[go: up one dir, main page]
More Web Proxy on the site http://driver.im/ Skip to main content
Springer Nature Link
Log in

Solving 0–1 Knapsack Problem using Cohort Intelligence Algorithm

  • Original Article
  • Published:
International Journal of Machine Learning and Cybernetics Aims and scope Submit manuscript

Abstract

An emerging technique, inspired from the natural and social tendency of individuals to learn from each other referred to as Cohort Intelligence (CI) is presented. Learning here refers to a cohort candidate’s effort to self supervise its own behavior and further adapt to the behavior of the other candidate which it intends to follow. This makes every candidate improve/evolve its behavior and eventually the entire cohort behavior. This ability of the approach is tested by solving an NP-hard combinatorial problem such as Knapsack Problem (KP). Several cases of the 0–1 KP are solved. The effect of various parameters on the solution quality has been discussed.The advantages and limitations of the CI methodology are also discussed.

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

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
£29.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price includes VAT (United Kingdom)

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10

Similar content being viewed by others

Explore related subjects

Discover the latest articles, news and stories from top researchers in related subjects.

References

  1. Deb K (2000) An efficient constraint handling method for genetic algorithms. Comput Meth Appl Mech Eng 186:311–338

    Article  MATH  Google Scholar 

  2. Ray T, Tai K, Seow KC (2001) Multiobjective design optimization by an evolutionary algorithm. Eng Optim 33(4):399–424

    Article  Google Scholar 

  3. Kennedy J, Eberhart R (1995) Particle swarm optimization. In: Proceedings of IEEE international conference on neural networks, pp 1942–1948 (1995)

  4. Dorigo M, Birattari M, Stitzle T (2006) Ant colony optimization: artificial ants as a computational intelligence technique. IEEE Comput Intell Mag 1:28–39

    Article  Google Scholar 

  5. Pham DT, Ghanbarzadeh A, Koc E, Otri S, Rahim S, Zaidi M (2005) The Bees algorithm, technical note. Manufacturing Engineering Centre, Cardiff University

  6. Feng Y, Jia K, He Y (2014) An improved hybrid encoding cuckoo search algorithm for 0–1 Knapsack Problems. Comput Intell Neurosci 2014:1–9

    Google Scholar 

  7. Kulkarni AJ, Durugkar IP, Kumar MR (2013) Cohort intelligence: a self supervised learning behavior. In: Proc. of IEEE international conference on systems, man, and cybernetics, pp 396–400

  8. Liu L, Zhong WM, Qian F (2010) An improved chaos-particle swarm optimization algorithm. J East China Univ Sci Technol (Nat Sci Ed) 36:267–272

    Google Scholar 

  9. Xu W, Geng Z, Zhu Q, Gu X (2013) A piecewise linear chaotic map and sequential quadratic programming based robust hybrid particle swarm optimization. Inf Sci 218:85–102

    Article  MathSciNet  MATH  Google Scholar 

  10. Kennedy J (2003) Bare bones particle swarms. In: Proceedings of the IEEE swarm intelligence symposium (SIS’03), pp 80–87

  11. Mendes R, Kennedy J, Neves J (2004) The fully informed particle swarm: simpler. Maybe better. IEEE Trans Evol Comput 8(3):204–210

    Article  Google Scholar 

  12. Chen L, Sun H, Wang S (2009) Solving continuous optimization using ant colony algorithm. In: Second international conference on future information technology and management engineering, pp 92–95

  13. Dorigo M, Maniezzo V, Colorni A (1996) Ant system: optimization by a colony of cooperating agents. IEEE Trans Syst Man Cybern Part B Cybern 26(1):29–41

    Article  Google Scholar 

  14. Krishnasamy G, Kulkarni AJ, Paramesran R (2014) A hybrid approach for data clustering based on modified cohort intelligence and K-means. Exp Syst Appl 41(3):6009–6016

  15. Hernández PR, Dimopoulos NJ (2005) A new heuristic for solving the multichoice multidimensional Knapsack Problem. In: Proc. of IEEE transactions on systems, man, and cybernetics—part A : systems and humans, vol 35, no 5, pp 708–717

  16. Martello S, Toth P (1990) Knapsack Problems: algorithms and computer implementations. Wiley, New York, pp 1–296 (1990)

