Computer-aided mathematical and structural optimization using an advanced stochastic algorithm

V Goodarzimehr and N Fanaie and S Mirjalili, MECHANICS BASED DESIGN OF STRUCTURES AND MACHINES, 53, 7485-7512 (2025).

DOI: 10.1080/15397734.2025.2487168

In this study, the Special Relativity Search convergence rate is boosted based on the Gradient Descent mechanism for the optimum design of numerical and engineering problems. The mathematical model presented for Special Relativity Search is based on the interaction of particles in a magnetic field that moves under the effect of the Lorentz force. Because the particles in the magnetic field are lightweight and are moving at a high speed, Newtonian physics cannot be used to provide a mathematical model. Therefore, the physics of special relativity is used to develop the equations. Gradient Descent starts processing with a random point in the feasible space and moves in the negative direction from the gradient of the objective function toward the optimal point. Standard Special Relativity Search suffers from a weak local search and cannot search all the possible local optima, which leads to premature convergence. Applying Gradient Descent in the Special Relativity Search's velocity vector, it is possible to find the local optima with higher accuracy and move the swarm toward the optimal point. Then, in the next step, Special Relativity Search, which has a high exploratory capability, moves toward the global optimum. A total of 160 bound constraints CEC-2021 and seven engineering problems with continuous, discrete, and combinatorial variables are presented. Friedman's statistical test is utilized to rank and select the best algorithm. The results show that Special Relativity Search based Gradient Descent provides better outcomes compared to other metaheuristic methods in the majority of case studies.

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