Formulation of Modified Artificial Bee Colony (R_ABC) Optimization Algorithm to Minimize Economic Load Dispatch

The standard Artificial Bee Colony (ABC) algorithm's effectiveness is tempered by its slow convergence and high computational time. Two solutions were put in place: a rate of change approach was embedded for the scout bee phase and alterations to the mutation equation were applied in onlooker beech phase. The algorithm's exploration and exploitation capabilities were enhanced by these changes, leading to the creation of the Rate of change Artificial Bee Colony (<tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\mathbf{R}_{\mathbf{A}} \mathbf{B C}$</tex>) algorithm. The standard <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\mathbf{ABC}$</tex> algorithm was compared to <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$R_{A} B C$</tex> on 10 benchmark functions. Most benchmark functions were found to have lower minimum values and convergent convergence rates for <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$R_{A} B C. R_{A} B C$</tex> created the most cost-effective 6-unit generator system for solving Economic LD. ABC was beaten and Particle Swarm Optimization. The cost differences may seem insignificant, but they can result in substantial savings when dealing with large-scale power systems. The study suggests that <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\mathrm{R}_{\mathrm{A}} \text{BC}$</tex> is a significant advancement in power system optimization techniques, as it has demonstrated improved performance in both theoretical and practical ELD contexts but requires further refinement and parameter tuning to achieve optimal results.