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The Pareto-optimal Solution Set of the Equilibrium Network Design Problem with Multiple Commensurate Objectives

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Abstract

The focus of this paper is to develop a solution framework to study equilibrium transportation network design problems with multiple objectives that are mutually commensurate. Objective parameterization, or scalarization, forms the core idea of this solution approach, by which a multi-objective problem can be equivalently addressed by tackling a series of single-objective problems. In particular, we develop a parameterization-based heuristic that resembles an iterative divide-and-conquer strategy to locate a Pareto-optimal solution in each divided range of commensurate parameters. Unlike its previous counterparts, the heuristic is capable of asymptotically exhausting the complete Pareto-optimal solution set and identifying parameter ranges that exclude any Pareto-optimal solution. Its algorithmic effectiveness and solution characteristics are justified by a set of numerical examples, from which we also gain additional insights about its solution generation behavior and the tradeoff between the computation cost and solution quality.

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Notes

  1. The congestion-constrained, budget-minimization problem presented in Chan et al. (1989) is not a bi-level optimization problem because it assumes a system-optimal traffic assignment. However, this problem can be easily reformulated into a bi-level form, as we show in this text.

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Acknowledgements

The authors would like to thank The Editor-in-Chief, Professor Terry L. Friesz, and anonymous reviewers for their helpful comments on earlier version of this paper. The first author would also like to acknowledge the Research Center for Energy Technology and Strategy at National Cheng Kung University, Taiwan, R.O.C. for providing partial funding support. However, the content of this paper reflects only the view of the authors, who are solely responsible for the fact and the accuracy of the data presented herein.

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Correspondence to Dung-Ying Lin.

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Lin, DY., Xie, C. The Pareto-optimal Solution Set of the Equilibrium Network Design Problem with Multiple Commensurate Objectives. Netw Spat Econ 11, 727–751 (2011). https://doi.org/10.1007/s11067-010-9146-3

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