1. Paper Report in ECCO group
Yuxin Liu
19, Sept. 2017
An Evolutionary Approach to the Multidepot Capacitated Arc Routing Problem
IEEE Transactions on Evolutionary Computation, 2010, 14(3):
Authors: Lining Xing, Philipp Rohlfshagen, Yingwu Chen, and Xin Yao
First author address: National University of Defense Technology, Changsha, China

2. Outline Problem definition of CARP and individual representation
Framework of the algorithm
Two tips
Two heuristic information

3. Capacitated Arc Routing Problem
Network G=(V, E)
depot
vehicle
capacity
demand
serving cost
deadheading cost
edge
(task)

4. Capacitated Arc Routing Problem
Original network:
Objective:
A solution (represented by a set of routes) to serve all the tasks with minimal costs subject to the constraints.
Solution:
Constraints:
A vehicle must depart from and return to the depot in each route.
All tasks should be served exactly once.
The total demand of each route must not exceed the capacity of the vehicle.
Route 2
Route 1

5. Individual representation
Chromosome, e.g. (1, 3, 5, 7, 9, 11, 13)
The serving order of tasks
The vehicle follows the shortest path between two tasks
A giant route releasing the constraints, e.g. capacity
1(2)
11(12)
3(4)
13(14)
9(10)
5(6)
IDs:7(8)
The current direction
The inverse direction
Split Procedure
To meet the constraints, e.g. capacity
Feasible routes:
(1, 3, 5) (7, 9, 11, 13)
Chromosome:
(1, 3, 5, 7, 9, 11, 13)

6. Computational flow Start Tip (I):
Use some heuristics to generate good starting population, rather than only use random method.
Population Initialization
Selection Operation
Crossover Operation
Mutation Operation
Total cost
Partial Replacement Operation No
Stopping criterion?
Computation time
Yes
End

7. Computational flow Start Tip (I):
Use some heuristics to generate good starting population, rather than only use random method.
Population Initialization
Selection Operation
Crossover Operation
Mutation Operation
Tip (II):
Add a fixed number of short restart, in order to maintain the diversity of the population
Partial Replacement Operation No
Stopping criterion?
Yes
End

8. Two heuristic information
Start
Heuristic Information (I):
Learn the Performance Information of Operators (PIO) and apply it to select the appropriate operator
Population Initialization
Selection Operation
Crossover Operation
Heuristic Information (II):
Learn the Arc Assignment Priority Information (AAPI) and apply it to decide an appropriate broken position
Mutation Operation
Partial Replacement Operation No
Stopping criterion?
Yes
End

9. (I) Performance Information of Operators (PIO)
Selection Operation
Binary tournament
Rank order selection
More than one operators are employed to execute the operations of selection, crossover and mutation.
PIO is used to record the ability of each operator to produce good individuals.
N(i) means the accumulated number of successful operation by the ith operator.
P(i) is the probability of selecting the ith operator:
Crossover Operation
Order crossover
Linear order crossover
Mutation Operation
Inverse
Single insertion
Double insertion
Swap
2-Opt moves on one trip
2-Opt moves on two trips
𝑃 𝑖 = 𝑁(𝑖) 𝑖=1 𝑛 𝑁(𝑖)
For selection and crossover, n=2; for mutation, n=6

10. (II) Arc Assignment Priority Information (AAPI)
Used in the crossover and mutation operators to select broken points.
Idea: If the number of times a subsequence appears is large, then we select the break point of this sequence with a small probability.
Matrix M with the size of N * D
The 0.5*D closest tasks to the current line
Number of tasks
Predefined row dimension
The number of appearances of the subsequence
Number of appearances:
Chromosome:
0.5*D
0.5*D
Break probability: N

11. (II) Arc Assignment Priority Information (AAPI)
Idea: If the number of times a subsequence appears is large, then we select the break point of this sequence with a small probability.
Chromosome:
0.5*D
0.5*D N
My doubts:
How to deal with the sequences that don’t exist in the matrix?
The information of the first half part of the matrix (i.e. the distance information between two tasks) is not adequately utilized.

12. Heuristic Information
Interaction between evolution and learning [1-3].
These approaches keep useful features of previous individuals to improve the performance of current individuals.
Like training a learning module.
Balance the learning ability.
[1] Michalski, Ryszard S. "Learnable evolution model: Evolutionary processes guided by machine learning." Machine Learning 38.1 (2000): 9-40.
[2] Branke, Jürgen. "Memory enhanced evolutionary algorithms for changing optimization problems." Evolutionary Computation, CEC 99. Proceedings of the 1999 Congress on. Vol. 3. IEEE, 1999.
[3] Louis, Sushil J., and John McDonnell. "Learning with case-injected genetic algorithms." IEEE Transactions on Evolutionary Computation 8.4 (2004):