Combined models with hierarchical demand choices: A multiobjective entropy optimization approach. http://dx.doi.org/10.1080/01441640701763128

Abstract

This article proposes a multi-objective optimization approach to the formulation
of a number of equilibrium problems that typically arise in the transportation planning
process. These fall into two classes: combined demand and network equilibrium
problems, the latter here called performance-demand equilibrium problems. The demand
formulations are based on entropy maximization while the network equilibrium designs
are modelled on Wardrop’s first principle. Both are fully compatible with models based on
random utility maximization (multinomial and hierarchical logit). Given the entropymaximization
aspect of the demand models and the use of symmetric cost functions in the
networks, the multi-objective formulations yield classical single-objective convex optimization
programs. In the past, many such problems have not been obtained deductively,
their derivation being based rather on previous knowledge and the modeller’s intuition.
Of particular interest, therefore, is the simple deductive method presented here for formulating new problem, one that can accommodate new choices such as departure time and
transfer point for combined modes. This novel approach also facilitates a better interpretation
of the model parameters. In addition, we suggest a calibration procedure that permits
consistent estimation of the proposed model’s parameters.