This paper proposes collision-free optimal trajectory planning for autonomous vehicles in highway traffic, where vehicles need to deal with the interaction among each other. To address this issue, a novel optimal control framework is suggested, which couples the trajectory of surrounding vehicles with collision avoidance constraints. Additionally, we describe a trajectory optimization technique under state constraints, utilizing a planner based on Pontryagin's Minimum Principle, capable of numerically solving collision avoidance scenarios with surrounding vehicles. Simulation results demonstrate the effectiveness of the proposed approach regarding interaction-based motion planning for different scenarios.