Analysis of FPTASes for the Multi-Objective Shortest Path Problem

Thomas Breugem, Twan Dollevoet and Wilco van den Heuvel

No EI2016-03, Econometric Institute Research Papers from Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute

Abstract: We propose a new FPTAS for the multi-objective shortest path problem. The algorithm uses elements from both an exact labeling algorithm and an FPTAS proposed by Tsaggouris and Zaroliagis (2009). We analyze the running times of these three algorithms both from a the- oretical and a computational point of view. Theoretically, we show that there are instances for which the new FPTAS runs an arbitrary times faster than the other two algorithms. Fur- thermore, for the bi-objective case, the number of approximate solutions generated by the proposed FPTAS is at most the number of Pareto-optimal solutions 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 solutions is not too small.

Keywords: Shortest Path Problem; Multi-Objective Optimization; FPTAS; Complexity Analysis (search for similar items in EconPapers)
Pages: 25
Date: 2016-02-02
New Economics Papers: this item is included in nep-cmp
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Citations: View citations in EconPapers (1)

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