A surrogate-based multiobjective metaheuristic and network degradation simulation model for robust toll pricing
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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.
KeywordsMultiobjective Surrogate model Radial basis function Robust optimization Multivariate Bernoulli Toll pricing problem Network design
One of the authors, Joseph Chow, was financially supported while he was a Ph.D. student by the FHWA Office of Professional and Corporate Development under the Dwight D. Eisenhower Transportation Graduate Fellowship. The two authors were also partly supported by the University of California Transportation Center under the research project entitled “Large Scale Real Option Models for Network Investment Planning and Operational Risk Hedging”. The support is gratefully acknowledged. The algorithm presented here for the MO-RBF supercedes the one presented in Joseph Chow’s dissertation.
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