Abstract:

In order to solve the shortest path problem with fuzzy constraint, based on the fuzzy linear programming model, tolerance method and penalty function method were adopted to convert the original model to obtain a transformed model with the same optimal solution and optimal value as those of the original model. Then, a modified firefly algorithm was proposed to solve the transformed model. In addition, the computational complexities of the modified algorithm as well as the firefly algorithm were analyzed and compared. Finally, numerical example was given to illustrate the efficiency of the new model and algorithm to solve the shortest path problem with fuzzy constraint.

Key words: fuzzy constraints, shortest path problem, firefly algorithm, modified algorithm