A Novel Hybrid Metaheuristic Algorithm for Real-World Mechanical Engineering Optimization Problems

Real-world constrained optimization problems often are highly nonlinear and present non-convex design spaces. Metaheuristic algorithms (MHOAs) are naturally suited to solving real-world optimization problems in view of their global optimization capability, but may require too many analyses to complete the optimization process. Hybrid methods enhance searching by combining two or more algorithms to better balance exploration and exploitation. Elitist strategies may be utilized to generate high-quality trial designs, yet with no guarantee that each new design always improves the current best record. In order to solve these issues and minimize the number of analyses, this study presents the novel HALSGWJA (Hybrid Approximate Line Search Grey Wolf JAYA) algorithm. HALSGWJA combined grey wolf optimizer (GWO) and JAYA (two powerful MHOAs still attracting optimization experts), enhanced by approximate line search. HALSGWJA utilized approximate gradient information to perform line searches, providing descent directions with respect to the current best record. This results in a complete renewal of the current population and a much higher probability of improving all individuals with respect to the previous iteration. The proposed HALSGWJA algorithm was successfully tested on 20 real-world mechanical engineering problems: (i) the CEC2020 test suite of 19 real-world mechanical engineering examples with up to 30 optimization variables and 86 nonlinear constraints and (ii) the optimal crashworthiness design of a vehicle subject to side impact with 11 optimization variables and 10 highly nonlinear constraints. Sizing and topology optimization problems, as well as problems with discrete variables, were considered. Remarkably, HALSGWJA outperformed 18 other state-of-the-art metaheuristic algorithms in the CEC2020 problems and 25 other algorithms in the crashworthiness design problem. HALSGWJA practically converged to target optima in all test cases (the largest penalty on target optimized cost was only 0.0263% in problem 13 of the CEC2020 library). Furthermore, it obtained in many cases 0 or nearly 0 standard deviation on optimized cost. Lastly, HALSGWJA always ranked first in terms of computational speed, requiring fewer analyses than its competitors and exhibiting, in most cases, a moderate dispersion on the number of analyses entailed by the optimization process.