Scramjet engines are one of the most economical and reliable high-speed airbreathing propulsion technologies that can be used for low-cost satellite launchers and hypersonic atmospheric transportation. For access to space, the flight envelope practically comprises varying freestream conditions and altitude during ascent flight, constituting a complex optimization problem subject to various constraints from design and operation perspectives. This paper presents the results and insights obtained from a multi-objective optimization study of three classes of axisymmetric scramjet intakes, i.e., three-ramp, Busemann-based, and generic intakes represented by smooth Bézier curves, with the same intake mass flow rate for all classes. Optimization is conducted by means of surrogate-assisted evolutionary algorithms coupled with computational fluid dynamics simulations using a Reynolds-averaged Navier–Stokes flow solver for steady-state flowfields. It aims to minimize the intake drag and maximize the compression efficiency at Mach 7.7 at an altitude of 30 km simultaneously. It has been found that generic intakes, which offer greater local shape control, can achieve the highest compression efficiency of 94.8%, the highest total pressure recovery, and the highest flow uniformity at the intake exit. The Busemann-based intakes, on the other hand, can produce the highest static pressure ratio while incurring the lowest drag force. The utility of principal component analysis has effectively reduced the dimensions of the solutions, and has identified clusters of non-dominated solutions according to their characteristics such as geometric attributes, exit flow profiles, and wall property distributions, thereby conducing to obtain further physical insights into the optimal configurations.