Abstract
At the present time there are several types of metaheuristics which have been used to solve various types of problems in the real world. These metaheuristics contain parameters that are usually fixed throughout the iterations. However, various techniques exist to adjust the parameters of an algorithm such as probabilistic, fuzzy logic, among others. This work describes the methodology and equations for building Triangular and Gaussian interval type-2 membership functions, and this methodology was applied to the optimization of a benchmark control problem with an interval type-2 fuzzy logic controller. To validate in the best way the effect of uncertainty we perform experiments using noise (Pulse generator) and without noise. Also, a statistical z-test is presented to verify the effectiveness of the proposed method. The main contribution of this article is the proposed use of the theory of interval type-2 fuzzy logic to the dynamic adjustment of parameters for the harmony search algorithm and then its application to the optimal design of interval type-2 fuzzy logic controller.
Similar content being viewed by others
References
Amador-Angulo L, Castillo O (2014) Comparison of the optimal design of fuzzy controllers for the water tank using ant colony optimization. In: Castillo O, Melin P, Pedrycz W, Kacprzyk J (eds) Recent advances on hybrid approaches for designing intelligent systems, vol 547. Springer, Cham, pp 255–273
Amador-Angulo L, Castillo O (2018) A new fuzzy bee colony optimization with dynamic adaptation of parameters using interval type-2 fuzzy logic for tuning fuzzy controllers. Soft Comput 22(2):571–594
Amador-Angulo L, Mendoza O, Castro J, Rodríguez-Díaz A, Melin P, Castillo O (2016) Fuzzy sets in dynamic adaptation of parameters of a bee colony optimization for controlling the trajectory of an autonomous mobile robot. Sensors 16(9):1458
Bansal JC, Singh PK, Pal NR (eds) (2019) Evolutionary and swarm intelligence algorithms, vol 779. Springer, Cham
Basu S, Pramanik S, Dey S, Panigrahi G, Jana DK (2019) Fire monitoring in coal mines using wireless underground sensor network and interval type-2 fuzzy logic controller. Int J Coal Sci Technol 29:335
Bernal E, Castillo O, Soria J, Valdez F (2019) Optimization of fuzzy controller using galactic swarm optimization with type-2 fuzzy dynamic parameter adjustment. Axioms 8(1):26
Bernal E, Castillo O, Soria J, Valdez F (2017) Imperialist competitive algorithm with dynamic parameter adaptation using fuzzy logic applied to the optimization of mathematical functions. Algorithms 10(1):18
Boryczka U, Szwarc K (2019) The harmony search algorithm with additional improvement of harmony memory for asymmetric traveling salesman problem. Expert Syst Appl 122:43–53
Castillo O, Amador-Angulo L (2017) A generalized type-2 fuzzy logic approach for dynamic parameter adaptation in bee colony optimization applied to fuzzy controller design. Inf Sci 1:11
Castillo O, Valdez F, Soria J, Amador-Angulo L, Ochoa P, Peraza C (2018) Comparative study in fuzzy controller optimization using bee colony, differential evolution, and harmony search algorithms. Algorithms 12(1):9
Castillo O et al (2019a) Shadowed type-2 fuzzy systems for dynamic parameter adaptation in harmony search and differential evolution algorithms. Algorithms 12(1):17
Castillo O, Cervantes L, Melin P, Pedrycz W (2019b) A new approach to control of multivariable systems through a hierarchical aggregation of fuzzy controllers. Granul Comput 4(1):1–13
Castro JR, Castillo O, Melin P (2007) An interval type-2 fuzzy logic toolbox for control applications. In: 2007 IEEE international fuzzy systems conference, London, pp 1–6
Dechter R (2019) Reasoning with probabilistic and deterministic graphical models: exact algorithms, second edition. Synth Lect Artif Intell Mach Learn 13(1):1–199
