Mechanical structures in engineering are increasingly designed under stringent requirements for low-weight, high-stiffness, and safety, making multi-objective structural optimization central to innovative, cost-effective-products. This work introduces two multi-objective variants of the Genghis Khan Shark Optimizer (GKSO) for structural design. Both retain GKSO’s four phases-hunting, moving, foraging, and self-protection-while differing in how convergence and diversity are managed. MOGKSO-I follows NSGAII-principles: external Pareto archive is maintained, leaders for guidance are drawn by roulette with probabilities proportional to crowding-distance, replacements use Pareto dominance with probabilistic tie-acceptance, objective normalization and a light bounded differential mutation stabilize search and curb stagnation. MOGKSO-II adopts a MOPSO-style adaptive grid: the archive is governed by grid-occupancy without pairwise dominance, leaders are sampled from sparse cells, acceptance favors candidates that populate less-crowded cells, with a weak tie-break toward the ideal and occasional random admits for exploration. The variants are evaluated against competitive algorithms on CEC’20 benchmarks, representative constrained engineering designs, and large-scale truss structures using indicators (IGDX/IGDF, HV, PSP, STE). Results show competitive hypervolume and spread, well-distributed Pareto sets, and lighter feasible designs under stress and displacement limits, with complementary strengths: MOGKSO-I exhibits stronger convergence on smooth fronts, whereas MOGKSO-II excels at preserving diversity on irregular or disconnected fronts.
Daqaq et al. (Sun,) studied this question.