The Approach-dependent, Time-dependent, Label-constrained Shortest Path Problem and Enhancements for the CART Algorithm with Application to Transportation Systems
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Extensive computational testing has been conducted using available data from the Portland, Oregon, and Blacksburg, Virginia, transportation networks to investigate the efficacy of the developed procedures. In particular, we have tested twenty-five different combinations of network curtailment and algorithmic strategies on three test networks: the Blacksburg-light, the Blacksburg-full, and the BigNet network. The results indicate that the Heap-Dijkstra algorithm implementations are much faster than the PSP algorithmic approaches for solving the underlying problem exactly. Furthermore, mong the curtailment schemes, the ETHP-Dijkstra with p=5%, yields the best overall results. This method produces solutions within 0.37-1.91% of optimality, while decreasing CPU effort by 56.68% at an average, as compared with applying the best available exact algorithm.
The second part of this dissertation is concerned with the Classification and Regression Tree (CART) algorithm, and its application to the Activity Generation Module of TRANSIMS. The CART algorithm has been popularly used in various contexts by transportation engineers and planners to correlate a set of independent household demographic variables with certain dependent activity or travel time variables. However, the algorithm lacks an automated mechanism for deriving classification trees based on optimizing specified objective functions and handling desired side-constraints that govern the structure of the tree and the statistical and demographic nature of its leaf nodes. Using a novel set partitioning formulation, we propose new tree development, and more importantly, optimal pruning strategies to accommodate the consideration of such objective functions and side-constraints, and establish the theoretical validity of our approach. This general enhancement of the CART algorithm is then applied to the Activity Generator module of TRANSIMS. Related computational results are presented using real data pertaining to the Portland, Oregon, and Blacksburg, Virginia, transportation networks to demonstrate the flexibility and effectiveness of the proposed approach in classifying data, as well as to examine its numerical performance. The results indicate that a variety of objective functions and constraints can be readily accommodated to efficiently control the structural information that is captured by the developed classification tree as desired by the planner or analyst, dependent on the scope of the application at hand.
- Doctoral Dissertations