Congestion Control for Mixed-Mode Traffic with Emission Cost

Table 1

Algorithm frame.

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Step 1. Initialization , tolerances , and maximum iterations .

Step 2. Find the feasible paths with distance limit of BEVs and feasible paths of GVs.

Step 3. Input A, b, Aeq, beq, lb, ub, nonlcon, and the constraints.

Step 4. Set such that the strict inequalities in (16)–(18) hold. Let be the unit matrix.

Step 5. Solve the approximation quadratic programming problem

to get Lagrange multiplier and the search direction . Here, is the objective function in model (11)–(18).

Step 6. Calculate the new iteration point , where is a stepsize calculated by one-dimensional search.

Step 7. If , stop. Otherwise, go to step 8.

Step 8. Update the Hessian matrix by BFGS algorithm, let , and go to Step 4.

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