Analysis of FPTASes for the multi-objective shortest path problem

作者：Breugem Thomas^*; Dollevoet Twan; van den Heuvel Wilco

来源：Computers & Operations Research, 2017, 78: 44-58.

DOI：10.1016/j.cor.2016.06.022

• Shortest path problem
• Multi-objective optimization
• FPTAS
• Complexity analysis

We propose a new FPTAS for the multi-objective shortest path problem with non-negative and integer arc costs. The algorithm uses elements from both an exact labeling algorithm and an FPTAS proposed by Tsaggouris and Zaroliagis [25]. We analyze the running times of these three algorithms both from a theoretical and a computational point of view. Theoretically, we show that there are instances for which the new FPTAS runs arbitrarily faster than the other two algorithms. Furthermore, for the bi-objective case, the number of approximate solutions generated by the proposed FPTAS is at most the number of Pareto-optimal points multiplied by the number of nodes. By performing a set of computational tests, we show that the new FPTAS performs best in terms of running time in case there are many dominated paths and the number of Pareto-optimal points is not too small.

• 出版日期2017-2