets | Approximate normal parameter reduction of fuzzy soft | [140] |

Fuzzy rough set reduct | [141] | |

Fuzzy Regression | The design of FLR models | [142] |

Fuzzy Programming Model | Fuzzy aggregate production planning | [144] |

Type of Combination | Problem | Reference | Year | Fuzzy Model/Technique | Variants of HS |
---|---|---|---|---|---|

Hybrid HS Algorithm and FL | Buffer allocation problems | [60] | 2020 | FO | SHS |

High–order fuzzy time Series forecasting model | [68] | 2019 | FTS | SHS | |

Machining system | [64] | 2019 | FO | SHS | |

Unit commitment problem | [54] | 2018 | FO | SHS | |

Optimization of a benchmark set of functions | [55] | 2018 | FO | SHS | |

Optimization of a benchmark set of functions | [58] | 2018 | FO | SHS | |

Load frequency control (LFC) | [70] | 2018 | FNS | SHS | |

Food transportation problem | [61] | 2017 | FO | IHS | |

Congestion management problem in an electricity market | [45] | 2016 | FO | SHS | |

Optimal power flow (OPF) | [48] | 2016 | FO | SHS | |

Optimization problems | [49] | 2016 | FO | SHS | |

Multi-objective optimization in the drilling of CFRP (polyester) composites | [63] | 2016 | FO | SHS | |

Electric load forecasting | [67] | 2016 | FTS | IHS | |

Efficient stock price prediction | [69] | 2016 | FNS | IHS | |

Flexible job shop scheduling problem | [46] | 2015 | FO | IHS | |

Multi-objective optimization of water distribution networks | [53] | 2015 | FO | SHS | |

Placement of dg units in electrical distribution systems | [51] | 2015 | FO | SHS | |

Placement and sizing of passive and active power filters | [57] | 2015 | FO | IHS | |

Dynamic reconfiguration of distribution network | [47] | 2014 | FO | IHS | |

Short-term load forecasting | [66] | 2014 | FTS | IHS | |

Short-term wind power forecasting | [71] | 2014 | FNS | SHS | |

Simultaneous reconfiguration and capacitor placement | [52] | 2014 | FO | SHS | |

Image thresholding method | [59] | 2014 | FO | SHS | |

Multi-objective optimal location of SSSC and STATCOM | [56] | 2013 | FO | SHS | |

Benchmarks problems | [65] | 2012 | FO | SHS | |

Aggregate production planning | [62] | 2011 | FO | HHS | |

Image segmentation | [145] | 2009 | FO | SHS | |

Fuzzy HS | Optimization of PWR nuclear power plant | [88] | 2019 | FLC | SHS |

Mathematical functions and controller optimization. | [13] | 2019 | Shadowed T2-FIS | IHS | |

Benchmarks functions | [94] | 2019 | T2-FLS | IHS | |

Mathematical functions | [93] | 2018 | T1 and IT2-FLS | IHS | |

Mathematical functions | [92] | 2018 | T1 and IT2-FLS | IHS | |

Capacitor placement in distribution systems | [90] | 2016 | FO | IHS | |

Benchmark mathematical functions | [91] | 2016 | T2-FLS | SHS | |

Optimization of mathematical functions | [89] | 2015 | FLC | SHS | |

Optimization problems | [74] | 2015 | FLC | SHS | |

HS and Fuzzy Controllers | T2-FLC | [108] | 2020 | Interval type-2 fuzzy logic controller | SHS |

Optimization problems | [107] | 2020 | FO | SHS | |

Fuzzy controller | [101] | 2019 | T1-FLS | SHS | |

Design of a fuzzy PID controller for load frequency control | [97] | 2018 | FLC | SHS | |

FCMAC | [102] | 2018 | Fuzzy Cerebellar Model Articulation Controller | IHS | |

Optimization of the ball and beam controller | [113] | 2018 | FO | SHS | |

Frequency and power control of an IHPS | [105] | 2017 | FLC | IHS | |

FCMACNN | [112] | 2017 | FNS | IHS | |

Benchmark control problems | [72] | 2017 | T1 and T2-FLS | SHS | |

Benchmark control problems | [73] | 2017 | FO | SHS | |

LFC | [118] | 2016 | FLC | SHS | |

Load frequency stabilization of an isolated hybrid power system | [99] | 2015 | FLC | IHS | |

