Abstract: In this paper,we study one bi-objective shortest path problem with one ∑ objective and one max objective.Firstly,an algorithm with time complexity O(m² log n) is given to obtain the presenting efficient solution set.Then two algorithms with the same time complexity O(m² log n) are given to obtain the ∑ and max optimal solutions for the static and dynamic combined problems.Lastly,two algorithms with the same time complexity O(m log n) are given to obtain the lexicographic order-optimal solution.

Key words: objective, shortest path, efficient solution, algorithm