### Abstract

Robust transportation network design problems generally rely on systems engineering methods that share common research gaps. First, problem sizes are constrained due to the use of multi-objective solution algorithms that are notoriously inefficient due to computationally expensive function evaluations. Second, link disruptions at a network level are difficult to model realistically. In this paper, a stochastic search metaheuristic based on radial basis functions is proposed for constrained multiobjective problems. It is proven to converge, and compared with conventional metaheuristics for four representative test problems. A scenario simulation method based on multivariate Bernoulli random variables that accounts for correlations between link failures is proposed to sample scenarios for a mean-variance toll pricing problem. Four tests are conducted on the classical Sioux Falls network to gain some insights into the algorithm, the simulation model, and to the robust toll pricing problem. The first test empirically measures the efficiency of the simulation algorithm and approximate Pareto set by obtaining a standard error in the ε-indicator measure for a given number of scenarios and iterations. The second test compares the dominance of the proposed heuristic's solutions with a conventional multiobjective genetic algorithm by comparing the average ε-indicator. The third test quantifies the gap due to falsely assuming that link failures are independent of each other when they are not. The last test quantifies the value of having the flexibility to adapt a Pareto set of toll pricing solutions to changing probability regimes such as peak and off-peak hurricane or snow seasons.

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

Pages (from-to) | 137-165 |

Number of pages | 29 |

Journal | Optimization and Engineering |

Volume | 15 |

Issue number | 1 |

DOIs | |

State | Published - 2014 |

### Fingerprint

### Keywords

- Multiobjective
- Multivariate Bernoulli
- Network design
- Radial basis function
- Robust optimization
- Surrogate model
- Toll pricing problem

### ASJC Scopus subject areas

- Control and Optimization
- Electrical and Electronic Engineering
- Software
- Mechanical Engineering
- Civil and Structural Engineering
- Aerospace Engineering

### Cite this

**A surrogate-based multiobjective metaheuristic and network degradation simulation model for robust toll pricing.** / Chow, Joseph Ying Jun; Regan, Amelia C.

Research output: Contribution to journal › Article

*Optimization and Engineering*, vol. 15, no. 1, pp. 137-165. https://doi.org/10.1007/s11081-013-9227-5

}

TY - JOUR

T1 - A surrogate-based multiobjective metaheuristic and network degradation simulation model for robust toll pricing

AU - Chow, Joseph Ying Jun

AU - Regan, Amelia C.

PY - 2014

Y1 - 2014

N2 - Robust transportation network design problems generally rely on systems engineering methods that share common research gaps. First, problem sizes are constrained due to the use of multi-objective solution algorithms that are notoriously inefficient due to computationally expensive function evaluations. Second, link disruptions at a network level are difficult to model realistically. In this paper, a stochastic search metaheuristic based on radial basis functions is proposed for constrained multiobjective problems. It is proven to converge, and compared with conventional metaheuristics for four representative test problems. A scenario simulation method based on multivariate Bernoulli random variables that accounts for correlations between link failures is proposed to sample scenarios for a mean-variance toll pricing problem. Four tests are conducted on the classical Sioux Falls network to gain some insights into the algorithm, the simulation model, and to the robust toll pricing problem. The first test empirically measures the efficiency of the simulation algorithm and approximate Pareto set by obtaining a standard error in the ε-indicator measure for a given number of scenarios and iterations. The second test compares the dominance of the proposed heuristic's solutions with a conventional multiobjective genetic algorithm by comparing the average ε-indicator. The third test quantifies the gap due to falsely assuming that link failures are independent of each other when they are not. The last test quantifies the value of having the flexibility to adapt a Pareto set of toll pricing solutions to changing probability regimes such as peak and off-peak hurricane or snow seasons.

AB - Robust transportation network design problems generally rely on systems engineering methods that share common research gaps. First, problem sizes are constrained due to the use of multi-objective solution algorithms that are notoriously inefficient due to computationally expensive function evaluations. Second, link disruptions at a network level are difficult to model realistically. In this paper, a stochastic search metaheuristic based on radial basis functions is proposed for constrained multiobjective problems. It is proven to converge, and compared with conventional metaheuristics for four representative test problems. A scenario simulation method based on multivariate Bernoulli random variables that accounts for correlations between link failures is proposed to sample scenarios for a mean-variance toll pricing problem. Four tests are conducted on the classical Sioux Falls network to gain some insights into the algorithm, the simulation model, and to the robust toll pricing problem. The first test empirically measures the efficiency of the simulation algorithm and approximate Pareto set by obtaining a standard error in the ε-indicator measure for a given number of scenarios and iterations. The second test compares the dominance of the proposed heuristic's solutions with a conventional multiobjective genetic algorithm by comparing the average ε-indicator. The third test quantifies the gap due to falsely assuming that link failures are independent of each other when they are not. The last test quantifies the value of having the flexibility to adapt a Pareto set of toll pricing solutions to changing probability regimes such as peak and off-peak hurricane or snow seasons.

KW - Multiobjective

KW - Multivariate Bernoulli

KW - Network design

KW - Radial basis function

KW - Robust optimization

KW - Surrogate model

KW - Toll pricing problem

UR - http://www.scopus.com/inward/record.url?scp=84898541122&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84898541122&partnerID=8YFLogxK

U2 - 10.1007/s11081-013-9227-5

DO - 10.1007/s11081-013-9227-5

M3 - Article

VL - 15

SP - 137

EP - 165

JO - Optimization and Engineering

JF - Optimization and Engineering

SN - 1389-4420

IS - 1

ER -