Optimization of Intelligent Controllers Using a Type-1 and Interval Type-2 Fuzzy Harmony Search Algorithm
<p>Flowchart of the FHS.</p> "> Figure 2
<p>Scheme of the Type-1 fuzzy system method (FHS).</p> "> Figure 3
<p>Input and output of the Type-1 fuzzy system.</p> "> Figure 4
<p>Scheme of the interval Type-2 fuzzy system method (FHS2).</p> "> Figure 5
<p>Input and output of the interval Type-2 fuzzy system.</p> "> Figure 6
<p>Diagram of the water tank controller.</p> "> Figure 7
<p>Structure of the water tank fuzzy system for control.</p> "> Figure 8
<p>Diagram of the temperature controller.</p> "> Figure 9
<p>Structure of the water tank fuzzy system for control.</p> "> Figure 10
<p>Diagram of the robot mobile controller.</p> "> Figure 11
<p>Structure of the mobile robot fuzzy system for control.</p> "> Figure 12
<p>Simulation results of the water tank controller for the three methods. (<b>a</b>) The best result is shown using original harmony search algorithm (HS); (<b>b</b>) the best result is shown using the Type-1 fuzzy harmony search (FHS); (<b>c</b>) the best result is shown using the Type-2 fuzzy harmony search (FHS2). These methods were applied with noise to verify the stability of the methods. The blue line represents the desired trajectory and the pink line the obtained trajectory; the objective is for the obtained line to resemble the desired one.</p> "> Figure 13
<p>Simulation results of the temperature controller for the three methods. (<b>a</b>) The best result is shown using original harmony search algorithm (HS); (<b>b</b>) the best result is shown using the Type-1 fuzzy harmony search (FHS); (<b>c</b>) the best result is shown using the Type-2 fuzzy harmony search (FHS2). These methods were applied with noise to verify the stability of the methods. The blue line represents the desired trajectory and the pink line the obtained trajectory; the objective is for the obtained line to resemble the desired one.</p> "> Figure 14
<p>Simulation results of the robot mobile controller for the three methods. (<b>a</b>) The best result is shown using original harmony search algorithm (HS); (<b>b</b>) the best result is shown using the Type-1 fuzzy harmony search (FHS); (<b>c</b>) the best result is shown using the Type-2 fuzzy harmony search (FHS2). These methods were applied with noise to verify the stability of the methods. The green line is the desired trajectory and the blue line the obtained trajectory, and the objective is for the obtained line to resemble the desired one.</p> "> Figure 14 Cont.
<p>Simulation results of the robot mobile controller for the three methods. (<b>a</b>) The best result is shown using original harmony search algorithm (HS); (<b>b</b>) the best result is shown using the Type-1 fuzzy harmony search (FHS); (<b>c</b>) the best result is shown using the Type-2 fuzzy harmony search (FHS2). These methods were applied with noise to verify the stability of the methods. The green line is the desired trajectory and the blue line the obtained trajectory, and the objective is for the obtained line to resemble the desired one.</p> ">
Abstract
:1. Introduction
2. Harmony Search Algorithm
3. Fuzzy Harmony Search Algorithm with Dynamic Parameter Adaptation
4. Control Cases
4.1. Water Tank Controller
- Vol is the volume of water in the tank
- V is the voltage applied to the pump
- A is the cross-sectional area of the tank
- b is a constant related to the flow rate into the tank
- a is a constant related to the flow rate out of the tank
4.2. Temperature Controller
4.3. Mobile Robot Controller
- is the vector of the configuration coordinates;
- is the vector of velocities;
- is the vector of torques applied to the wheels of the robot where and denote the torques of the right and left wheel, respectively;
- is the uniformly bounded disturbance vector;
- is the positive-definite inertia matrix;
- is the vector of centripetal and Coriolis forces;
- is a diagonal positive-definite damping matrix.
