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): 356-374. Authors: Lining Xing, Philipp Rohlfshagen, Yingwu Chen, and Xin Yao First author address: National University of Defense Technology, Changsha, China

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

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

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

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)

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

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

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

(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

(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

(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.

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, 1999. 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): 316-328.