Multi-Objective Robotics Optimization Using Improved MO-BxR Algorithms

Robotics optimization is essential for improving the performance, efficiency, and reliability of robotic systems, especially when dealing with complex engineering problems involving multiple conflicting objectives. Algorithm-specific parameter-free metaheuristic algorithms have gained attention in such applications because they eliminate the need for problem-specific parameter tuning. However, their performance can be further enhanced by improving convergence and maintaining solution diversity in multi-objective optimization. This paper proposes three multi-objective variants—archive, opposition, and self-adaptive multi-population (SAMP)—for the algorithm-specific parameter-free BxR algorithms such as Best–Mean–Random (BMR), Best–Worst–Random (BWR), and Best–Mean–Worst–Random (BMWR). The proposed variants are evaluated on five robotic optimization problems spanning two to six objectives, including Autonomous Underwater Vehicle shape optimization, power line inspection robot design, inverse kinematics of a 4-DOF manipulator, wall-building robot trajectory planning, and optimization of a reconfigurable parallel cutting and grinding mechanism. Their performance is compared with several established multi-objective algorithms using metrics such as GD, IGD, SPC, and HV, supported by rigorous statistical testing involving Friedman tests, Conover post hoc analysis with Holm correction, and Vargha–Delaney A12 effect sizes over 30 independent runs. The results show that archive variants achieve the best IGD rank in four of the five case studies and the best HV rank in three of them, with the five-objective trajectory planning problem being the sole exception where SAMP and base BxR variants show improved IGD performance. The base BxR algorithms prove to be strong competitors, consistently outperforming established parameter-dependent methods on IGD across all five problems. The opposition variants do not provide consistent improvement; however, they also do not cause catastrophic degradation, suggesting that refined opposition strategies warrant further investigation. The study demonstrates the effectiveness of the proposed algorithms as practical optimization tools for complex robotic optimization problems.