  17. Tavares J, Pereira FB, Costa E (2008) Multidimensional Knapsack Problem: a fitness landscape analysis. In: Proc. of IEEE transactions on systems, man, and cybernetics—part B. Cybernetics 38(3):604–616

    Google Scholar 

  18. Moser M (1996) Declarative scheduling for optimally graceful QoS degradation. In: Proc. IEEE international conference multimedia computing systems, pp 86–93 (1996)

  19. Khan MS (1998) Quality adaptation in a multisession multimedia system: model, algorithms and architecture. Ph.D. dissertation, Department of Electrical and Computer Engineering, University of Victoria, Victoria, BC, Canada (1998)

  20. Warner D, Prawda J (1972) A mathematical programming model for scheduling nursing personnel in a hospital. Manag Sci (Application Series Part 1) 19(4):411–422

  21. Psinger D (1995) Algorithms for Knapsack Problems. PhD thesis, Department of Computer Science, University of Copenhagen, Copenhagen, Denmark (1995)

  22. Laporte G (1992) The vehicle routing problem: an overview of exact and approximate algorithms. Eur J Oper Res 59:345–358

    Article  MATH  Google Scholar 

  23. Granmo OC, Oommen BJ, Myrer SA, Olsen MG (2007) Learning automata-based solutions to the nonlinear fractional Knapsack Problem with applications to optimal resource allocation. Proc IEEE Trans Syst Man Cybern Part B Cybern 37(1):166–175

    Article  Google Scholar 

  24. Zou D, Gao L, Li S, Wu J (2011) Solving 0–1 Knapsack Problem by a Novel Global Harmony Search algorithm. Appl Soft Comput 11:1556–1564

    Article  Google Scholar 

  25. Layeb A (2013) A hybrid Quantum Inspired Harmony Search algorithm for 0–1 optimization problems. J Comput Appl Math 253:14–25

    Article  MathSciNet  MATH  Google Scholar 

  26. Layeb A (2011) A novel Quantum Inspired Cuckoo Search for Knapsack Problems. Int J Bio-Inspired Comput 3(5):297–305

    Article  Google Scholar 

  27. Geem ZW, Kim JH, Loganathan GV (2001) A new heuristic optimization algorithm: harmony search. Simulation 76(2):60–68

    Article  Google Scholar 

  28. Mahdavi M, Fesanghary M, Damangir E (2007) An Improved Harmony Search algorithm for solving optimization problems. Appl Math Comput 188:1567–1579

    MathSciNet  MATH  Google Scholar 

  29. Deb K (2000) An efficient constraint handling method for genetic algorithms. Comput Meth Appl Mech Eng 186:311–338

    Article  MATH  Google Scholar 

  30. Kulkarni AJ, Tai K (2011) Solving constrained optimization problems using probability collectives and a penalty function approach. Int J Comput Intell Appl 10(4):445–470

    Article  MATH  Google Scholar 

  31. Kulkarni AJ, Tai K (2011) A probability collectives approach with a feasibility-based rule for constrained optimization. Appl Comput Intell Soft Comput 2011, Article ID 980216

  32. Ma W, Wang M, Zhu X (2014) Improved particle swarm optimization based approach for bilevel programming problem-an application on supply chain model. Int J Mach Learn Cybernet 5(2):281–292

    Article  Google Scholar 

  33. Chen CJ (2012) Structural vibration suppression by using neural classifier with genetic algorithm. Int J Mach Learn Cybernet 3(3):215–221

    Article  Google Scholar 

  34. Wang XZ, He Q, Chen DG, Yeung D (2005) A genetic algorithm for solving the inverse problem of support vector machines. Neurocomputing 68:225–238

    Article  Google Scholar 

  35. Wang XZ, He YL, Dong LC, Zhao HY (2011) Particle swarm optimization for determining fuzzy measures from data. Inf Sci 181(19):4230–4252

    Article  MATH  Google Scholar 

Download references

Acknowledgments

The authors would like to thank Abdesslem Layeb from MISC Lab, Computer Science Department, University of Constantine, Algeria for his useful discussion in the regard of the Knapsack Problem test cases.

Author information

Authors and Affiliations

  1. Odette School of Business, University of Windsor, 401 Sunset Avenue, Windsor, ON, N9B 3P4, Canada

    Anand J. Kulkarni

  2. Optimization and Agent Technology (OAT) Research Lab, Maharashtra Institute of Technology, 124 Paud Road, Kothrud, Pune, 411038, India

    Anand J. Kulkarni & Hinna Shabir

Authors
  1. Anand J. Kulkarni
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Hinna Shabir
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Anand J. Kulkarni.

