Sub module: Search Space Control Method

Sub Module 2: Search Space Control Method

This module explores the extent of the search space to supplement the inadequate prior knowledge of a bounded region that restricts the search of the mode choice model's extrema. The pseudo-code can be summarized as follows:

This module is composed of two sequential stages:

1. The first stage returns the nudges based on the following points:

   • how much L1 norm for a mode split is reduced?
   • which directionality (+ve or -ve) is required for such L1 norm reduction?
   • magnitude of relative scaled (up/ down) d_L1/d_intercept intercept to achieve holistic L1 improvement?

2. The second stage returns the nudges based on the exponentially weighted average of the gradients and uses these gradients to update the intercept values. This method optimizes the mode choice analysis objective function reducing the oscillations (overshooting and diverging) that occur before reaching the global minimum. The parameter beta = 0.9 provides friction to the acceleration term d_L1/d_intercept (denoted as d_L1/d_m) and the velocity term v_dintercept (denoted as v_dm) while the optimizer finds the path to the lowest L1 norm.