Stochastic user equilibrium model with a tradable credit scheme and application in maximizing network reserve capacity

<p>The tradable credit scheme (TCS) outperforms congestion pricing in terms of social equity and revenue neutrality, apart from the same perfect performance on congestion mitigation. This article investigates the effectiveness and efficiency of TCS on enhancing transportation network capacity in a stochastic user equilibrium (SUE) modelling framework. First, the SUE and credit market equilibrium conditions are presented; then an equivalent general SUE model with TCS is established by virtue of two constructed functions, which can be further simplified under a specific probability distribution. To enhance the network capacity by utilizing TCS, a bi-level mathematical programming model is established for the optimal TCS design problem, with the upper level optimization objective maximizing network reserve capacity and lower level being the proposed SUE model. The heuristic sensitivity analysis-based algorithm is developed to solve the bi-level model. Three numerical examples are provided to illustrate the improvement effect of TCS on the network in different scenarios.</p

The top ten frequently selected genes with the proposed method on the LUNG data.

<p>The top ten frequently selected genes with the proposed method on the LUNG data.</p

The top ten frequently selected genes with the proposed method on the Lymphoma data.

<p>The top ten frequently selected genes with the proposed method on the Lymphoma data.</p

The LOOCV classification accuracies of five methods on the Brain cancer and Lymphoma data.

<p>The LOOCV classification accuracies of five methods on the Brain cancer and Lymphoma data.</p

The correlation between the ranks of genes from two independent runs on the six data to assess reproducibility of the proposed approach (A) Leukemia (B) Colon (C) SRBCT (D) LUNG (E) Brain cancer (F) Lymphoma.

<p>The correlation between the ranks of genes from two independent runs on the six data to assess reproducibility of the proposed approach (A) Leukemia (B) Colon (C) SRBCT (D) LUNG (E) Brain cancer (F) Lymphoma.</p

The GCS values for all reserved genes (A) Leukemia (B) Colon (C) SRBCT (D) LUNG (E) Brain cancer (F) Lymphoma.

<p>The GCS values for all reserved genes (A) Leukemia (B) Colon (C) SRBCT (D) LUNG (E) Brain cancer (F) Lymphoma.</p

The top ten frequently selected genes with the proposed method on the SRBCT data.

†<p>Also selected by the method in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0097530#pone.0097530-Khan1" target="_blank">[33]</a>.</p>‡<p>Also selected by the method in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0097530#pone.0097530-Chu1" target="_blank">[43]</a>.</p

The 5-fold CV classification accuracies of the KNN-classifier and SVM-classifier based on six gene selection methods on the LUNG data.

<p>The 5-fold CV classification accuracies of the KNN-classifier and SVM-classifier based on six gene selection methods on the LUNG data.</p

The number of the clusters (<i>N_c</i>) versus the classification accuracy obtained by ELM with the genes selected by the KMeans-GCSI-MBPSO-ELM method on the six data.

<p>The number of the clusters (<i>N_c</i>) versus the classification accuracy obtained by ELM with the genes selected by the KMeans-GCSI-MBPSO-ELM method on the six data.</p

The frame of the proposed hybrid gene selection method.

<p>The frame of the proposed hybrid gene selection method.</p