Appendix

Appendix

$$\begin{gathered} f_{11} \,\,{\text{N}} = 30,{\text{ W}} = { 577} \hfill \\ {\text{w}} = \, \left\{ { 4 6,{ 17},{ 35},{ 1},{ 26},{ 17},{ 17},{ 48},{ 38},{ 17},{ 32},{ 21},{ 29},{ 48},{ 31},{ 8},{ 42},{ 37},{ 6},{ 9},{ 15},{ 22},{ 27},{ 14},{ 42},{ 4}0,{ 14},{ 31},{ 6},{ 34}} \right\} \hfill \\ {\text{v}} = \, \left\{ { 5 7,{ 64},{ 5}0,{ 6},{ 52},{ 6},{ 85},{ 6}0,{ 7}0,{ 65},{ 63},{ 96},{ 18},{ 48},{ 85},{ 5}0,{ 77},{ 18},{ 7}0,{ 92},{ 17},{ 43},{ 5},{ 23},{ 67},{ 88},{ 35},{ 3},{ 91},{ 48}} \right\} \hfill \\ \end{gathered}$$
$$\begin{gathered} f_{12} \,\,{\text{N}} = 3 5,{\text{ W}} = { 655} \hfill \\ {\text{w}} = \, \left\{ { 7,{ 4},{ 36},{ 47},{ 6},{ 33},{ 8},{ 35},{ 32},{ 3},{ 4}0,{ 5}0,{ 22},{ 18},{ 3},{ 12},{ 3}0,{ 31},{ 13},{ 33},{ 4},{ 48},{ 5},{ 17},{ 33},{ 26},{ 27},{ 19},{ 39},{ 15},{ 33},{ 47},{ 17},{ 41},{ 4}0} \right\} \hfill \\ {\text{v}} = \, \left\{ { 3 5,{ 67},{ 3}0,{ 69},{ 4}0,{ 4}0,{ 21},{ 73},{ 82},{ 93},{ 52},{ 2}0,{ 61},{ 2}0,{ 42},{ 86},{ 43},{ 93},{ 38},{ 7}0,{ 59},{ 11},{ 42},{ 93},{ 6},{ 39},{ 25},{ 23},{ 36},{ 93},{ 51},{ 81},{ 36},{ 46},{ 96}} \right\} \hfill \\ \end{gathered}$$
$$\begin{gathered} f_{13} \,\,{\text{N}} = 40,{\text{ W}} = { 819} \hfill \\ {\text{w}} = \, \left\{ { 2 8,{ 23},{ 35},{ 38},{ 2}0,{ 29},{ 11},{ 48},{ 26},{ 14},{ 12},{ 48},{ 35},{ 36},{ 33},{ 39},{ 3}0,{ 26},{ 44},{ 2}0,{ 13},{ 15},{ 46},{ 36},{ 43},{ 19},{ 32},{ 2},{ 47},{ 24},{ 26},{ 39},{ 17},{ 32},{ 17},{ 16},{ 33},{ 22},{ 6},{ 12}} \right\} \hfill \\ {\text{v}} = \, \left\{ { 1 3,{ 16},{ 42},{ 69},{ 66},{ 68},{ 1},{ 13},{ 77},{ 85},{ 75},{ 95},{ 92},{ 23},{ 51},{ 79},{ 53},{ 62},{ 56},{ 74},{ 7},{ 5}0,{ 23},{ 34},{ 56},{ 75},{ 42},{ 51},{ 13},{ 22},{ 3}0,{ 45},{ 25},{ 27},{ 9}0,{ 59},{ 94},{ 62},{ 26},{ 11}} \right\} \hfill \\ \end{gathered}$$
