Applied Intelligence

, Volume 48, Issue 8, pp 2268–2283 | Cite as

MOGOA algorithm for constrained and unconstrained multi-objective optimization problems

  • Alaa TharwatEmail author
  • Essam H. Houssein
  • Mohammed M. Ahmed
  • Aboul Ella Hassanien
  • Thomas Gabel


Grasshopper Optimization Algorithm (GOA) was modified in this paper, to optimize multi-objective problems, and the modified version is called Multi-Objective Grasshopper Optimization Algorithm (MOGOA). An external archive is integrated with the GOA for saving the Pareto optimal solutions. The archive is then employed for defining the social behavior of the GOA in the multi-objective search space. To evaluate and verify the effectiveness of the MOGOA, a set of standard unconstrained and constrained test functions are used. Moreover, the proposed algorithm was compared with three well-known optimization algorithms: Multi-Objective Particle Swarm Optimization (MOPSO), Multi-Objective Ant Lion Optimizer (MOALO), and Non-dominated Sorting Genetic Algorithm version 2 (NSGA-II); and the obtained results show that the MOGOA algorithm is able to provide competitive results and outperform other algorithms.


Multi-objective optimization Grasshopper optimization algorithm Pareto optimal solutions Evolutionary algorithm Constrained optimization Unconstrained optimization 