- (x,y) is the position in the (world) reference frame;
- is the angle between the heading direction and the x-axis;
- are the linear and angular velocities, respectively
5. Simulation Results
6. Statistical Comparison
7. Conclusions
Acknowledgments
Author Contributions
Conflicts of Interest
References
- Precup, R.-E.; David, R.-V.; Petriu, E.M.; Preitla, S.; Rădac, M.-B. Novel adaptive charged system search algorithm for optimal tuning of fuzzy controllers. Exp. Syst. Appl. 2014, 41, 1168–1175. [Google Scholar] [CrossRef]
- Kiran, M.S.; Findik, O. A directed artificial bee colony algorithm. Appl. Soft Comput. 2015, 26, 454–462. [Google Scholar]
- Osaba, E.; Onieva, E.; Diaz, F.; Diaz, F.; Carballedo, R.; Lopez, P.; Perallo, A. A migration strategy for distributed evolutionary algorithms based on stopping non-promising subpopulations: A case study on routing problems. Int. J. Artif. Intell. 2015, 13, 46–56. [Google Scholar]
- Solos, I.P.; Tassopoulos, I.X.; Beligiannis, G.N. Optimizing shift scheduling for tank trucks using an effective stochastic variable neighbourhood approach. Int. J. Artif. Intell. 2016, 14, 1–26. [Google Scholar]
- Geem, Z. Multiobjective optimization of water distribution networks using fuzzy theory and harmony search. Water 2015, 7, 3613–3625. [Google Scholar] [CrossRef]
- Kar, P.; Swain, S.C. A harmony search-firefly algorithm based controller for damping power oscillations. Comput. Intell. Commun. Technol. 2016, 8, 351–355. [Google Scholar]
- Roy, N.; Ghosh, A.; Sanyal, K. Normal boundary intersection based multi-objective harmony search algorithm for environmental economic load dispatch problem. Power Syst. 2016, 10, 1–6. [Google Scholar]
- Gao, K.Z.; Suganthan, P.N.; Pan, Q.K.; Chua, T.J.; Cai, T.X.; Chong, C.S. Discrete harmony search algorithm for flexible job shop scheduling problem with multiple objectives. J. Intell. Manuf. 2016, 27, 363–374. [Google Scholar] [CrossRef]
- Alia, O.M. Dynamic relocation of mobile base station in wireless sensor networks using a cluster-based harmony search algorithm. Inf. Sci. 2017, 385, 76–95. [Google Scholar] [CrossRef]
- Olivas, F.; Valdez, F.; Castillo, O.; Gonzalez, C.I.; Martinez, G.; Melin, P. Ant colony optimization with dynamic parameter adaptation based on interval Type-2 fuzzy logic systems. Appl. Soft Comput. 2017, 53, 74–87. [Google Scholar] [CrossRef]
- Gonzalez, C.I.; Castro, J.R.; Mendoza, O.; Melin, P.; Castillo, O. Optimization by cuckoo search of interval Type-2 fuzzy logic systems for edge detection. In Recent Developments and New Direction in Soft-Computing Foundations and Applications; Springer: Basel, Switzerland, 2016; pp. 141–154. [Google Scholar]
- Castillo, O.; Ochoa, P.; Soria, J. Differential Evolution with Fuzzy Logic for Dynamic Adaptation of Parameters in Mathematical Function Optimization. In Imprecision and Uncertainty in Information Representation and Processing; Springer: Basel, Switzerland, 2016; pp. 361–374. [Google Scholar]
