Lagrangian Relaxation in Iterated Local Search for the Workforce Scheduling and Routing Problem

The efficiency of local search algorithms for vehicle routing problems often increases if certain constraints can be violated during the search. The penalty for such violation is included as part of the objective function. Each constraint, which can be violated, has the associated parameters that specify the corresponding penalty. The values of these parameters and the method of their modification are usually a result of computational experiments with no guarantee that the obtained values and methods are equally suitable for other instances. In order to make the optimisation procedure more robust, the paper suggests to view the penalties as Lagrange multipliers and modify them as they are modified in Lagrangian relaxation. It is shown that such modification of the Xie-Potts-Bektas Algorithm for the Workforce Scheduling and Routing Problem permits to achieve without extra tuning the performance comparable with that of the original Xie-Potts-Bektas Algorithm.