This paper presents a new accurate and efficient design methodology for complex integrated lens antenna (ILA), to achieve wide-angle beam coverage with scan loss mitigation at the millimeter-wave (mmWave) spectrum. The proposed ILA comprises inhomogeneous curvatures with internal and external center off-sets, in which multiple parameters instigate high order and non-linear behaviors. A two-dimensional (2-D) ray-tracing model is used to estimate the refractions on the elliptically curved boundaries based on geometrical optics. This approach is integrated into the particle swarm optimization of the 2-D ray-tracing model to determine the near-optimum geometric configuration of the ILA. Denoted as Geometric Optics-based Multiple Scattering (GOMS), the computational memory usage is reduced by a factor of 10,000 using this approach. The devised ILA achieves a wide-angle beam coverage of 156<sup>°</sup> with a scan loss of 2.10 dB alongside a broad impedance bandwidth of 35.0 GHz to 42.0 GHz. The measurement results for the performance of the fabricated prototype of the ILA validate the wide-angle scanning with scan loss mitigation inferred from the simulation results. This confirms the effectiveness of this method for complex design challenges involving multi-variants and restricted computational resources.