- Bernal, E.; Castillo, O.; Soria, J.; Valdez, F. Imperialist Competitive Algorithm with Dynamic Parameter Adaptation Using Fuzzy Logic Applied to the Optimization of Mathematical Functions. Algorithms 2017, 10, 18. [Google Scholar] [CrossRef]
- Caraveo, C.; Valdez, F.; Castillo, O. Optimization mathematical functions for multiple variables using the algorithm of self-defense of the plants. In Nature-Inspired Design of Hybrid Intelligent Systems; Springer: Basel, Switzerland, 2017; pp. 631–640. [Google Scholar]
- Castillo, O.; Amador-Angulo, L.; Castro, J.R.; Garcia-Valdez, M. A comparative study of Type-1 fuzzy logic systems, interval Type-2 fuzzy logic systems and generalized Type-2 fuzzy logic systems in control problems. Inf. Sci. 2016, 354, 257–274. [Google Scholar] [CrossRef]
- Peraza, C.; Valdez, F.; Garcia, M.; Melin, P.; Castillo, O. A new fuzzy harmony search algorithm using fuzzy logic for dynamic parameter adaptation. Algorithms 2016, 9, 69. [Google Scholar] [CrossRef]
- Peraza, C.; Valdez, F.; Castillo, O. An adaptive fuzzy control based on harmony search and its application to optimization. In Nature-Inspired Design of Hybrid Intelligent Systems; Springer: Basel, Switzerland, 2017; pp. 269–283. [Google Scholar]
- Peraza, C.; Valdez, F.; Castillo, O. Interval Type-2 fuzzy logic for dynamic parameter adaptation in the harmony search algorithm. Intell. Syst. 2016, 10, 106–112. [Google Scholar]
- Mahdavi, M.; Fesanghary, M.; Damangir, E. An improved harmony search algorithm for solving optimization problems. Appl. Math. Comput. 2007, 188, 1567–1579. [Google Scholar] [CrossRef]
- Zadeh, L.A. Fuzzy sets. Inf. Control. 1965, 8, 338–353. [Google Scholar] [CrossRef]
- Zadeh, L.A. Fuzzy logic. Computer 1988, 21, 83–93. [Google Scholar] [CrossRef]
- Zadeh, L.A. The concept of a linguistic variable and its application to approximate reasoning—I. Inf. Sci. 1975, 8, 199–249. [Google Scholar] [CrossRef]
- Lee, K.S.; Geem, Z.W. A new meta-heuristic algorithm for continuous engineering optimization: Harmony search theory and practice. Comput. Methods Appl. Mech. Eng. 2005, 194, 3902–3933. [Google Scholar] [CrossRef]
- Lee, K.S.; Geem, Z.W. A new structural optimization method based on the harmony search algorithm. Comput. Struct. 2004, 82, 781–798. [Google Scholar] [CrossRef]
- Geem, Z.W. State-of-the-art in the structure of harmony search algorithm. In Recent Advances in Harmony Search Algorithm; Springer: Berlin/Heidelberg, Germany, 2010; pp. 1–10. [Google Scholar]
- Geem, Z.W.; Choi, J.-Y. Music composition using harmony search algorithm. In Applications of Evolutinary Computing; Springer: Berlin/Heidelberg, Germany, 2007; pp. 593–600. [Google Scholar]
- Manjarres, D.; Landa-Torresa, I.; Gil-Lopeza, S.; Sera, J.D.; Bilbaob, M.N.; Salcedo-Sanzc, S.; Geemd, Z.W. survey on applications of the harmony search algorithm. Eng. Appl. Artif. Intell. 2013, 26, 1818–1831. [Google Scholar] [CrossRef]
- Alia, O.M.; Mandava, R. The variants of the harmony search algorithm: An overview. Artif. Intell. Rev. 2011, 36, 49–68. [Google Scholar] [CrossRef]
- Omran, M.G.H.; Mahdavi, M. Global-best harmony search. Appl. Math. Comput. 2008, 198, 643–656. [Google Scholar] [CrossRef]
