Toward the modification of flower pollination algorithm in clustering-based image segmentation

  • Krishna Gopal DhalEmail author
  • Jorge Gálvez
  • Sanjoy Das
Original Article


Flower pollination algorithm (FPA) is a new bio-inspired optimization algorithm, which has shown an effective performance on solving many optimization problems. However, the effectiveness of FPA significantly depends on the balance achieved by the exploration and exploitation evolutionary stages. Since purely exploration procedure promotes non-accurate solutions, meanwhile, purely exploitation operation promotes sub-optimal solutions in the presence of multiple optima. In this study, three global search and two local search strategies have been designed to improve balance among evolutionary stages, increasing the efficiency and robustness of the original FPA methodology. Additionally, some parameter adaptation techniques are also incorporated in the proposed methodology. The modified FPA has been successfully applied for histopathological image segmentation problem. The experimental and computational effort results indicate its effectiveness over existing swarm intelligence algorithms and machine learning methods.


Optimization Meta-heuristics Classification Histopathological image segmentation 

List of symbols


Number of classes


Number of dimensions


ith solution within an optimization technique


jth centroid for the ith solution


Training sample


Centroid of a given class


Number of samples


Global best solution


Population size


Iteration number


Maximum number of generations


Step size


Number of neighbors


Logistic map

\(fit \left( {X_{i} } \right)\)

Fitness value

\(fit_{w} \left( {X_{i} } \right)\)

Normalized fitness value

\(fit_{{\tilde{w}}} \left( {X_{i} } \right)\)

Normalized average fitness value


Lower bound for a given dimension


Upper bound for a given dimension


Chaotic number


Inverse golden ratio value



Solution within an optimization technique


Centroid for each i th solution


Training sample number


Previous best


Global best



This work was funded by DST-PURSE.


This study was funded under DST-PURSE scheme.

Compliance with ethical standards

Conflict of interest

Author Krishna Gopal Dhal has received research grants from PURSE scheme, DST, India. Authors Jorge Gálvez and Sanjoy Das declare that they 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.


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Copyright information

© Springer-Verlag London Ltd., part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of Computer Science and ApplicationMidnapore College (Autonomous)Paschim MedinipurIndia
  2. 2.Departamento de ElectrónicaUniversidad de GuadalajaraGuadalajaraMexico
  3. 3.Department of Engineering and Technological StudiesUniversity of KalyaniKalyani, NadiaIndia

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