$$\begin{gathered} f_{14} \,\,{\text{N}} = 4 5,{\text{ W}} = { 9}0 7\hfill \\ {\text{w}} = \, \left\{ { 1 8,{ 12},{ 38},{ 12},{ 23},{ 13},{ 18},{ 46},{ 1},{ 7},{ 2}0,{ 43},{ 11},{ 47},{ 49},{ 19},{ 5}0,{ 7},{ 39},{ 29},{ 32},{ 25},{ 12},{ 8},{ 32},{ 41},{ 34},{ 24},{ 48},{ 3}0,{ 12},{ 35},{ 17},{ 38},{ 5}0,{ 14},{ 47},{ 35},{ 5},{ 13},{ 47},{ 24},{ 45},{ 39},{ 1}} \right\} \hfill \\ {\text{v}} = \, \left\{ { 9 8,{ 7}0,{ 66},{ 33},{ 2},{ 58},{ 4},{ 27},{ 2}0,{ 45},{ 77},{ 63},{ 32},{ 3}0,{ 8},{ 18},{ 73},{ 9},{ 92},{ 43},{ 8},{ 58},{ 84},{ 35},{ 78},{ 71},{ 6}0,{ 38},{ 4}0,{ 43},{ 43},{ 22},{ 5}0,{ 4},{ 57},{ 5},{ 88},{ 87},{ 34},{ 98},{ 96},{ 99},{ 16},{ 1},{ 25}} \right\} \hfill \\ \end{gathered}$$
$$\begin{gathered} f_{15} \,\,{\text{N}} = 50,{\text{ W}} = { 882} \hfill \\ {\text{w}} = \, \left\{ { 1 5,{ 4}0,{ 22},{ 28},{ 5}0,{ 35},{ 49},{ 5},{ 45},{ 3},{ 7},{ 32},{ 19},{ 16},{ 4}0,{ 16},{ 31},{ 24},{ 15},{ 42},{ 29},{ 4},{ 14},{ 9},{ 29},{ 11},{ 25},{ 37},{ 48},{ 39},{ 5},{ 47},{ 49},{ 31},{ 48},{ 17},{ 46},{ 1},{ 25},{ 8},{ 16},{ 9},{ 3}0,{ 33},{ 18},{ 3},{ 3},{ 3},{ 4},{ 1}} \right\} \hfill \\ {\text{v}} = \, \left\{ { 7 8,{ 69},{ 87},{ 59},{ 63},{ 12},{ 22},{ 4},{ 45},{ 33},{ 29},{ 5}0,{ 19},{ 94},{ 95},{ 6}0,{ 1},{ 91},{ 69},{ 8},{ 1}00,{ 32},{ 81},{ 47},{ 59},{ 48},{ 56},{ 18},{ 59},{ 16},{ 45},{ 54},{ 47},{ 84},{ 1}00,{ 98},{ 75},{ 2}0,{ 4},{ 19},{ 58},{ 63},{ 37},{ 64},{ 9}0,{ 26},{ 29},{ 13},{ 53},{ 83}} \right\} \hfill \\ \end{gathered}$$
$$\begin{gathered} f_{16} \,\,{\text{N}} = 5 5,{\text{ W}} = { 1}0 50 \hfill \\ {\text{w}} = \, \{ 2 7,{ 15},{ 46},{ 5},{ 4}0,{ 9},{ 36},{ 12},{ 11},{ 11},{ 49},{ 2}0,{ 32},{ 3},{ 12},{ 44},{ 24},{ 1},{ 24},{ 42},{ 44},{ 16},{ 12},{ 42},{ 22},{ 26},{ 1}0,{ 8},{ 46},{ 5}0,{ 2}0, \hfill \\ 4 2,{ 48},{ 45},{ 43},{ 35},{ 9},{ 12},{ 22},{ 2},{ 14},{ 5}0,{ 16},{ 29},{ 31},{ 46},{ 2}0,{ 35},{ 11},{ 4},{ 32},{ 35},{ 15},{ 29},{ 16}\} \hfill \\ {\text{v}} = \, \{ 9 8,{ 74},{ 76},{ 4},{ 12},{ 27},{ 9}0,{ 98},{ 1}00,{ 35},{ 3}0,{ 19},{ 75},{ 72},{ 19},{ 44},{ 5},{ 66},{ 79},{ 87},{ 79},{ 44},{ 35},{ 6},{ 82},{ 11},{ 1},{ 28},{ 95},{ 68},{ 39}, \hfill \\ 8 6,{ 68},{ 61},{ 44},{ 97},{ 83},{ 2},{ 15},{ 49},{ 59},{ 3}0,{ 44},{ 4}0,{ 14},{ 96},{ 37},{ 84},{ 5},{ 43},{ 8},{ 32},{ 95},{ 86},{ 18}\} \hfill \\ \end{gathered}$$
