Integrated Optimization in Public Transport Planning by Philine Schiewe

Author:Philine Schiewe
Language: eng
Format: epub
ISBN: 9783030462703
Publisher: Springer International Publishing

3.4.4 Finding Solutions for Different Preferences

In this section, we investigate the influence of the weights (α, β) on the solution quality of (LinTimPass). In Figure 3.11, we see optimal solutions for routing all 46 OD pairs for various weights. According to Theorem 1.​40 these solutions are weakly Pareto optimal as the weights are positive. Increasing α, i.e., the weight of the costs in the objective leads to cheaper solutions with longer travel times. Focusing more on travel time, see weights (1,1), leads to a solution with minimal travel time according to the lower bound. This solution dominates the initialization direct solution as it has the same low travel time but significantly lower line costs. While we find a solution with the same costs and travel time as initialization costs, see weights (400,1), we do not find an equally cheap solution that dominates it. As the line concept costs for initialization cost are a lower bound on the costs, we cannot expect to find a cheaper solution.

Fig. 3.11Comparison of different weights (α, β) for the scalarization of the objective for data set toy.

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