This paper considers a graph G in a network in which each arc (i,j) is weighted with a vector (kij,ρij,cij) where kij is the capacity of arc (i,j), ρij is its reliability and cij is the cost associated with traversing the arc (i,j). The problem is to find the route from source to sink with maximum capacity, within a threshold reliability R and at a total cost of no more than C. This problem has a particular type of Pareto optimal solution and is distinct from the problem discussed by Sancho in which all Pareto optimal solutions are found. In theory, many Pareto optimal solutions can exist; hence the need for finding a method in which the particular optimal solution can be found. The application of transporting hazardous material is an example of this particular problem.