Frequency stabilization of an isolated hybrid power system | [98] | 2015 | FLC | IHS | |

The design of fuzzy logic power system stabilizer (FPSS) | [100] | 2015 | FLC | SHS | |

Temperature control of air heater system | [110] | 2014 | Lyapunov-based adaptive fuzzy control | SHS | |

[111] | 2014 | Lyapunov-based adaptive fuzzy control | IHS | ||

Power plant control | [95] | 2013 | Lyapunov-based adaptive fuzzy control | IHS | |

Improving the electronic throttle valve | [104] | 2013 | FLC | SHS | |

Design of fuzzy power system stabilizer | [106] | 2013 | FLC | SHS | |

Multi-stage fuzzy LFC | [117] | 2013 | FLC | MOHSA | |

Stable fuzzy controller design | [109] | 2013 | Fuzzy Logic Controller | IHS | |

Designing stable adaptive fuzzy controllers | [103] | 2013 | Lyapunov-based adaptive fuzzy control | IHS | |

Multi-area restructure problem | [116] | 2012 | FLC | MOHSA | |

Optimization of FLC | [96] | 2010 | Lyapunov-based adaptive fuzzy control | IHS | |

HS and Fuzzy Clustering | Optimization of wireless sensor networks | [135] | 2020 | Fuzzy clustering | Hybridization of FL and HS |

FTS optimization | [126] | 2019 | Fuzzy clustering | Hybridization of K-means and HS | |

Enodeb position forecasting of LTE based on BTS existing | [134] | 2019 | Fuzzy clustering | SHS | |

Energy-efficient wireless sensor networks | [131] | 2018 | Fuzzy clustering | SHS | |

Image segmentation | [133] | 2018 | Fuzzy clustering | IHS | |

Wireless sensor networks | [127] | 2017 | Fuzzy clustering | Hybridization of fuzzy suitable judgment method and HS | |

Scheme classification | [128] | 2017 | Fuzzy clustering | IHS | |

Image clustering method | [137] | 2016 | Fuzzy Clustering | IHS | |

Fuzzy classification systems | [138] | 2014 | Fuzzy clustering | Hybridization of GA and HS | |

[132] | 2011 | Fuzzy clustering | SHS | ||

MRI brain segmentation | [123] | 2011 | Fuzzy clustering | IHS | |

EEG signals classification | [136] | 2011 | Fuzzy clustering | SHS | |

Fuzzy c-means segmentation of MR images | [50] | 2009 | Fuzzy clustering | SHS | |

Sugeno fuzzy classification systems | [122] | 2009 | Fuzzy clustering | Hybridization of CSA and HS | |

Clustering to image segmentation | [130] | 2009 | Fuzzy clustering | IHS | |

Web document clustering | [120] | 2008 | Fuzzy clustering | IHS | |

Clustering web documents | [121] | 2008 | Fuzzy clustering | IHS | |

Fuzzy clustering | [125] | 2008 | Fuzzy clustering | IHS | |

Simultaneous determination of aquifer parameters and zone structures | [124] | 2007 | Fuzzy clustering | SHS | |

HS to Optimize FLSs | Stock market volatility prediction | [143] | 2015 | IT2-FLS | IHS |

Approximate normal parameter reduction of fuzzy soft | [140] | 2015 | Fuzzy soft set | SHS | |

Fuzzy rough set reduct | [141] | 2015 | Fuzzy rough set | IHS | |

Fuzzy aggregate production planning | [144] | 2012 | Fuzzy programming model | HHS | |

The design of FLR models | [142] | 2011 | Fuzzy Regression | Hybridization of TS and HS | |

