Network routing problems generally involve multiple objectives which may conflict one another. An effective way to solve such problems is to generate a set of Pareto-optimal solutions that is small enough to be handled by a decision maker and large enough to give an overview of all possible trade-offs among the conflicting objectives. To accomplish this, the present paper proposes an adaptive method based on compromise programming to assist decision makers in identifying Pareto-optimal paths, particularly for non-convex problems. This method can provide an unbiased approximation of the Pareto-optimal alternatives by adaptively changing the origin and direction of search in the objective space via the dynamic updating of the largest unexplored region till an appropriately structured Pareto front is captured. To demonstrate the efficacy of the proposed methodology, a case study is carried out for the transportation of dangerous goods in the road network of Hong Kong with the support of geographic information system. The experimental results confirm the effectiveness of the approach.