MOGOA algorithm for constrained and unconstrained multi-objective optimization problems


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.

This is a preview of subscription content, log in to check access.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9


  1. 1.

    Motevasel M, Seifi AR, Niknam T (2013) Multi-objective energy management of chp (combined heat and power)-based micro-grid. Energy 51:123–136

    Article  Google 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 Press

  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 309–319

  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):1–4

    Article  Google 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):279–292

    Article  Google 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):701

    Article  Google 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 161–170

  8. 8.

    Hassanien AE, Tharwat A, Own HS (2017) Computational model for vitamin d deficiency using hair mineral analysis. Comput Biol Chem 70:198–210

    Article  Google 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 491–521

  10. 10.

    Marler RT, Arora JS (2004) Survey of multi-objective optimization methods for engineering. Struct Multidiscip Optim 26(6):369–395

    MathSciNet  Article  MATH  Google Scholar 

  11. 11.

    Deb K (2012) Advances in evolutionary multi-objective optimization. In: Search based software engineering, pp 1–26

  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):18–30

    Article  Google Scholar 

  13. 13.

    Coello CAC, Lamont GB, Van Veldhuizen DA et al (2007) Evolutionary algorithms for solving multi-objective problems, 2nd edn. Springer, Berlin

    Google 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):851–890

    MathSciNet  Article  MATH  Google Scholar 

  15. 15.

    Coello CC (2006) Evolutionary multi-objective optimization: a historical view of the field. IEEE Comput Intell Mag 1(1):28–36

    MathSciNet  Article  Google Scholar 

  16. 16.

    Padhye N, Bhardawaj P, Deb K (2013) Improving differential evolution through a unified approach. J Glob Optim 55(4):771

    MathSciNet  Article  MATH  Google 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):761–794

    MathSciNet  Article  MATH  Google Scholar 

  18. 18.

    Srinivas N, Deb K (1994) Muiltiobjective optimization using nondominated sorting in genetic algorithms. Evol Comput 2(3):221–248

    Article  Google 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):182–197

    Article  Google 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):257–271

    Article  Google Scholar 

  21. 21.

    Coello CAC, Pulido GT, Lechuga MS (2004) Handling multiple objectives with particle swarm optimization. IEEE Trans Evol Comput 8(3):256–279

    Article  Google 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 2516–2523

  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 1755–1756

  24. 24.

    Zhang Q, Li H (2007) Moea/d: a multiobjective evolutionary algorithm based on decomposition. IEEE Trans Evol Comput 11(6):712–731

    Article  Google 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 971–978

  26. 26.

    Wolpert DH, Macready WG (1997) No free lunch theorems for optimization. IEEE Trans Evol Comput 1(1):67–82

    Article  Google Scholar 

  27. 27.

    Saremi S, Mirjalili S, Lewis A (2017) Grasshopper optimisation algorithm: theory and application. Adv Eng Softw 105:30– 47

    Article  Google Scholar 

  28. 28.

    Haupt RL, Haupt SE (2004) Practical genetic algorithms. Wiley, New York

    Google 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 264

  30. 30.

    Ščap D, Hoić M, Jokić A (2013) Determination of the Pareto frontier for multiobjective optimization problem. Transactions of FAMENA 37(2):15–28

    Google 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):149–158

    Article  Google 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):631–657

    MathSciNet  Article  MATH  Google 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 603–607

  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 3–34

  35. 35.

    Goldberg D (1989) Genetic algorithms in optimization, search and machine learning. Addison-Wesley, Reading

    Google 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 614–635

  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 3153–3160

  38. 38.

    Knowles J, Thiele L, Zitzler E (2006) A tutorial on the performance assessment of stochastic multiobjective optimizers. Tik Report 214:327–332

    Google Scholar 

  39. 39.

    Pradhan PM, Panda G (2012) Solving multiobjective problems using cat swarm optimization. Expert Syst Appl 39(3):2956–2964

    Article  Google 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):333–338

    Google 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 2420–2427

  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):1169–1182

    MathSciNet  Article  Google 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 1–8

  44. 44.

    Yamany W, El-Bendary N, Hassanien AE, Emary E (2016) Multi-objective cuckoo search optimization for dimensionality reduction. Procedia Computer Science 96:207–215

    Article  Google Scholar 

  45. 45.

    Emary E, Yamany W, Hassanien AE, Snasel V (2015) Multi-objective gray-wolf optimization for attribute reduction. Procedia Computer Science 65:623–632

    Article  Google 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):994–1007

    MathSciNet  Article  Google Scholar 

  47. 47.

    Coello CA (2000) An updated survey of ga-based multiobjective optimization techniques. ACM Comput Surv (CSUR) 32(2):109–143

    Article  Google Scholar 

  48. 48.

    Pareto V (1964) Cours d’économie politique, vol 1. Librairie Droz

  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):1053–1073

    Article  Google 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 Ohio

  51. 51.

    Coello CC, Pulido GT (2005) Multiobjective structural optimization using a microgenetic algorithm. Struct Multidiscip Optim 30(5):388–403

    Article  Google Scholar 

  52. 52.

    Sadollah A, Eskandar H, Kim JH (2015) Water cycle algorithm for solving constrained multi-objective optimization problems. Appl Soft Comput 27:279–298

    Article  Google Scholar 

  53. 53.

    Tharwat A, Hassanien AE, Elnaghi BE (2016) A ba-based algorithm for parameter optimization of support vector machine. Pattern Recogn Lett 93:13–22

    Article  Google 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 480–490

  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):79–95

    Article  Google Scholar 

  56. 56.

    Schott JR (1995) Fault tolerant design using single and multicriteria genetic algorithm optimization. Tech. rep., DTIC Document

  57. 57.

    Deb K (2001) Multi-objective optimization using evolutionary algorithms. Wiley, Chicheter

    Google 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):2044–2064

    Article  Google Scholar 

  59. 59.

    Zitzler E, Deb K, Thiele L (2000) Comparison of multiobjective evolutionary algorithms: empirical results. Evol Comput 8(2):173–195

    Article  Google 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 1556–1561

  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 27

  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):94–99

    Article  Google 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 504–512

  64. 64.

    Tharwat A, Hassanien AE (2017) Chaotic antlion algorithm for parameter optimization of support vector machine. Appl Intell 1–17, In Press

Download references

Author information



Corresponding author

Correspondence to Alaa Tharwat.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Tharwat, A., Houssein, E.H., Ahmed, M.M. et al. MOGOA algorithm for constrained and unconstrained multi-objective optimization problems. Appl Intell 48, 2268–2283 (2018).

Download citation


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