FLC parameters optimization | [139] | 2010 | FO | IHS |

Field of Study | Problems/Applications | Reference |
---|---|---|

Electrical Engineering | LFC | [70] |

Short-term wind power forecasting | [71] | |

Optimization of PWR nuclear power plant | [88] | |

Design of FPSS | [106] | |

Load frequency control | [118] | |

Congestion management problem in an electricity market | [45] | |

OPF | [48] | |

Placement of dg units in electrical distribution systems | [51] | |

Simultaneous reconfiguration and capacitor placement | [52] | |

Unit commitment problem | [54] | |

Multi-objective optimal location of SSSC and STATCOM | [56] | |

Multi-stage fuzzy load frequency control | [117] | |

Placement and sizing of passive and active power filters | [57] | |

Dynamic reconfiguration of distribution network | [47] | |

Short-term load forecasting | [66] | |

Electric load forecasting | [67] | |

Capacitor placement in distribution systems | [90] | |

Design of FPSS | [100] | |

Load frequency stabilization of an isolated hybrid power system | [99] | |

Frequency stabilization of an isolated hybrid power system | [98] | |

Frequency and power control of an IHPS | [105] | |

Electronic Engineering | Energy-efficient wireless sensor networks | [131] |

Wireless sensor networks | [127] | |

Optimization of wireless sensor networks | [135] | |

Mechanical engineering | Machining system | [64] |

Multi-area restructure problem | [116] | |

Improving the electronic throttle valve | [104] | |

Chemical engineering | Multi-objective optimization in the drilling of CFRP (polyester) composites | [63] |

Industrial engineering | Flexible job shop scheduling problem | [46] |

Buffer allocation problems | [60] | |

Water resources and hydropower engineering | Multi-objective optimization of water distribution networks | [53] |

[132] | ||

Control Engineering | Design of a fuzzy PID controller for load frequency control | [97] |

Temperature control of air heater system | [110] | |

Power plant control | [95] | |

Computer Engineering | Image thresholding method | [59] |

High–order FTS forecasting model | [68] | |

Fuzzy controller | [101] | |

Type-2 FL controllers | [108] | |

Fuzzy c-means segmentation of MR images | [50] | |

Image segmentation | [145] | |

Enodeb position forecasting of LTE based on BTS existing | [134] | |

EEG signals classification | [136] | |

Approximate normal parameter reduction of fuzzy soft | [140] | |

Optimization of FLC | [96] | |

FCMAC | [102] | |

Designing stable adaptive fuzzy controllers | [103] | |

[111] | ||

Stable fuzzy controller design | [109] | |

FCMACNN | [112] | |

Web document clustering | [120] | |

Clustering web documents | [121] | |

MRI brain segmentation | [123] | |

Fuzzy clustering | [125] | |

Scheme classification | [128] | |

Image segmentation | [133] | |

Clustering to image segmentation | [130] | |

Image clustering method | [137] | |

FLC parameters optimization | [139] | |

Fuzzy rough set reduct | [141] | |

Aggregate production planning | [62] | |

FTS optimization | [126] | |

Sugeno fuzzy classification systems | [122] | |

Fuzzy classification systems | [138] | |

The design of FLR models | [142] | |

Fuzzy aggregate production planning | [144] | |

Civil Engineering | Simultaneous determination of aquifer parameters and zone structures | [124] |

Optimization and Mathematics | Optimization of a benchmark set of functions | [58] |

Benchmarks problems | [65] | |

Optimization of mathematical functions | [89] | |

Optimization problems | [74] | |

Benchmark mathematical functions | [91] | |

Optimization problems | [107] | |

Benchmark control problems | [72] | |

Benchmark control problems | [73] | |

Optimization problems | [49] | |

Optimization of a benchmark set of functions | [55] | |

Mathematical functions and controller optimization | [13] | |

Mathematical functions | [93] | |

Mathematical functions | [92] | |

Benchmarks functions | [94] | |

Optimization of the ball and beam controller | [113] | |

Other | Food transportation problem | [61] |

Efficient stock price prediction | [69] | |

Stock market volatility prediction | [143] |

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## Share and Cite

**MDPI and ACS Style**

Nasir, M.; Sadollah, A.; Grzegorzewski, P.; Yoon, J.H.; Geem, Z.W.
Harmony Search Algorithm and Fuzzy Logic Theory: An Extensive Review from Theory to Applications. *Mathematics* **2021**, *9*, 2665.
https://doi.org/10.3390/math9212665

**AMA Style**

Nasir M, Sadollah A, Grzegorzewski P, Yoon JH, Geem ZW.
Harmony Search Algorithm and Fuzzy Logic Theory: An Extensive Review from Theory to Applications. *Mathematics*. 2021; 9(21):2665.
https://doi.org/10.3390/math9212665

**Chicago/Turabian Style**

Nasir, Mohammad, Ali Sadollah, Przemyslaw Grzegorzewski, Jin Hee Yoon, and Zong Woo Geem.
2021. "Harmony Search Algorithm and Fuzzy Logic Theory: An Extensive Review from Theory to Applications" *Mathematics* 9, no. 21: 2665.
https://doi.org/10.3390/math9212665