$$\begin{gathered} f_{17} \,\,{\text{N}} = 60,{\text{ W}} = { 1}00 6\hfill \\ {\text{w}} = \, \left\{ { 7,{ 13},{ 47},{ 33},{ 38},{ 41},{ 3},{ 21},{ 37},{ 7},{ 32},{ 13},{ 42},{ 42},{ 23},{ 2}0,{ 49},{ 1},{ 2}0,{ 25},{ 31},{ 4},{ 8},{ 33},{ 11},{ 6},{ 3},{ 9},{ 26},{ 44},{ 39},{ 7},{ 4},{ 34},{ 25},{ 25},{ 16},{ 17},{ 46},{ 23},{ 38},{ 1}0,{ 5},{ 11},{ 28},{ 34},{ 47},{ 3},{ 9},{ 22},{ 17},{ 5},{ 41},{ 2}0,{ 33},{ 29},{ 1},{ 33},{ 16},{ 14}} \right\} \hfill \\ {\text{v}} = \, \left\{ { 8 1,{ 37},{ 7}0,{ 64},{ 97},{ 21},{ 6}0,{ 9},{ 55},{ 85},{ 5},{ 33},{ 71},{ 87},{ 51},{ 1}00,{ 43},{ 27},{ 48},{ 17},{ 16},{ 27},{ 76},{ 61},{ 97},{ 78},{ 58},{ 46},{ 29},{ 76},{ 1}0,{ 11},{ 74},{ 36},{ 59},{ 3}0,{ 72},{ 37},{ 72},{ 1}00,{ 9},{ 47},{ 1}0,{ 73},{ 92},{ 9},{ 52},{ 56},{ 69},{ 3}0,{ 61},{ 2}0,{ 66},{ 7}0,{ 46},{ 16},{ 43},{ 6}0,{ 33},{ 84}} \right\} \hfill \\ \end{gathered}$$
$$\begin{gathered} f_{18} \,\,{\text{N}} = 6 5,{\text{ W}} = { 1319} \hfill \\ {\text{w}} = \, \{ 4 7,{ 27},{ 24},{ 27},{ 17},{ 17},{ 5}0,{ 24},{ 38},{ 34},{ 4}0,{ 14},{ 15},{ 36},{ 1}0,{ 42},{ 9},{ 48},{ 37},{ 7},{ 43},{ 47},{ 29},{ 2}0,{ 23},{ 36},{ 14},{ 2},{ 48},{ 5}0,{ 39}, \hfill \\ 50,{ 25},{ 7},{ 24},{ 38},{ 34},{ 44},{ 38},{ 31},{ 14},{ 17},{ 42},{ 2}0,{ 5},{ 44},{ 22},{ 9},{ 1},{ 33},{ 19},{ 19},{ 23},{ 26},{ 16},{ 24},{ 1},{ 9},{ 16},{ 38},{ 3}0,{ 36},{ 41},{ 43}, \hfill \\ 6\} \hfill \\ {\text{v}} = \, \{ 4 7,{ 63},{ 81},{ 57},{ 3},{ 8}0,{ 28},{ 83},{ 69},{ 61},{ 39},{ 7},{ 1}00,{ 67},{ 23},{ 1}0,{ 25},{ 91},{ 22},{ 48},{ 91},{ 2}0,{ 45},{ 62},{ 6}0,{ 67},{ 27},{ 43},{ 8}0,{ 94}, \hfill \\ 4 7,{ 31},{ 44},{ 31},{ 28},{ 14},{ 17},{ 5}0,{ 9},{ 93},{ 15},{ 17},{ 72},{ 68},{ 36},{ 1}0,{ 1},{ 38},{ 79},{ 45},{ 1}0,{ 81},{ 66},{ 46},{ 54},{ 53},{ 63},{ 65},{ 2}0,{ 81},{ 2}0,{ 42}, \hfill \\ 2 4,{ 28},{ 1}\} \hfill \\ \end{gathered}$$
$$\begin{gathered} f_{19} \,\,{\text{N}} = 70,{\text{ W}} = { 1426} \hfill \\ {\text{w}} = \, \left\{ { 4,{ 16},{ 16},{ 2},{ 9},{ 44},{ 33},{ 43},{ 14},{ 45},{ 11},{ 49},{ 21},{ 12},{ 41},{ 19},{ 26},{ 38},{ 42},{ 2}0,{ 5},{ 14},{ 4}0,{ 47},{ 29},{ 47},{ 3}0,{ 5}0,{ 39},{ 1}0,{ 26},{ 33},{ 44},{ 31},{ 5}0,{ 7},{ 15},{ 24},{ 