Freight tour synthesis based on entropy maximization with fuzzy logic constraints

This paper presents an improved entropy-based freight tour synthesis (FTS) using fuzzy logic (FL). One approach used in formulating FTS models is entropy maximization, which aims to obtain the most probable freight (trucks) tour flow distribution in a network based on traffic counts. These models consider fixed parameters and constraints. However, the variations in costs, traffic counts, and truck demands depending on human behavior, are not always captured in detail in such models. FL can include such variabilities in its modeling. The flexibility FL provides to the model allows to obtain solutions where some or all the constraints do not entirely satisfy—but are close to—their expected values. Moreover, the modeling approach used based on FL theory is the membership function, specifically the triangular membership function, which is defined by three points corresponding to the vertices. This optimization problem was transformed into a bi-objective problem when the optimization variables are the membership and the entropy. The performance of the proposed formulation was assessed in the Sioux Falls network. To solve the problem, the model was run in General Algebraic Modeling System (GAMS), applying the ε approach, where ε value (ε ∈ [0, 1] with steps of 0.01) represents the level of accomplishment that at least one of the constraints (but can be more) gets. The results show that the entropy value decreased as the accomplishment level increased, and this behavior indicates a Pareto frontier, which proves that the optimization problem is bi-objective.