MONRBO: A multi-objective Newton-Raphson-based optimizer with dynamic elimination-based crowding distance for numerical benchmark and engineering design problems

In the multi-objective optimization domain, where the aim is to handle multiple conflicting objectives simultaneously, the effectiveness of the optimization algorithm plays a critical role. The Newton-Raphson-Based Optimizer (NRBO) is initially developed for single-objective problems employs a Newton-Raphson-based search rule to navigate complex solution spaces. This study introduces a new extension of this approach, termed Multi-Objective NRBO (MONRBO), to solve multi-objective optimization problems. The proposed MONRBO incorporates non-dominated sorting and a dynamic elimination-based crowding distance mechanism to maintain solution diversity and improve convergence toward the true Pareto front. The performance of MONRBO is evaluated in three phases. First, it is tested on five standard bi-objective problems from the ZDT benchmark suite. Second, its capability is assessed on seven scalable tri-objective problems from the DTLZ test suite. Finally, its practical applicability is validated on six real-world constrained engineering design problems. MONRBO is compared with state-of-the-art algorithms using comprehensive performance metrics, including GD, IGD, HV, Spread, and Spacing in all phases. The results consistently demonstrate that MONRBO achieves competitive performance across test problems and real-world applications, highlighting its robustness, scalability, and effectiveness for solving complex multi-objective optimization problems.