An adaptive dung beetle optimizer based on an elastic annealing mechanism and its application to numerical problems and optimization of Reed–Muller logic circuits

Abstract

The dung beetle optimizer (DBO) is a metaheuristic algorithm with fast convergence and powerful search capabilities, which has shown excellent performance in solving various optimization problems. However, it suffers from the problems of easily falling into local optimal solutions and poor convergence accuracy when dealing with large-scale complex optimization problems. Therefore, we propose an adaptive DBO (ADBO) based on an elastic annealing mechanism to address these issues. First, the convergence factor is adjusted in a nonlinear decreasing manner to balance the requirements of global exploration and local exploitation, thus improving the convergence speed and search quality. Second, a greedy difference optimization strategy is introduced to increase population diversity, improve the global search capability, and avoid premature convergence. Finally, the elastic annealing mechanism is used to perturb the randomly selected individuals, helping the algorithm escape local optima and thereby improve solution quality and algorithm stability. The experimental results on the CEC 2017 and CEC 2022 benchmark function sets and MCNC benchmark circuits verify the effectiveness, superiority, and universality of ADBO.

1. Introduction

Optimization problems are prevalent in real life and engineering applications that are widely used in areas such as resource allocation, financial portfolio optimization, intelligent transportation (Han et al., 2024), drone path planning (Amores et al., 2024), and supply chain management (Li J et al., 2023). Metaheuristic algorithms, inspired by natural phenomena (e.g., biological evolution and physical dynamics), have emerged as mainstream solutions for complex optimization tasks, particularly in high-dimensional or uncertain problem spaces (Ali et al., 2015; Ikram et al., 2023).

These algorithms simulate natural processes (e.g., evolutionary mechanisms or collective behaviors) to approximate global optimal solutions. Their core strengths include robust global search to avoid local optima, flexibility without strict mathematical formulations, and inherent parallelism for scalability. Metaheuristic algorithms are broadly classified into four categories based on design principles: evolutionary algorithms (e.g., genetic algorithm (GA) (Grefenstette, 1993), differential evolution (DE) (Storn and Price, 1997), and cultural algorithm (CA) (Reynolds and Peng, 2004)), which mimic biological evolution using mechanisms such as selection, mutation, and social learning; swarm-based algorithms (e.g., artificial rabbits optimization (ARO) (Wang LY et al., 2022), tunicate swarm algorithm (TSA) (Kaur et al., 2020), and mountain gazelle optimizer (MGO) (Abdollahzadeh et al., 2022)), which are inspired by collective animal behaviors and address multimodal or high-dimensional optimization; physics-based algorithms (e.g., simulated annealing (SA) mechanism (Kirkpatrick et al., 1983), thermal exchange optimization (TEO) (Kaveh and Dadras, 2017), and gravitational search algorithm (GSA) (Rashedi et al., 2009)), which leverage natural phenomena such as thermodynamics and gravitational interactions for global search.