7},{ 12},{ 1}0,{ 34},{ 17},{ 4}0,{ 28},{ 12},{ 35},{ 3},{ 29},{ 5}0,{ 19},{ 28},{ 47},{ 13},{ 42},{ 9},{ 44},{ 14},{ 43},{ 41},{ 1}0,{ 49},{ 13},{ 39},{ 41},{ 25},{ 46},{ 6},{ 7},{ 43}} \right\} \hfill \\ {\text{v}} = \, \left\{ { 6 6,{ 76},{ 71},{ 61},{ 4},{ 2}0,{ 34},{ 65},{ 22},{ 8},{ 99},{ 21},{ 99},{ 62},{ 25},{ 52},{ 72},{ 26},{ 12},{ 55},{ 22},{ 32},{ 98},{ 31},{ 95},{ 42},{ 2},{ 32},{ 16},{ 1}00,{ 46},{ 55},{ 27},{ 89},{ 11},{ 83},{ 43},{ 93},{ 53},{ 88},{ 36},{ 41},{ 6}0,{ 92},{ 14},{ 5},{ 41},{ 6}0,{ 92},{ 3}0,{ 55},{ 79},{ 33},{ 1}0,{ 45},{ 3},{ 68},{ 12},{ 2}0,{ 54},{ 63},{ 38},{ 61},{ 85},{ 71},{ 4}0,{ 58},{ 25},{ 73},{ 35}} \right\} \hfill \\ \end{gathered}$$
$$\begin{gathered} f_{20} \,\,{\text{N}} = 7 5,{\text{ W}} = { 1433} \hfill \\ {\text{w}} = \, \{ 2 4,{ 45},{ 15},{ 4}0,{ 9},{ 37},{ 13},{ 5},{ 43},{ 35},{ 48},{ 5}0,{ 27},{ 46},{ 24},{ 45},{ 2},{ 7},{ 38},{ 2}0,{ 2}0,{ 31},{ 2},{ 2}0,{ 3},{ 35},{ 27},{ 4},{ 21},{ 22},{ 33},{ 11}, \hfill \\ 5,{ 24},{ 37},{ 31},{ 46},{ 13},{ 12},{ 12},{ 41},{ 36},{ 44},{ 36},{ 34},{ 22},{ 29},{ 5}0,{ 48},{ 17},{ 8},{ 21},{ 28},{ 2},{ 44},{ 45},{ 25},{ 11},{ 37},{ 35},{ 24},{ 9},{ 4}0,{ 45},{ 8}, \hfill \\ 4 7,{ 1},{ 22},{ 1},{ 12},{ 36},{ 35},{ 14},{ 17},{ 5}\} \hfill \\ {\text{v}} = \, \{ 2,{ 73},{ 82},{ 12},{ 49},{ 35},{ 78},{ 29},{ 83},{ 18},{ 87},{ 93},{ 2}0,{ 6},{ 55},{ 1},{ 83},{ 91},{ 71},{ 25},{ 59},{ 94},{ 9}0,{ 61},{ 8}0,{ 84},{ 57},{ 1},{ 26},{ 44},{ 44}, \hfill \\ 8 8,{ 7},{ 34},{ 18},{ 25},{ 73},{ 29},{ 24},{ 14},{ 23},{ 82},{ 38},{ 67},{ 94},{ 43},{ 61},{ 97},{ 37},{ 67},{ 32},{ 89},{ 3}0,{ 3}0,{ 91},{ 5}0,{ 21},{ 3},{ 18},{ 31},{ 97},{ 79},{ 68}, \hfill \\ 8 5,{ 43},{ 71},{ 49},{ 83},{ 44},{ 86},{ 1},{ 1}00,{ 28},{ 4},{ 16}\} \hfill \\ \end{gathered}$$

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Kulkarni, A.J., Shabir, H. Solving 0–1 Knapsack Problem using Cohort Intelligence Algorithm. Int. J. Mach. Learn. & Cyber. 7, 427–441 (2016). https://doi.org/10.1007/s13042-014-0272-y

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s13042-014-0272-y

Keywords

Search

Navigation