- Wang, C.-M.; Huang, Y.-F. Self-adaptive harmony search algorithm for optimization. Expert Syst. Appl. 2010, 37, 2826–2837. [Google Scholar] [CrossRef]
- Melin, P.; Astudillo, L.; Castillo, O.; Valdez, F.; Garcia, M. Optimal design of Type-2 and Type-1 fuzzy tracking controllers for autonomous mobile robots under perturbed torques using a new chemical optimization paradigm. Expert Syst. Appl. 2013, 40, 3185–3195. [Google Scholar] [CrossRef]
HMR | Low | Medium | High | |
---|---|---|---|---|
Iteration | ||||
Low | Low | - | - | |
Medium | - | Medium | - | |
High | - | - | High |
Rule Number | Inputs | Output | ||
---|---|---|---|---|
Level | Operator | Rate | Valve | |
1 | okay | - | - | no change |
2 | low | - | - | open fast |
3 | high | - | - | close fast |
4 | okay | and | positive | close slow |
5 | okay | and | negative | open slow |
Rule Number | Inputs | Output | |||
---|---|---|---|---|---|
Temp | Operator | Flow | Cold | Hot | |
1 | cold | and | soft | open slow | open fast |
2 | cold | and | good | close slow | open slow |
3 | cold | and | hard | close fast | close slow |
4 | good | and | soft | open slow | open slow |
5 | good | and | good | steady | steady |
6 | good | and | hard | close slow | close slow |
7 | hot | and | soft | open fast | open slow |
8 | hot | and | good | open slow | close slow |
9 | hot | and | hard | close slow | close fast |
Rule Number | Inputs | Output | |||
---|---|---|---|---|---|
Ev | Operator | Ew | T1 | T2 | |
1 | N | and | N | N | N |
2 | N | and | Z | N | Z |
3 | N | and | P | N | P |
4 | Z | and | N | Z | N |
5 | Z | and | Z | Z | Z |
6 | Z | and | P | Z | P |
7 | P | and | N | P | N |
8 | P | and | Z | P | Z |
9 | P | and | P | P | P |
Performance Index | HS | FHS | FHS2 |
---|---|---|---|
RMSE | 3.18 × 10−2 | 2.61 × 10−1 | 2.49 × 10−2 |
MSE | 4.58 × 10−2 | 7.56 × 10−2 | 5.75 × 10−2 |
ITAE | 3.87 × 104 | 9.93 × 105 | 3.68 × 104 |
ITSE | 2.57 × 104 | 2.43 × 106 | 2.39 × 104 |
IAE | 7.91 × 10 | 2.01 × 103 | 7.53 × 10 |
ISE | 5.28 × 10 | 4.96 × 103 | 4.90 × 10 |
Performance Index | HS | FHS | FHS2 |
---|---|---|---|
RMSE | 6.34 × 10−2 | 6.75 × 10−2 | 6.25 × 10−2 |
MSE | 2.44 × 10−2 | 4.55 × 10−3 | 4.62 × 10−3 |
ITAE | 7.01 × 105 | 7.04 × 105 | 7.03 × 105 |
ITSE | 1.06 × 106 | 1.07 × 106 | 1.07 × 106 |
IAE | 1.40 × 103 | 1.41 × 103 | 1.41 × 103 |
ISE | 2.11 × 103 | 2.12 × 103 | 2.12 × 103 |
Performance Index | HS | FHS | FHS2 |
---|---|---|---|
RMSE | 2.33 × 10−1 | 1.37 × 10−1 | 1.11 × 10−1 |
MSE | 8.56 × 10 | 5.07 × 10 | 6.06 × 10 |
ITAE | 2.18 × 105 | 2.11 × 105 | 3.03 × 106 |
ITSE | 1.05 × 105 | 9.44 × 104 | 2.86 × 107 |
IAE | 4.38 × 102 | 4.24 × 102 | 6.09 × 103 |
ISE | 2.11 × 102 | 1.90 × 102 | 5.72 × 104 |
Performance Index | HS | FHS | FHS2 |
---|---|---|---|
RMSE | 3.18 × 10−2 | 2.49 × 10−2 | 1.32 × 10−2 |
MSE | 4.58 × 10−2 | 5.75 × 10−2 | 6.36 × 10−2 |
ITAE | 3.87 × 104 | 3.68 × 104 | 3.49 × 104 |
ITSE | 2.57 × 104 | 2.39 × 104 | 2.08 × 104 |
IAE | 7.91 × 10 | 7.53 × 10 | 7.17 × 10 |
ISE | 5.28 × 10 | 4.90 × 10 | 4.29 × 10 |
