Differential evolution variants and MILP for the pipeline network schedule optimization problem

This paper presents two variants of the Differential Evolution (DE) algorithm, with binary and continuous encoding, for the pipeline network schedule problem. A binary mathematical model is proposed to represent the flow of oil products in a 48 hours horizon period. Although computationally expensive, a Mixed Integer Linear Programming (MILP) approach was also used to obtain optimal solutions so as to compare results with the other methods. In this paper, we introduced a benchmark of scheduling problems for testing the algorithms with a fixed network topology, but with different number of products and demands by final clients. MILP results determined optimal solutions for six of the proposed benchmarks, but it required far more computational effort than the DE-variants. Even though it is a real-parameter algorithm, the DE presented itself as a good heuristic alternative for the discrete problem approached here. The overall comparison of results between the proposed DE-variants and MILP supports the efficiency, robustness and convergence speed of DE algorithm.