Integrating the artificial bee colony and bees algorithm to face constrained optimization problems

• ABC–BA algorithm integrates artificial bee colony (ABC) and bees algorithm (BA).
• Population sizes of ABC and BA sub-swarms vary based on sub-swarm fitness values.
• Constrained optimization problems with equality or inequality constraints are conducted.
• Constraints are used to determine variables in addressing equality constraints.
• ABC–BA performance approximates or exceeds the winner of either ABC or BA.

Swarm intelligence (SI) has generated growing interest in recent decades as an algorithm replicating biological and other natural systems. Several SI algorithms have been developed that replicate the behavior of honeybees. This study integrates two of these, the artificial bee colony (ABC) and bees algorithms (BA), into a hybrid ABC–BA algorithm. In ABC–BA, an agent can perform as an ABC agent in the ABC sub-swarm and/or a BA agent in the BA sub-swarm. Therefore, the ABC and BA formulations coexist within ABC–BA. Moreover, the population sizes of the ABC and BA sub-swarms vary stochastically based on the current best fitness values obtained by the sub-swarms.This paper conducts experiments on six constrained optimization problems (COPs) with equality or inequality constraints. In addressing equality constraints, this paper proposes using these constraints to determine function variables rather than directly converting them into inequality constraints, an approach that perfectly satisfies the equality constraints. Experimental results demonstrate that the performance of the ABC–BA approximates or exceeds the winner of either ABC or BA. Therefore, the ABC–BA is recommended as an alternative to ABC and BA for handling COPs.