  1. 1.
    Motevasel M, Seifi AR, Niknam T (2013) Multi-objective energy management of chp (combined heat and power)-based micro-grid. Energy 51:123–136CrossRefGoogle Scholar
  2. 2.
    Elhoseny M, Tharwat A, Hassanien AE (2017) Bezier curve based path planning in a dynamic field using modified genetic algorithm. J Comput Sci, In PressGoogle Scholar
  3. 3.
    Tharwat A, Gabel T, Hassanien AE (2017) Parameter optimization of support vector machine using dragonfly algorithm. In: International conference on advanced intelligent systems and informatics. Springer, Berlin, pp 309–319Google Scholar
  4. 4.
    Elhoseny M, Tharwat A, Farouk A, Hassanien AE (2017) K-coverage model based on genetic algorithm to extend wsn lifetime. IEEE Sensors Lett 1(4):1–4CrossRefGoogle Scholar
  5. 5.
    Handl J, Kell DB, Knowles J (2007) Multiobjective optimization in bioinformatics and computational biology. IEEE/ACM Trans Comput Biol Bioinform 4(2):279–292CrossRefGoogle Scholar
  6. 6.
    Kipouros T, Jaeggi DM, Dawes WN, Parks GT, Savill AM, Clarkson PJ (2008) Biobjective design optimization for axial compressors using tabu search. AIAA J 46(3):701CrossRefGoogle Scholar
  7. 7.
    Tharwat A, Gabel T, Hassanien AE (2017) Classification of toxicity effects of biotransformed hepatic drugs using optimized support vector machine. In: International conference on advanced intelligent systems and informatics. Springer, Berlin, pp 161–170Google Scholar
  8. 8.
    Hassanien AE, Tharwat A, Own HS (2017) Computational model for vitamin d deficiency using hair mineral analysis. Comput Biol Chem 70:198–210CrossRefGoogle Scholar
  9. 9.
    Rizk-Allah RM, Hassanien AE (2017) A hybrid optimization algorithm for single and multi-objective optimization problems. In: Handbook of research on machine learning innovations and trends. IGI Global, Hershey, pp 491–521Google Scholar
  10. 10.
    Marler RT, Arora JS (2004) Survey of multi-objective optimization methods for engineering. Struct Multidiscip Optim 26(6):369–395MathSciNetCrossRefzbMATHGoogle Scholar
  11. 11.
    Deb K (2012) Advances in evolutionary multi-objective optimization. In: Search based software engineering, pp 1–26Google Scholar
  12. 12.
    Coello CAC (2009) Evolutionary multi-objective optimization: some current research trends and topics that remain to be explored. Front Comput Sci Chin 3(1):18–30CrossRefGoogle Scholar
  13. 13.
    Coello CAC, Lamont GB, Van Veldhuizen DA et al (2007) Evolutionary algorithms for solving multi-objective problems, 2nd edn. Springer, BerlinzbMATHGoogle Scholar
  14. 14.
    Padhye N, Mittal P, Deb K (2015) Feasibility preserving constraint-handling strategies for real parameter evolutionary optimization. Comput Optim Appl 62(3):851–890MathSciNetCrossRefzbMATHGoogle Scholar
  15. 15.
    Coello CC (2006) Evolutionary multi-objective optimization: a historical view of the field. IEEE Comput Intell Mag 1(1):28–36MathSciNetCrossRefGoogle Scholar
  16. 16.
    Padhye N, Bhardawaj P, Deb K (2013) Improving differential evolution through a unified approach. J Glob Optim 55(4):771MathSciNetCrossRefzbMATHGoogle Scholar
  17. 17.
    Deb K, Padhye N (2014) Enhancing performance of particle swarm optimization through an algorithmic link with genetic algorithms. Comput Optim Appl 57(3):761–794MathSciNetCrossRefzbMATHGoogle Scholar
  18. 18.
    Srinivas N, Deb K (1994) Muiltiobjective optimization using nondominated sorting in genetic algorithms. Evol Comput 2(3):221–248CrossRefGoogle Scholar
  19. 19.
    Deb K, Pratap A, Agarwal S, Meyarivan T (2002) A fast and elitist multiobjective genetic algorithm: Nsga-ii. IEEE Trans Evol Comput 6(2):182–197CrossRefGoogle Scholar
  20. 20.
    Zitzler E, Thiele L (1999) Multiobjective evolutionary algorithms: a comparative case study and the strength Pareto approach. IEEE Trans Evol Comput 3(4):257–271CrossRefGoogle Scholar
  21. 21.
    Coello CAC, Pulido GT, Lechuga MS (2004) Handling multiple objectives with particle swarm optimization. IEEE Trans Evol Comput 8(3):256–279CrossRefGoogle Scholar
  22. 22.
    Padhye N, Branke J, Mostaghim S (2009) Empirical comparison of mopso methods-guide selection and diversity preservation. In: IEEE congress on evolutionary computation (CEC’09). IEEE, New York, pp 2516–2523Google Scholar
  23. 23.
    Padhye N (2009) Comparison of archiving methods in multi-objectiveparticle swarm optimization (mopso): empirical study. In: Proceedings of the 11th annual conference on genetic and evolutionary computation. ACM, New York, pp 1755–1756Google Scholar
