This paper presents a comparison of the Artificial Bee Colony (ABC) algorithm's performance in solving constrained optimization problems. The ABC algorithm, initially proposed for unconstrained optimization, has shown superior performance in such problems. This study extends the ABC algorithm to handle constrained optimization and applies it to a set of constrained problems. The general form of a constrained optimization problem is to minimize an objective function \( f(\mathbf{x}) \) within a feasible region \( \mathbb{F} \subseteq \mathbb{S} \), where \( \mathbb{S} \) is the search space defined by lower and upper bounds, and \( \mathbb{F} \) is defined by additional constraints \( g_j(\mathbf{x}) \leq 0 \) and equality constraints \( h_j(\mathbf{x}) = 0 \).
The paper reviews both deterministic and stochastic algorithms for constrained optimization, highlighting the limitations of deterministic approaches and the success of stochastic algorithms like Genetic Algorithms, Evolution Strategies, and Particle Swarm Optimization (PSO). The ABC algorithm, inspired by honey bees' foraging behavior, is adapted to handle constraints by replacing the selection mechanism with Deb's method. The performance of the extended ABC algorithm is tested on 13 well-known constrained optimization problems and compared with PSO and Differential Evolution (DE) algorithms. The paper is structured into sections covering the ABC algorithm, its extension for constrained problems, benchmark testing, and results.This paper presents a comparison of the Artificial Bee Colony (ABC) algorithm's performance in solving constrained optimization problems. The ABC algorithm, initially proposed for unconstrained optimization, has shown superior performance in such problems. This study extends the ABC algorithm to handle constrained optimization and applies it to a set of constrained problems. The general form of a constrained optimization problem is to minimize an objective function \( f(\mathbf{x}) \) within a feasible region \( \mathbb{F} \subseteq \mathbb{S} \), where \( \mathbb{S} \) is the search space defined by lower and upper bounds, and \( \mathbb{F} \) is defined by additional constraints \( g_j(\mathbf{x}) \leq 0 \) and equality constraints \( h_j(\mathbf{x}) = 0 \).
The paper reviews both deterministic and stochastic algorithms for constrained optimization, highlighting the limitations of deterministic approaches and the success of stochastic algorithms like Genetic Algorithms, Evolution Strategies, and Particle Swarm Optimization (PSO). The ABC algorithm, inspired by honey bees' foraging behavior, is adapted to handle constraints by replacing the selection mechanism with Deb's method. The performance of the extended ABC algorithm is tested on 13 well-known constrained optimization problems and compared with PSO and Differential Evolution (DE) algorithms. The paper is structured into sections covering the ABC algorithm, its extension for constrained problems, benchmark testing, and results.