In real-world applications, multiple robots need to be dynamically deployed to their appropriate locations as teams while the distance cost between robots and goals is minimized, which is known to be an NP-hard problem. In this paper, a new framework of team-based multi-robot task allocation and path planning is developed for robot exploration missions through a convex optimization-based distance optimal model. A new distance optimal model is proposed to minimize the traveled distance between robots and their goals. The proposed framework fuses task decomposition, allocation, local sub-task allocation, and path planning. To begin, multiple robots are firstly divided and clustered into a variety of teams considering interrelation and dependencies of robots, and task decomposition. Secondly, the teams with various arbitrary shape enclosing intercorrelative robots are approximated and relaxed into circles, which are mathematically formulated to convex optimization problems to minimize the distance between teams, as well as between a robot and their goals. Once the robot teams are deployed into their appropriate locations, the robot locations are further refined by a graph-based Delaunay triangulation method. Thirdly, in the team, a self-organizing map-based neural network (SOMNN) paradigm is developed to complete the dynamical sub-task allocation and path planning, in which the robots are dynamically assigned to their nearby goals locally. Simulation and comparison studies demonstrate the proposed hybrid multi-robot task allocation and path planning framework is effective and efficient.