### Abstract

In this paper we present a model for continuous multiobjective optimal design of a transportation network. The model presented here explicitly incorporates user equilibrium constraints and takes the form of a difficult nonlinear, nonconvex mathematical program. The user equilibrium constraints form a finite set of nonlinear, albeit nonconvex, inequalities, and give rise to a single level mathematical program, as opposed to the now standard mathematical programming/variational inequality representation which leads to a bilevel formulation of the equilibrium network design problem. We show that simulated annealing is ideally suited for solving multiobjective versions of the equilibrium network design problem articulated in this fashion. We employ the 'weighting' method together with simulated annealing to generate the Pareto optimal set. A numerical example is provided to demonstrate the efficacy of this solution methodology.

Original language | English (US) |
---|---|

Pages (from-to) | 44-57 |

Number of pages | 14 |

Journal | European Journal of Operational Research |

Volume | 65 |

Issue number | 1 |

DOIs | |

State | Published - Feb 19 1993 |

### Fingerprint

### All Science Journal Classification (ASJC) codes

- Computer Science(all)
- Modeling and Simulation
- Management Science and Operations Research
- Information Systems and Management

### Cite this

*European Journal of Operational Research*,

*65*(1), 44-57. https://doi.org/10.1016/0377-2217(93)90143-B

}

*European Journal of Operational Research*, vol. 65, no. 1, pp. 44-57. https://doi.org/10.1016/0377-2217(93)90143-B

**The multiobjective equilibrium network design problem revisited : A simulated annealing approach.** / Friesz, Terry L.; Anandalingam, G.; Mehta, Nihal J.; Nam, Keesung; Shah, Samir J.; Tobin, Roger L.

Research output: Contribution to journal › Article

TY - JOUR

T1 - The multiobjective equilibrium network design problem revisited

T2 - A simulated annealing approach

AU - Friesz, Terry L.

AU - Anandalingam, G.

AU - Mehta, Nihal J.

AU - Nam, Keesung

AU - Shah, Samir J.

AU - Tobin, Roger L.

PY - 1993/2/19

Y1 - 1993/2/19

N2 - In this paper we present a model for continuous multiobjective optimal design of a transportation network. The model presented here explicitly incorporates user equilibrium constraints and takes the form of a difficult nonlinear, nonconvex mathematical program. The user equilibrium constraints form a finite set of nonlinear, albeit nonconvex, inequalities, and give rise to a single level mathematical program, as opposed to the now standard mathematical programming/variational inequality representation which leads to a bilevel formulation of the equilibrium network design problem. We show that simulated annealing is ideally suited for solving multiobjective versions of the equilibrium network design problem articulated in this fashion. We employ the 'weighting' method together with simulated annealing to generate the Pareto optimal set. A numerical example is provided to demonstrate the efficacy of this solution methodology.

AB - In this paper we present a model for continuous multiobjective optimal design of a transportation network. The model presented here explicitly incorporates user equilibrium constraints and takes the form of a difficult nonlinear, nonconvex mathematical program. The user equilibrium constraints form a finite set of nonlinear, albeit nonconvex, inequalities, and give rise to a single level mathematical program, as opposed to the now standard mathematical programming/variational inequality representation which leads to a bilevel formulation of the equilibrium network design problem. We show that simulated annealing is ideally suited for solving multiobjective versions of the equilibrium network design problem articulated in this fashion. We employ the 'weighting' method together with simulated annealing to generate the Pareto optimal set. A numerical example is provided to demonstrate the efficacy of this solution methodology.

UR - http://www.scopus.com/inward/record.url?scp=0027541681&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0027541681&partnerID=8YFLogxK

U2 - 10.1016/0377-2217(93)90143-B

DO - 10.1016/0377-2217(93)90143-B

M3 - Article

AN - SCOPUS:0027541681

VL - 65

SP - 44

EP - 57

JO - European Journal of Operational Research

JF - European Journal of Operational Research

SN - 0377-2217

IS - 1

ER -