Adjustment of term weights in an energy function used in the simulated annealing approach to vehicle scheduling problems

Although the vehicle scheduling problem (VSP) is a difficult optimization problem with multiple objectives and many constraints, the simulated annealing (SA) method with a string model can solve it quickly and precisely. In the SA method, the importance of the objectives or constraints is expressed by the coefficients (weights) of the terms of the energy function. But the values of weights are usually determined by trial and error, In this paper, we propose a new method for adjusting the weights of terms automatically. This method can adjust the weights in the annealing process by using the "two-layer random field model" (TRFM). Aspiration levels given by the scheduling planner for every objective and constraint are defined and used as targets for adjusting the weights. Our new method is applied to an actual VSP which has 50 stores and 10 vehicles and confirms that adjustment of the weights of terms in the energy function is effective and suitable for the SA method.