NSGA-II based multi-objective pollution routing problem with higher order uncertainty

Pollution routing problem (PRP) is an NP-hard multi-objective optimization problem. The main goal is pollution reduction and secondary goals are cost/distance minimization, profit maximization etc. We have considered two unique models with two different set of objectives viz. (i) distance and fuel consumption, and (ii) weighted load and fuel consumption. Here, system parameters like demand, driver wages, timing constraints etc. can't be predicted a-priori and involve multiple opinions from the designers. Thus, such uncertain system parameters can be modelled using fuzzy sets. As type-1 fuzzy sets (T1 FSs) has limitations in modelling higher order uncertainty, this paper models these uncertain parameters with interval type-2 fuzzy sets (IT2 FSs). We have solved the problem by an efficient multi-objective evolutionary algorithm viz. NSGA-II (non-dominated sorting genetic algorithm-II). Numerical examples demonstrate the efficiency of the proposed technique over existing (crisp and type-1 fuzzy set based) approaches.