Superior rotor tip geometries possess the potential to simultaneously mitigate aerodynamic losses and severe thermal loads onto the rotor overtip region. However, classical design strategies are usually constrained to a specific type of geometry, narrowing the spread of shape topologies considered during the design phase. The current paper presents two novel multi-objective optimization methodologies that enable the exploration of a broad range of distinct tip configurations for unshrouded rotor blades. The first methodology is a shape optimization process that creates a fully carved blade tip shape defined through a Bezier surface controlled by 40 parameters. Combined with a differential evolution (DE) optimization strategy, this approach is applied to a rotor blade for two tip gap sizes: 0.85% (tight) and 1.38% (design) of the blade span. The second methodology is based on a topology optimization process that targets the creation of arbitrary tip shapes comprising one or multiple rims with a fixed height. The tip section of the blade has been divided into more than 200 separate zones, where each zone can be either part of an upstanding rim or part of the cavity floor. This methodology was tested with a level-set approach in combination with a DE optimizer and coupled to an optimization routine based on genetic algorithms (GAs). The current study was carried out on a modern high-pressure turbine operating at engine-like Reynolds and high subsonic outlet Mach numbers. A fully hexahedral unstructured mesh was used to discretize the fluid domain. The aerothermal performance of each tip profile was evaluated accurately through Reynolds-averaged Navier–Stokes (RANS) simulations adopting the shear-stress transport (SST) turbulence model. Multi-objective optimizations were set for both design strategies that target higher aerodynamic rotor efficiencies and simultaneous minimization of the heat load. This paper illustrates a wide variety of profiles obtained throughout the optimization and compares the performance of the different strategies. The research shows the potential of such novel methodologies to reach new unexplored types of blade tip designs with enhanced aerothermal performances.