A hybrid genetic algorithm for solving the length-balanced two arc-disjoint shortest paths problem

Abstract

We consider a HAZMAT transportation problem, which is modeled as the length-balanced two arc-disjoint shortest paths problem (LB2SP). In LB2SP, we try to find two arc-disjoint paths on a given network. We hope to reach two objectives: a minimized sum of the path lengths, and a minimized length difference between the paths. These two objectives are independent and even conflicting. Therefore, the objective function of LB2SP is expressed as a weighted sum of two terms: sum of the path lengths and the length difference between the paths. LB2SP is known to be NP-Hard, and can be formulated as an Integer Programming (IP) model. We propose a genetic algorithm (GA) and hybridize a quick Lagrangian relaxation-based heuristic (LRBH) as a module with the proposed GA. Computational experiments are conducted to compare the performance of the hybrid GA with the CPLEX solver, showing that the GA with hybridization of LRBH Is efficient for LB2SP. © Springer-Verlag Berlin Heidelberg 2006.