Performance Index | HS | FHS | FHS2 |
---|---|---|---|
RMSE | 6.34 × 10−2 | 1.24 × 10−1 | 6.29 × 10−4 |
MSE | 2.44 × 10−2 | 1.54 × 10−2 | 3.64 × 10−2 |
ITAE | 7.01 × 105 | 6.98 × 105 | 6.98 × 105 |
ITSE | 1.06 × 106 | 1.05 × 106 | 1.05 × 106 |
IAE | 1.40 × 103 | 1.39 × 103 | 1.40 × 103 |
ISE | 2.11 × 103 | 2.10 × 103 | 2.10 × 103 |
Performance Index | HS | FHS | FHS2 |
---|---|---|---|
RMSE | 2.33 × 10−1 | 3.82 × 10−2 | 3.69 × 10−2 |
MSE | 8.56 × 10 | 7.67 × 10 | 6.06 × 10 |
ITAE | 2.18 × 105 | 3.09 × 106 | 3.10 × 106 |
ITSE | 1.05 × 105 | 3.26 × 107 | 3.28 × 107 |
IAE | 4.38 × 102 | 6.46 × 103 | 6.47 × 103 |
ISE | 2.11 × 102 | 6.47 × 104 | 6.49 × 104 |
Parameter | Value |
---|---|
Level of Significance | 95% |
Alpha | 0.05% |
Ha | µ1 < µ2 |
H0 | µ1 ≥ µ2 |
Critical Value | −1.645 |
Water Tank Controller | ||||
---|---|---|---|---|
Method | Mean | Standard Deviation | z-Value | Evidence |
HS | 3.19 × 10−2 | 3.13 × 10−2 | 35.8789 | N.S |
FHS | 2.60 × 10−1 | 1.55 × 10−2 | −50.7296 | S |
FHS2 | 2.56 × 10−2 | 1.97 × 10−2 | −1.1733 | N.S |
Temperature Controller | ||||
---|---|---|---|---|
Method | Mean | Standard Deviation | z-Value | Evidence |
HS | 6.34 × 10−2 | 3.12 × 10−3 | 6.4226 | N.S |
FHS | 6.75 × 10−2 | 1.59 × 10−3 | −14.0672 | S |
FHS2 | 6.25 × 10−2 | 1.13 × 10−3 | −1.4778 | N.S |
Robot Mobile Controller | ||||
---|---|---|---|---|
Method | Mean | Standard Deviation | z-Value | Evidence |
HS | 2.33 × 10−1 | 2.18 × 10−1 | −2.0706 | S |
FHS | 1.37 × 10−1 | 1.57 × 10−1 | −0.7959 | N.S |
FHS2 | 1.11 × 10−1 | 1.37 × 10−1 | −2.7100 | S |
Water Tank Controller | ||||
---|---|---|---|---|
Method | Mean | Standard Deviation | z-Value | Evidence |
HS | 3.18 × 10−2 | 3.13 × 10−2 | −1.0134 | N.S |
FHS | 2.49 × 10−2 | 2.01 × 10−2 | −2.5236 | S |
FHS2 | 1.32 × 10−2 | 1.54 × 10−2 | −2.9164 | S |
Temperature Controller | ||||
---|---|---|---|---|
Method | Mean | Standard Deviation | z-Value | Evidence |
HS | 6.34 × 10−2 | 3.12 × 10−3 | 72.5412 | N.S |
FHS | 1.24 × 10−1 | 3.34 × 10−3 | −201.3932 | S |
FHS2 | 6.29 × 10−4 | 1.07 × 10−4 | −109.8982 | S |
Robot Controller | ||||
---|---|---|---|---|
Method | Mean | Standard Deviation | z-Value | Evidence |
HS | 2.33 × 10−1 | 2.18 × 10−1 | −4.8553 | S |
FHS | 3.82 × 10−2 | 4.22 × 10−2 | −0.2277 | N.S |
FHS2 | 3.69 × 10−2 | 4.20 × 10−2 | −4.8866 | S |
© 2017 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).
Share and Cite
Peraza, C.; Valdez, F.; Melin, P. Optimization of Intelligent Controllers Using a Type-1 and Interval Type-2 Fuzzy Harmony Search Algorithm. Algorithms 2017, 10, 82. https://doi.org/10.3390/a10030082
Peraza C, Valdez F, Melin P. Optimization of Intelligent Controllers Using a Type-1 and Interval Type-2 Fuzzy Harmony Search Algorithm. Algorithms. 2017; 10(3):82. https://doi.org/10.3390/a10030082
Chicago/Turabian StylePeraza, Cinthia, Fevrier Valdez, and Patricia Melin. 2017. "Optimization of Intelligent Controllers Using a Type-1 and Interval Type-2 Fuzzy Harmony Search Algorithm" Algorithms 10, no. 3: 82. https://doi.org/10.3390/a10030082