MORKO: A multi-objective Runge-Kutta optimizer for multi-domain optimization problems

Abstract

In the current landscape, there is a rapid increase in the creation of new algorithms designed for specialized problem scenarios. The performance of these algorithms in unfamiliar or practical settings often remains untested. This paper presents a new development, the multi-objective Runge-Kutta optimizer (MORKO), which is built upon the principles of elitist non-dominated sorting and crowding distance. The goal is to achieve superior efficiency, diversity, and robustness in solutions. MORKO effectiveness is further enhanced by incorporating various strategies that maintain a balance between diversity and execution efficiency. This approach not only directs the search toward optimal regions but also ensures that the process does not become stagnant. The efficiency of MORKO is compared against renowned algorithms like the multi-objective marine predicator algorithm (MOMPA), multi-objective gradient-based optimizer (MOGBO), multi-objective evolutionary algorithm based on decomposition (MOEA/D), and non-dominated sorting genetic algorithm (NSGA-II) on several test benchmarks such as ZDT, DTLZ, constraint (CONSTR, TNK, SRN, BNH, OSY and KITA) and real-world engineering design (brushless DC wheel motor, safety isolating transformer, helical spring, two-bar truss, welded beam, disk brake, tool spindle and cantilever beam) problems. We used unique, non-overlapping performance metrics for this comparison and suggested a fresh correlation analysis technique for exploration. The MORKO algorithm outcomes were rigorously tested and confirmed using the non-parametric statistical evaluations. The MORKO algorithm proves to excel in deriving comprehensive and varied solutions for many tests and practical challenges, owing to its multifaceted features. Looking ahead, MORKO has potential applications in complex engineering and management tasks.