Treatment of Multi-objective Shortest Path Problem by Means of Probability-Based Multi-objective Optimization

An actual transportation process is with multiple objectives generally. However, the previous approaches could not derive the rational shortest path with optimizing all multiple objectives at the same time appropriately. In this chapter, the multi-objective shortest path problem of transportation process is treated by means of probabilistic methodology to obtain a rational solution. Each objective is analogically taken as an “individual event,” the simultaneous optimization of multiple objectives is equivalent of the “joint event” of simultaneous occurrence of the “multiple events”; thus the simultaneous optimization of multiple objectives can be conducted analogically by means of probabilistic methodology. The partial preferable probability of each objective of every routine (scheme) is evaluated according to the actual preference degree of utility index of the objective. Moreover, the product of all partial preferable probabilities of utility indexes of objective of each routine (scheme) forms the total preferable probability of the corresponding routine (scheme), which indicates the uniquely decisive index of the routine (scheme) in the multi-objective shortest path problem in spirit of probability theory. The optimal solution of the multi-objective shortest path problem is the routine (scheme) with the highest total preferable probability. Finally, two application examples are given to illuminate the approach.