Interior Permanent-magnet Machines (IPMs) have seen wide usage in industry due to their robustness, high efficiency, and low manufacturing cost. Among various IPM topologies, V-shape IPMs have been claimed to exhibit higher power densities. However, designing an IPM has been a challenging task due to the complexity of the rotor structure and magnetic saturation. The objective of this work is to set forth a rigorous design paradigm for V-shape IPMs based on multi-objective optimization. The proposed approach aims to address the multi-disciplinary nature of the design process by incorporating electromagnetic, structural, and thermal analyses. The electromagnetic analysis combines the advantage of an analytical field solution and a magnetic-equivalent-circuit (MEC) approach so it is both computationally efficient and is able to address magnetic nonlinearity in the rotor. The structural analysis uses static stress/strain methods to compute the stress distribution within critical regions in the machine. A thermal analysis based on thermal-equivalent-circuit (TEC) is proposed and the impact of including the thermal analysis on the machine metrics is discussed. Using the proposed approaches, the computational cost is significantly reduced compared to traditional FEA methods. A multi-objective design paradigm incorporating relevant design constraints is set forth. A performance comparison between IPMs and SPMs is conducted for a 2.5-hp motor application.