Introducing CNSABC Algorithm for Enhanced Convergence and Solution Quality

By Soham NandiReviewed by Susha Cheriyedath, M.Sc.Nov 24 2023

In an article published in the journal Nature, researchers introduced the Chaotic and Neighborhood Search-based Artificial Bee Colony (CNSABC) algorithm, a novel variant addressing the limitations of the traditional Artificial Bee Colony (ABC) algorithm in optimization problems.

Background

Optimization problems, pervasive in diverse fields like engineering, finance, and design, prompt the continual evolution of global optimization algorithms. Among these, the ABC algorithm, simulating honeybee foraging behavior, stands out for its simplicity and exploration capability. However, traditional ABC has faced criticism for slow convergence and a tendency toward under-exploitation. Previous research efforts have proposed enhancements to ABC, addressing specific shortcomings, such as one-dimensional variation and weak exploitation capability. Despite these improvements, challenges persist in terms of convergence speed, premature convergence, and overall solution quality.

In response to these challenges, this study presented the CNSABC algorithm. The study conducted a series of experiments, comparing CNSABC with other algorithms and evaluating its performance on real-world engineering optimization problems. Results demonstrated the superior convergence speed and solution quality of CNSABC, positioning it as a promising advancement in the domain of optimization algorithms. This novel variant not only addressed existing gaps in ABC but also showcased potential applicability in practical problem-solving scenarios.

Improved ABC Algorithm

The researchers introduced a novel variant of the ABC algorithm, termed CNSABC, to address limitations in traditional ABC. The ABC algorithm, inspired by honeybee foraging behavior, involved employed bees, onlooker bees, and scout bees. The CNSABC incorporated three key enhancements.

Firstly, it introduced a Bernoulli chaotic mapping with a mutual exclusion mechanism to improve the uniformity of the initial population in high-dimensional problems. Secondly, a neighborhood search mechanism with a compression factor was proposed to balance exploration and exploitation, tailoring the search strategy for employed and onlooker bees. The compression factor was adaptively adjusted to enhance local exploration and global exploration. Lastly, the study introduced sustained bees, a new bee species without an upper limit of exploitation, influenced by the global optimal solution to continuously exploit the current optimal honey source.

The proposed CNSABC algorithm combined these improvements with traditional ABC, demonstrating superior convergence speed and solution quality. The time complexity analysis indicated the algorithm's efficiency in terms of population size, variable dimensionality, and fitness function calculations. Experimental results on benchmark functions and engineering optimization problems affirmed the effectiveness of CNSABC, showcasing its potential in practical problem-solving scenarios. The introduced mechanisms contributed to overcoming challenges in the exploration and exploitation balance, presenting CNSABC as a promising advancement in optimization algorithms.

Experimental Result and Analysis

The CNSABC algorithm was rigorously evaluated through extensive experiments using 26 benchmark test functions. These functions were categorized into unimodal separable, unimodal non-separable, multimodal separable, and multimodal non-separable types. Three key enhancements in the CNSABC, namely the Bernoulli chaotic mapping with mutual exclusion mechanism, neighborhood search mechanism with compression factor, and sustained bees, were individually tested with the ABC algorithm to validate their effectiveness. The CNSABC was then compared with standard algorithms and advanced improved ABC variants.

Results indicate that the CNSABC outperformed other algorithms, achieving the best results in terms of mean, standard deviation, and minimum values across various benchmark functions. The algorithm excelled in both exploitation and exploration capabilities, demonstrating a well-balanced convergence accuracy and process. Comparative analyses revealed CNSABC's superiority over other improved ABC algorithms, showcasing its robust performance across different benchmark functions.

The convergence curves visually depicted the CNSABC's efficient exploration and exploitation.
Additionally, statistical tests confirmed the significant distinctions between CNSABC and other algorithms. The proposed CNSABC algorithm, with its integrated improvements, emerged as a promising optimization technique, offering enhanced performance in solving complex optimization problems.

CNSABC for Solving Engineering Optimization Problems

The CNSABC algorithm was applied to solve two engineering optimization problems: the Tension/Compression Spring Design and the Speed Reducer Design. In the Tension/Compression Spring problem, the objective was to minimize the mass of the spring while satisfying constraints related to shear stress, surge frequency, and minimum deflection. CNSABC outperformed other algorithms, demonstrating a 3.67% to 4.88% improvement over various comparison algorithms.

In the Speed Reducer Design problem, the goal was to minimize the mass of the reducer with seven design variables. CNSABC achieved superior results compared to several algorithms, showcasing improvements ranging from 0.11% to 2.38% over other optimization techniques. Convergence analysis of CNSABC for the Tension/Compression Spring Design problem indicated its efficient exploration and exploitation capabilities.

The results highlighted the effectiveness of CNSABC in solving complex engineering optimization problems, emphasizing its superior performance and robustness over other algorithms in achieving optimal solutions for both the Tension/Compression Spring and Speed Reducer Design challenges.