Dhiman G, Kumar V (2019a) Spotted hyena optimizer for solving complex and non-linear constrained engineering problems. In: Yadav N, Yadav A, Bansal JC, Deep K, Kim JH (eds) Harmony search and nature inspired optimization algorithms, vol 741. Springer, Singapore, pp 857–867
Dhiman G, Kumar V (2019b) Seagull optimization algorithm: theory and its applications for large-scale industrial engineering problems. Knowl Based Syst 165:169–196
El-Shorbagy MA, Farag MA, Mousa AA, El-Desoky IM (2002) A hybridization of sine cosine algorithm with steady state genetic algorithm for engineering design problems. Springer, Heidelberg, pp 143–155
Geem ZW (2008) Novel derivative of harmony search algorithm for discrete design variables. Appl Math Comput 199(1):223–230
Geem ZW, Kim JH, Loganathan GV (2001) A new heuristic optimization algorithm: harmony search. Simulation 76(2):60–68
Guzmán J, Miramontes I, Melin P, Prado-Arechiga G (2019) Optimal genetic design of type-1 and interval type-2 fuzzy systems for blood pressure level classification. Axioms 8(1):8
Halim AH, Ismail I (2019) Combinatorial optimization: comparison of heuristic algorithms in travelling salesman problem. Arch Comput Methods Eng 26(2):367–380
Jana DK, Pramanik S, Sahoo P, Mukherjee A (2019) Interval type-2 fuzzy logic and its application to occupational safety risk performance in industries. Soft Comput 23(2):557–567
Karagul K, Sahin Y, Aydemir E, Oral A (2019) A simulated annealing algorithm based solution method for a green vehicle routing problem with fuel consumption. In: Paksoy T, Weber G-W, Huber S (eds) Lean and green supply chain management, vol 273. Springer, Cham, pp 161–187
Lee KS, Geem ZW (2005) A new meta-heuristic algorithm for continuous engineering optimization: harmony search theory and practice. Comput Methods Appl Mech Eng 194(36–38):3902–3933
Lee HM, Jung D, Sadollah A, Lee EH, Kim JH (2019) Performance comparison of metaheuristic optimization algorithms using water distribution system design benchmarks. In: Yadav N, Yadav A, Bansal JC, Deep K, Kim JH (eds) Harmony search and nature inspired optimization algorithms, vol 741. Springer, Singapore, pp 97–104
Mahdavi M, Fesanghary M, Damangir E (2007) An improved harmony search algorithm for solving optimization problems. Appl Math Comput 188(2):1567–1579
Mitra S, Mahapatra G, Balas VE, Chattaraj R (2019) Public key cryptography using harmony search algorithm. In: Deb D, Balas VE, Dey R (eds) Innovations in infrastructure, vol 757. Springer, Singapore, pp 1–11
Nazari-Heris M, Mohammadi-Ivatloo B, Asadi S, Geem ZW (2019) Large-scale combined heat and power economic dispatch using a novel multi-player harmony search method. Appl Therm Eng 154:493–504
Ochoa P, Castillo O, Soria J (2019) Interval type-2 fuzzy logic dynamic mutation and crossover parameter adaptation in a fuzzy differential evolution method. In: Hadjiski M, Atanassov KT (eds) Intuitionistic fuzziness and other intelligent theories and their applications. Springer, Cham, pp 81–94
Olivas F, Valdez F, Castillo O (2018) Comparison of bio-inspired methods with parameter adaptation through interval type-2 fuzzy logic. In: Castillo O, Melin P, Kacprzyk J (eds) Fuzzy logic augmentation of neural and optimization algorithms: theoretical aspects and real applications, vol 749. Springer, Cham, pp 39–53
Olivas F, Valdez F, Melin P, Sombra A, Castillo O (2019) Interval type-2 fuzzy logic for dynamic parameter adaptation in a modified gravitational search algorithm. Inf Sci 476:159–175
Ontiveros E, Melin P, Castillo O (2018) High order α-planes integration: a new approach to computational cost reduction of general type-2 fuzzy systems. Eng Appl Artif Intell 74:186–197
Ontiveros-Robles E, Melin P, Castillo O (2017) New methodology to approximate type-reduction based on a continuous root-finding Karnik mendel algorithm. Algorithms 10(3):77
Peraza C, Valdez F, Melin P (2017) Optimization of intelligent controllers using a type-1 and interval type-2 fuzzy harmony search algorithm. Algorithms 10(3):82
