International Journal of Combinatorics

Research Article

Application of the Firefly Algorithm for Solving the Economic Emissions Load Dispatch Problem

Pseudocode 1

The proposed implemented firefly algorithm.
Input: 𝛼 , 𝛾 , 𝛽 0 , 𝑛 , MaxGeneration, 𝐡 , cost-emission-capacities coefficients
Output: 𝑃 G i for 𝑖 = 1 , … 6 , 𝑓 ( 𝑋 ) , 𝑓 1 ( 𝑋 ) , 𝑓 2 ( 𝑋 )
Begin of algorithm
Define the multiobjective function: max βˆ’ 𝑓 ( 𝑃 G i ) , with 𝑖 = 1 , … , 6
Generate initial population of fireflies 𝑛 = 1 , … , 1 2   %generate 𝑛 = 1 2 initial solutions
Light Intensity of firefly 𝑛 is determined by objective function, 𝐼 𝑛 ∼ 𝑓 ( 𝑃 G i )
Define 𝛼 = 0 . 2 , 𝛽 0 = 1 . 0 and 𝛾 = 1 . 0   %necessary algorithm’s parameters
While ( 𝑑 ≀ MaxGeneration = 50)
 For 𝑖 = 1 ∢ 1 2   %for all fireflies (solutions)
  For 𝑗 = 1 ∢ 1 2   %for all fireflies (solutions)
   If ( 𝐼 𝑖 < 𝐼 𝑗 )
   Then move firefly 𝑖 towards firefly 𝑗 (move towards brighter one)
   Attractiveness varies with distance π‘Ÿ 𝑖 𝑗 via exp ( βˆ’ 𝛾 π‘Ÿ 𝑖 𝑗 )
   Generate and evaluate new solutions and update Light Intensity
  End for 𝑗 loop
 End for 𝑖 loop
Check the ranges of the given solutions and update them as appropriate
Rank the fireflies, find and display the current best %max solution for each iteration
End of while loop
% Post-process results and visualization
Find the firefly with the highest Light Intensity among all fireflies %optimal solution
Plot the increase of the Light Intensity with timeβˆ–iterations
Plot the two objectives with time %best solution with time
End of algorithm