With the increasing number of medical tasks, the existing medical robotic task allocation systems are facing significant pressure. This paper proposes a multi-objective optimization model based on goal programming to address this issue. The model prioritizes urgent medical tasks with the primary goal of minimizing task value loss, thereby reducing patient health risks. Additionally, it aims to minimize resource consumption to ensure task sustainability. To solve this model, an efficient multi-objective improved ant colony optimization algorithm (MOIACO) is proposed. This algorithm employs an adaptive heuristic function and a non-uniform pheromone initialization mechanism to guide task selection decisions, enhancing efficiency and accuracy. Experimental results demonstrate that the algorithm exhibits excellent convergence speed, solution quality, and flexibility in solving MRTAS problems, potentially reducing the burden on medical staff and improving the efficiency of medical institutions.