Peraza C, Valdez F, Castro JR, Castillo O (2018) Fuzzy dynamic parameter adaptation in the harmony search algorithm for the optimization of the ball and beam controller. Adv Oper Res 2018:1–16
Peraza C, Valdez F, Castillo O (2019) Fuzzy harmony search algorithm using an interval type-2 fuzzy logic applied to benchmark mathematical functions. In: Hadjiski M, Atanassov KT (eds) Intuitionistic fuzziness and other intelligent theories and their applications, vol 757. Springer, Cham, pp 13–28
Pongchairerks P (2019) A two-level metaheuristic algorithm for the job-shop scheduling problem. Complexity 2019:1–11
Ramirez E, Melin P, Prado-Arechiga G (2019) Hybrid model based on neural networks, type-1 and type-2 fuzzy systems for 2-lead cardiac arrhythmia classification. Expert Syst Appl 126:295–307
Rodríguez L et al (2017) A fuzzy hierarchical operator in the grey wolf optimizer algorithm. Appl Soft Comput 57:315–328
Roy B, Sen AK (2019) Meta-heuristic techniques to solve resource-constrained project scheduling problem. In: Bhattacharyya S, Hassanien AE, Gupta D, Khanna A, Pan I (eds) International conference on innovative computing and communications, vol 56. Springer, Singapore, pp 93–99
Roy K, Mukherjee A, Jana DK (2019) Prediction of maximum oil-yield from almond seed in a chemical industry: a novel type-2 fuzzy logic approach. S Afr J Chem Eng 29:1–9
Sanchez MA, Castillo O, Castro JR (2015) Generalized type-2 fuzzy systems for controlling a mobile robot and a performance comparison with interval type-2 and type-1 fuzzy systems. Expert Syst Appl 42(14):5904–5914
Santiago A, Dorronsoro B, Nebro AJ, Durillo JJ, Castillo O, Fraire HJ (2019) A novel multi-objective evolutionary algorithm with fuzzy logic based adaptive selection of operators: FAME. Inf Sci 471:233–251
Schaedler de Almeida F (2019) Optimization of laminated composite structures using harmony search algorithm. Compos Struct 221:110852
Selvakumar S, Abdullah AS, Suganya R (2019) Decision support system for type II diabetes and its risk factor prediction using bee-based harmony search and decision tree algorithm. Int J Biomed Eng Technol 29(1):46
Wang C-M, Huang Y-F (2010) Self-adaptive harmony search algorithm for optimization. Expert Syst Appl 37(4):2826–2837
Wang X, Chang M-C, Wang L, Lyu S (2019) Efficient algorithms for graph regularized PLSA for probabilistic topic modeling. Pattern Recognit 86:236–247
Yang L, Liu Z, Chen Y (2019) Energy efficient walking control for biped robots using interval type-2 fuzzy logic systems and optimized iteration algorithm. ISA Trans 87:143–153
Yi J, Li X, Chu C-H, Gao L (2019a) Parallel chaotic local search enhanced harmony search algorithm for engineering design optimization. J Intell Manuf 30(1):405–428
Yi J, Gao L, Li X, Shoemaker CA, Lu C (2019b) An on-line variable-fidelity surrogate-assisted harmony search algorithm with multi-level screening strategy for expensive engineering design optimization. Knowl Based Syst 170:1–19
Zadeh LA (1988) Fuzzy logic. Computer 21(4):83–93
Zadeh LA (1975) The concept of a linguistic variable and its application to approximate reasoning—I. Inf Sci 8(3):199–249
Funding
Funding was provided by Consejo Nacional de Ciencia y Tecnología (Grant No. 122).
Author information
Authors and Affiliations
Corresponding author
Ethics declarations
Conflict of interest
All the authors in the paper have no conflict of interest.
Ethical approval
This article does not contain any studies with human participants or animals performed by any of the authors.
Additional information
Communicated by O. Castillo, D. K. Jana.
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations
Rights and permissions
About this article
Cite this article
Valdez, F., Peraza, C. Dynamic parameter adaptation in the harmony search algorithm for the optimization of interval type-2 fuzzy logic controllers. Soft Comput 24, 179–192 (2020). https://doi.org/10.1007/s00500-019-04124-x
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00500-019-04124-x