  24. 24.
    Zhang Q, Li H (2007) Moea/d: a multiobjective evolutionary algorithm based on decomposition. IEEE Trans Evol Comput 11(6):712–731CrossRefGoogle Scholar
  25. 25.
    Abbass HA, Sarker R, Newton C (2001) Pde: a Pareto-frontier differential evolution approach for multi-objective optimization problems. In: Proceedings of the 2001 congress on evolutionary computation, vol 2. IEEE, New York, pp 971–978Google Scholar
  26. 26.
    Wolpert DH, Macready WG (1997) No free lunch theorems for optimization. IEEE Trans Evol Comput 1(1):67–82CrossRefGoogle Scholar
  27. 27.
    Saremi S, Mirjalili S, Lewis A (2017) Grasshopper optimisation algorithm: theory and application. Adv Eng Softw 105:30– 47CrossRefGoogle Scholar
  28. 28.
    Haupt RL, Haupt SE (2004) Practical genetic algorithms. Wiley, New YorkzbMATHGoogle Scholar
  29. 29.
    Zhang Q, Zhou A, Zhao S, Suganthan PN, Liu W, Tiwari S (2008) Multiobjective optimization test instances for the cec 2009 special session and competition. University of Essex, Colchester, UK and Nanyang Technological University, Singapore, special session on performance assessment of multi-objective optimization algorithms, technical report 264Google Scholar
  30. 30.
    Ščap D, Hoić M, Jokić A (2013) Determination of the Pareto frontier for multiobjective optimization problem. Transactions of FAMENA 37(2):15–28Google Scholar
  31. 31.
    Kim IY, de Weck OL (2005) Adaptive weighted-sum method for bi-objective optimization: Pareto front generation. Struct Multidiscip Optim 29(2):149–158CrossRefGoogle Scholar
  32. 32.
    Das I, Dennis JE (1998) Normal-boundary intersection: a new method for generating the Pareto surface in nonlinear multicriteria optimization problems. SIAM J Optim 8(3):631–657MathSciNetCrossRefzbMATHGoogle Scholar
  33. 33.
    Parsopoulos KE, Vrahatis MN (2002) Particle swarm optimization method in multiobjective problems. In: Proceedings of the 2002 ACM symposium on applied computing. ACM, New York, pp 603–607Google Scholar
  34. 34.
    Deb K (2011) Multi-objective optimisation using evolutionary algorithms: an introduction. In: Multi-objective evolutionary optimisation for product design and manufacturing. Springer, Berlin, pp 3–34Google Scholar
  35. 35.
    Goldberg D (1989) Genetic algorithms in optimization, search and machine learning. Addison-Wesley, ReadingzbMATHGoogle Scholar
  36. 36.
    Tharwat A, Gaber T, Hassanien AE, Elnaghi BE (2017) Particle swarm optimization: a tutorial. In: Handbook of research on machine learning innovations and trends. IGI Global, Hershey, pp 614–635Google Scholar
  37. 37.
    Nebro AJ, Durillo JJ, Coello CAC (2013) Empirical comparison of mopso methods-guide selection and diversity preservation. In: IEEE congress on evolutionary computation (CEC). IEEE, New York, pp 3153–3160Google Scholar
  38. 38.
    Knowles J, Thiele L, Zitzler E (2006) A tutorial on the performance assessment of stochastic multiobjective optimizers. Tik Report 214:327–332Google Scholar
  39. 39.
    Pradhan PM, Panda G (2012) Solving multiobjective problems using cat swarm optimization. Expert Syst Appl 39(3):2956–2964CrossRefGoogle Scholar
  40. 40.
    Shi X, Kong D (2015) A multi-objective ant colony optimization algorithm based on elitist selection strategy. Metallurgical & Mining Industry 7(6):333–338Google Scholar
  41. 41.
    Hancer E, Xue B, Zhang M, Karaboga D, Akay B (2015) A multi-objective artificial bee colony approach to feature selection using fuzzy mutual information. In: IEEE congress on evolutionary computation (CEC). IEEE, New York, pp 2420–2427Google Scholar
  42. 42.
    Hemmatian H, Fereidoon A, Assareh E (2014) Optimization of hybrid laminated composites using the multi-objective gravitational search algorithm (mogsa). Eng Optim 46(9):1169–1182MathSciNetCrossRefGoogle Scholar
  43. 43.
    Velazquez JMO, Coello CAC, Arias-Montano A (2014) Multi-objective compact differential evolution. In: IEEE symposium on differential evolution (SDE). IEEE, New York, pp 1–8Google Scholar
  44. 44.
    Yamany W, El-Bendary N, Hassanien AE, Emary E (2016) Multi-objective cuckoo search optimization for dimensionality reduction. Procedia Computer Science 96:207–215CrossRefGoogle Scholar
  45. 45.
    Emary E, Yamany W, Hassanien AE, Snasel V (2015) Multi-objective gray-wolf optimization for attribute reduction. Procedia Computer Science 65:623–632CrossRefGoogle Scholar
  46. 46.
