Adaptive Bee Colony in an Artificial Bee Colony for Solving Engineering Design Problems

A wide range of engineering design problems have been solved by the algorithms that simulates collective intelligence in swarms of birds or insects. The Artificial Bee Colony or ABC is one of the recent additions to the class of swarm intelligence based algorithms that mimics the foraging behavior of honey bees. ABC consists of three groups of bees namely employed, onlooker and scout bees. In ABC, the food locations represent the potential candidate solution. In the present study an attempt is made to generate the population of food sources (Colony Size) adaptively and the variant is named as A-ABC. A-ABC is further enhanced to improve convergence speed and exploitation capability, by employing the concept of elitism, which guides the bees towards the best food source. This enhanced variant is called E-ABC. The proposed algorithms are validated on a set of standard benchmark problems with varying dimensions taken from literature and on five engineering design problems. The numerical results are compared with the basic ABC and three recent variant of ABC. Numerically and statistically simulated results illustrate that the proposed method is very efficient and competitive.

💡 Research Summary

The paper addresses two notable limitations of the standard Artificial Bee Colony (ABC) algorithm—its fixed colony size and relatively weak exploitation capability—by introducing two novel variants: Adaptive‑ABC (A‑ABC) and Elite‑ABC (E‑ABC). In the classic ABC framework, employed bees exploit known food sources, onlooker bees probabilistically select sources based on shared information, and scout bees replace stagnating sources. While this division of labor balances exploration and exploitation, a static number of food sources often leads to either insufficient diversity in high‑dimensional problems or unnecessary computational overhead as the algorithm converges.

A‑ABC tackles this issue through a dynamic colony‑size adjustment mechanism. At each iteration the algorithm evaluates two indicators: the improvement rate of the best fitness (Δf) and the success ratio of successful foraging moves (σ). Their product is compared against two thresholds, θ₁ (upper) and θ₂ (lower). If Δf·σ > θ₁, the algorithm injects M new food sources, where M scales with problem dimensionality, thereby enriching the search space during early stages. Conversely, if Δf·σ < θ₂, the poorest food source is removed, shrinking the colony and reducing computational load as the search stabilizes. This adaptive scheme preserves diversity when needed and curtails wasteful evaluations near convergence.

E‑ABC builds on A‑ABC by incorporating elitism. The current globally best food source, denoted xₑ, is treated as an elite guide for all subsequent moves. Both onlooker and scout bees generate new candidates by perturbing around xₑ rather than around randomly chosen sources. The mutation formula is x′ = xₑ + φ·(xᵢ – xₑ), where φ ∈