Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  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.  analyze the running times of these three algorithms both from a theoretical and a computational point of view. Theoretically,  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,  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. HighlightsA new FPTAS for a multi-objective shortest path (MOSP) problem is developed.The running time of this FPTAS decreases with the size of the Pareto-optimal frontier.The FPTAS can be arbitrarily faster than one from literature and an exact algorithm. provide an instance with maximum sized Pareto-optimal frontier w.r.t. the nodes. extensively test FPTASes for the MOSP problem in a computational study.
['T. Breugem', 'Twan Dollevoet', 'Wilco van den Heuvel']
I am writing a research paper on a idea Analysis of FPTASes for the multi-objective shortest path problem
[{"from": "human", "value": "I am writing a research paper on a idea Analysis of FPTASes for the multi-objective shortest path problem"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  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.  analyze the running times of these three algorithms both from a theoretical and a computational point of view. Theoretically,  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,  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. HighlightsA new FPTAS for a multi-objective shortest path (MOSP) problem is developed.The running time of this FPTAS decreases with the size of the Pareto-optimal frontier.The FPTAS can be arbitrarily faster than one from literature and an exact algorithm. provide an instance with maximum sized Pareto-optimal frontier w.r.t. the nodes. extensively test FPTASes for the MOSP problem in a computational study."}]