Enhancing backtracking search with a hybrid approach for constrained optimization and nonlinear equations

Purpose This paper introduces a novel algorithm, the Differential Evolution-based Backtracking Search Algorithm (DEBSA), designed to address the computational limitations of the Backtracking Search Algorithm (BSA) for complex constraint satisfaction problems. Design/methodology/approach DEBSA merges the core structure of BSA with three innovative mutation strategies derived from Differential Evolution (DE). These strategies focus on directing a random individual toward a historical individual and utilizing a random individual in conjunction with a perturbation vector as well as leveraging a historical best position with two perturbation vectors. Furthermore, DEBSA incorporates a unique crossover mechanism for combining solutions and a strategy selection approach to dynamically choose the most suitable mutation strategy during the search process. Findings DEBSA’s performance is evaluated on constrained optimization problems and systems of nonlinear equations. The results demonstrate exceptional performance, particularly in terms of convergence speed, surpassing traditional benchmark evolutionary algorithms. DEBSA exhibits a high success rate in achieving globally optimal solutions. Originality/value The proposed DEBSA offers a potentially efficient solution for tackling general optimization challenges in engineering design and solving nonlinear equations in applied mathematics due to its enhanced performance and ability to find global optima.