Optimization of Train Energy-Efficient Operation Using Simulated Annealing Algorithm - Intelligent Computing for Sustainable Energy and Environment - page 355

3.4 Constraints

Constraints should include speed limits and maximum running time. The former
has discussed in section C, the following is the constraint of maximum running
time:

T ≤ T M . (11)

In addition, the boundary conditions of variable should be set:

S 0 <x 1 <S 3 . (12)

v

V2

V1

V3

XZ2

XZ1 XZ3

S0 Fig. 2. Preprocessing of speed limit ranges S1 X1 S2 S3 S

4 Solution Algorithm

The study's coasting point optimization problem is a large combinatorial op-
timization one. The classical mathematical method has great limitations for
solving this problem.
Therefore, a metaheuristic method is desirable. Comparing to other heuris-
tic search algorithms, Simulated Annealing(SA) algorithm has advantages of
descriptive simplicity and e ciency, which is also less affected by initial condi-
tions. Due to inequality constraints, the terminal solution in this study implies
an acceptable and close to optimal solution within a reasonable time frame rather
than the ideally optimal solution. The steps to execute the proposed SA are as
follows:
Step1: Set the initial parameters, initial temperature ( T temp

n =0 ), the number of
trials per temperature(L), temperature change function and minimum temper-
ature;
Step2: Generate the initial solution, and set m=0, repeat step3 and step4 for
m=1,2L;
Step3: reproduce a new solution, and set m=m+1, calculate ΔE ;