Computational Results

1
Generalized Cycle Crossover for Graph
Partitioning
A. Moraglio, Y-H Kim, Y. Yoon, B-R Moon and R.
Poli
Abstract We propose a new crossover that
generalizes cycle crossover to permutations with
repetitions and naturally suits partition
problems. We tested it on graph partitioning
problems obtaining excellent results.
Generalized Cycle Crossover
Multiway Graph Partitioning
Searching Balanced Solution Space

• Representation permutation with repetitions.
  Each Position in the permutation corresponds to a
  vertex in the graph. Each element of the
  permutation corresponds to a group
• Initial Population equally balanced solutions
  belonging to the same repetition class
• Crossover cycle crossover that preserves
  repetition class, hence balancedness
• Mutation swap mutation that preserves repetition
  class, hence balancedness

2
6
1
4
7
3
5
Cut size 5
Permutation with Repetitions
Simple permutation (21453) Permutation with
repetitions (214151232) Repetition class (33111)
Cut size 6
Computational Results
Feasible Solutions

• Properties of the New Crossover
• it preserves repetition class
• it is a proper generalization of the cycle
  crossover (when applied to simple permutations,
  it behaves exactly like the cycle crossover)
• it searches only a fraction of the space
  searched by traditional crossover
• when applied to parent permutations with
  repetitions of different repetition class,
  offspring have intermediate repetition class

• Balanced Solution the difference in cardinality
  between the largest and the smallest subsets is
  at most one
• Balancedness is a hard constraint feasible
  solutions are balanced, infeasible solution are
  not balanced
• Our evolutionary algorithm does not use any
  repairing mechanism. It restricts the search to
  the space of the balanced solutions using search
  operators that preserve balancedness