Memetic Algorithm for ATSP

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Memetic Algorithm for ATSP

• KC Tsui
• Based on 1

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S/A-TSP

• Let cij be the cost to travel from city i to city
  j
• Given a directed graph G(V,A), where V1, ,
  n and A(i, j) i, j ? V, i ? j, a feasible
  solution for a TSP is a Hamiltonian circuit and
  the objective is to minimum the total tour length
• In STSP, cij cji for all cities i, j.
• In ATSP, cij ? cji

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Memetic Algorithms

• Memetic Algorithms is a population-based
  approach for heuristic search in optimization
  problems. They have shown that they are orders of
  magnitude faster than traditional Genetic
  Algorithms for some problem domains. Basically,
  they combine local search heuristics with
  crossover operators. For this reason, some
  researchers have viewed them as Hybrid Genetic
  Algorithms. However, combinations with
  constructive heuristics or exact methods may also
  belong to this class of metaheuristics. excerpt
  from Memetic Algorithms Home Page
  (http//www.ing.unlp.edu.ar/cetad/mos/memetic_home
  .html)

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Features of the new MA

• Local search engine
• Topological organization a complete tenary tree
  of 13 agents
• Selection and reproduction scheme in a hierarchy
  of overlapping clusters

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Program Structure
begin initialize (13 agents) repeat
for i1 to popSize do
evaluate(Currenti) updatePocket(i)
endfor PocketPropagation() If
diversity_crisis Restart() for i1 to
popSize do select parents a,b
PopiSAX(a,b) endfor for i1
to popSize do if (rand()lt0.3)
PopiMutate(Popi) endfor until
termination end
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The Population

• A complete tenery tree of 13 agents clustered in
  4 subpopulations
• Each subpopulation has 4 individuals a leader
  and 3 supporters
• The supports are located one level below in the
  hierarchy

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Population Operations

• Each agent is handling two feasible solutions,
  Pocket and Current, created by local search
• Recombination is between Pocket and Current
  solutions
• UpdatePocket() switch Pocket and Current when
  curCost lt pocCost
• PocketPropagation() exchange Pocket solutions of
  a leader and one of its supporters if the latter
  has a better Pocket solution

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Strategic Arc Crossover

• Given two parents A and B, construct a graph G
  consisting of the union of arcs in the two tours
• Pick randomly an unused vertex v in G
• While head h has at least one out-arc to an
  unused vertex
• Randomly choose one of the unused vertices to
  which h has an out-arc
• Make h to be tail t
• While the tail t has at least one in-arc from an
  unused vertex
• Randomly choose one of the unused vertices to
  which t has an in-arc
• Goto 1 if there is no unused vertex

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Recursive Arc Insertion
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Restart

• If the subpopulation has not changed for a
  certain number of generations, apply mutation to
  the Pockets a few time (except the root)

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Reference

1. L. Buriol, P. M. Franca and P. Moscato, A New
   Memetic Algorithm for the Asymmetric Traveling
   Salesman Problem.