Hierarchical Bayesian approach for improving weights for solving multi-objective route optimization problem

Abstract

The weighted sum method is a simple and widely used technique that scalarizes multiple conflicting objectives into a single objective function. It suffers from the problem of determining the appropriate weights corresponding to the objectives. This paper proposes a novel Hierarchical Bayesian model based on multinomial distribution and Dirichlet prior to refine the weights for solving such multi-objective route optimization problems. The model and methodologies revolve around data obtained from a small-scale pilot survey. The method aims at improving the existing methods of weight determination in the field of Intelligent Transport Systems as data driven choice of weights through appropriate probabilistic modelling ensures, on an average, much reliable results than non-probabilistic techniques. Application of this model and methodologies to simulated as well as real data sets revealed quite encouraging performances with respect to stabilizing the estimates of weights. Generation of weights using the proposed Bayesian methodology can be used to develop a bona-fide Bayesian posterior distribution for the optima, thus properly and coherently quantifying the uncertainty about the optima.