    Lin W, Yu D, Wang S, Zhang C, Zhang S, Tian H, Luo M, Liu S (2015) Multi-objective teaching–learning-based optimization algorithm for reducing carbon emissions and operation time in turning operations. Eng Optim 47(7):994–1007MathSciNetCrossRefGoogle Scholar
  47. 47.
    Coello CA (2000) An updated survey of ga-based multiobjective optimization techniques. ACM Comput Surv (CSUR) 32(2):109–143CrossRefGoogle Scholar
  48. 48.
    Pareto V (1964) Cours d’économie politique, vol 1. Librairie DrozGoogle Scholar
  49. 49.
    Mirjalili S (2016) Dragonfly algorithm: a new meta-heuristic optimization technique for solving single-objective, discrete, and multi-objective problems. Neural Comput Applic 27(4):1053–1073CrossRefGoogle Scholar
  50. 50.
    Van Veldhuizen DA, Lamont GB (1998) Multiobjective evolutionary algorithm research: a history and analysis. Tech. rep., Technical Report TR-98-03, Department of Electrical and Computer Engineering, Graduate School of Engineering, Air Force Institute of Technology, Wright-Patterson AFB OhioGoogle Scholar
  51. 51.
    Coello CC, Pulido GT (2005) Multiobjective structural optimization using a microgenetic algorithm. Struct Multidiscip Optim 30(5):388–403CrossRefGoogle Scholar
  52. 52.
    Sadollah A, Eskandar H, Kim JH (2015) Water cycle algorithm for solving constrained multi-objective optimization problems. Appl Soft Comput 27:279–298CrossRefGoogle Scholar
  53. 53.
    Tharwat A, Hassanien AE, Elnaghi BE (2016) A ba-based algorithm for parameter optimization of support vector machine. Pattern Recogn Lett 93:13–22CrossRefGoogle Scholar
  54. 54.
    Tharwat A, Elnaghi BE, Hassanien AE (2016) Meta-heuristic algorithm inspired by grey wolves for solving function optimization problems. In: International conference on advanced intelligent systems and informatics. Springer, Berlin, pp 480–490Google Scholar
  55. 55.
    Mirjalili S, Jangir P, Saremi S (2017) Multi-objective ant lion optimizer: a multi-objective optimization algorithm for solving engineering problems. Appl Intell 46(1):79–95CrossRefGoogle Scholar
  56. 56.
    Schott JR (1995) Fault tolerant design using single and multicriteria genetic algorithm optimization. Tech. rep., DTIC DocumentGoogle Scholar
  57. 57.
    Deb K (2001) Multi-objective optimization using evolutionary algorithms. Wiley, ChicheterzbMATHGoogle Scholar
  58. 58.
    García S, Fernández A, Luengo J, Herrera F (2010) Advanced nonparametric tests for multiple comparisons in the design of experiments in computational intelligence and data mining: experimental analysis of power. Inform Sci 180(10):2044–2064CrossRefGoogle Scholar
  59. 59.
    Zitzler E, Deb K, Thiele L (2000) Comparison of multiobjective evolutionary algorithms: empirical results. Evol Comput 8(2):173–195CrossRefGoogle Scholar
  60. 60.
    Tanaka M, Watanabe H, Furukawa Y, Tanino T (1995) Ga-based decision support system for multicriteria optimization. In: IEEE international conference on systems, man and cybernetics. Intelligent systems for the 21st century, vol 2. IEEE, New York, pp 1556–1561Google Scholar
  61. 61.
    Binh TT, Korn U (1997) Mobes: a multiobjective evolution strategy for constrained optimization problems. In: The third international conference on genetic algorithms (Mendel 97), vol 25, p 27Google Scholar
  62. 62.
    Osyczka A, Kundu S (1995) A new method to solve generalized multicriteria optimization problems using the simple genetic algorithm. Struct Multidiscip Optim 10(2):94–99CrossRefGoogle Scholar
  63. 63.
    Kita H, Yabumoto Y, Mori N, Nishikawa Y (1996) Multi-objective optimization by means of the thermodynamical genetic algorithm. In: Parallel problem solving from nature—PPSN IV, pp 504–512Google Scholar
  64. 64.
    Tharwat A, Hassanien AE (2017) Chaotic antlion algorithm for parameter optimization of support vector machine. Appl Intell 1–17, In PressGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2017

Authors and Affiliations

  • Alaa Tharwat
    • 1
    • 2
    • 5
    Email author
  • Essam H. Houssein
    • 3
    • 5
  • Mohammed M. Ahmed
    • 3
    • 5
  • Aboul Ella Hassanien
    • 4
    • 5
  • Thomas Gabel
    • 1
  1. 1.Faculty of Computer Science and EngineeringFrankfurt University of Applied SciencesFrankfurt am MainGermany
  2. 2.Faculty of EngineeringSuez Canal UniversityIsmailiaEgypt
  3. 3.Faculty of Computers and InformationMinia UniversityMiniaEgypt
  4. 4.Faculty of Computers and InformationCairo UniversityGizaEgypt
  5. 5.Scientific Research Group in Egypt (SRGE)CairoEgypt

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