Flower pollination algorithm

Flower pollination algorithm (FPA) is a metaheuristic algorithm for optimization and this algorithm was developed by Xin-She Yang, based on the pollination process of flowering plants. FPA has been applied to solve practical problems in engineering, solar PV parameter estimation, and fuzzy selection for dynamic economic dispatch.

Main Characteristics

This algorithm has 4 rules or assumptions:

1. Biotic and cross-pollination is considered as global pollination process with pollen carrying pollinators performing Levy flights.

2. Abiotic and self-pollination are considered as local pollination.

3. Flower constancy can be considered as the reproduction probability is proportional to the similarity of two flowers involved.

4. Local pollination and global pollination is controlled by a switch probability $p\in [0,1]$. Due to the physical proximity and other factors such as wind, local pollination can have a significant fraction p in the overall pollination activities.

These rules can be translated into the following updating equations:

$x_{i}^{t+1}=x_{i}^{t}+L(x_{i}^{t}-g_{*})$

$x_{i}^{t+1}=x_{i}^{t}+\epsilon (x_{i}^{t}-x_{k}^{t})$

where $x_{i}^{t}$ is the solution vector and $g_{*}$ is the current best found so far during iteration. The switch probability between two equations during iterations is $p$. In addition, $\epsilon$ is a random number drawn from a uniform distribution. $L$ is a step size drawn from a Lévy distribution.

A matlab demo program is available for function optimization