CONTINUOUS EQUILIBRIUM NETWORK DESIGN PROBLEM WITH ELASTIC DEMAND: DERIVATIVE-FREE SOLUTION METHODS

Abstract

Three representative algorithms, namely the Hooke-Jeeves method, the equilibrium decomposed optimization heuristic and simulated annealing, which have been applied to the equilibrium network design problem (ENDP) with fixed demand, are compared by numerical examples. The comparison is extended to cover the ENDP with elastic demand. A bi-level formulation of the ENDP with elastic demand is presented and validated. Experiments on simple and complex networks reveal some interesting and important phenomena, for instance, these three algorithms can give very different results when different values of the algorithm's parameters are used. The simulated annealing approach can always obtain the best solution while its computation time requirement is the most too. The equilibrium decomposed optimization heuristic is the most computationally efficient, but the solutions it yields are not quite as good as those given by the Hooke-Jeeves method, in most cases. A warning and suggestions are given in the last section.

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