Deep neural networks (DNNs) frequently present behaviorally irregular
patterns, significantly limiting their practical potentials and theoretical
validity in travel behavior modeling. This study proposes strong and weak
behavioral regularities as novel metrics to evaluate the monotonicity of
individual demand functions (a.k.a. law of demand), and further designs a
constrained optimization framework with six gradient regularizers to enhance
DNNs' behavioral regularity. The proposed framework is applied to travel survey
data from Chicago and London to examine the trade-off between predictive power
and behavioral regularity for large vs. small sample scenarios and in-domain
vs. out-of-domain generalizations. The results demonstrate that, unlike models
with strong behavioral foundations such as the multinomial logit, the benchmark
DNNs cannot guarantee behavioral regularity. However, gradient regularization
(GR) increases DNNs' behavioral regularity by around 6 percentage points (pp)
while retaining their relatively high predictive power. In the small sample
scenario, GR is more effective than in the large sample scenario,
simultaneously improving behavioral regularity by about 20 pp and
log-likelihood by around 1.7%. Comparing with the in-domain generalization of
DNNs, GR works more effectively in out-of-domain generalization: it drastically
improves the behavioral regularity of poorly performing benchmark DNNs by
around 65 pp, indicating the criticality of behavioral regularization for
enhancing model transferability and application in forecasting. Moreover, the
proposed framework is applicable to other NN-based choice models such as
TasteNets. Future studies could use behavioral regularity as a metric along
with log-likelihood in evaluating travel demand models, and investigate other
methods to further enhance behavioral regularity when adopting complex machine
learning models.

该研究提出了强行为规律和弱行为规律作为评估个体需求函数单调性的新指标，并设计了带有六个梯度正则化器的约束优化框架，以提高深度神经网络的行为规律性。研究结果表明，相比于具有较强行为基础的模型如多项逻辑回归，传统深度神经网络无法保证行为规律性，然而梯度正则化器能显著提高深度神经网络的行为规律性。此外，梯度正则化对在跨领域的泛化中更加有效，能够显著改善性能较差的深度神经网络行为规律性，从而提高模型的传递性和预测应用。未来的研究可以将行为规律性与对数似然一起作为评估交通需求模型的指标，并探索其他方法来进一步提高复杂机器学习模型的行为规律性。