Ant%20Colony%20Optimization%20(ACO):%20Applications%20to%20Scheduling

1
Ant Colony Optimization (ACO)Applications to
Scheduling

• Franco Villongco
• IEOR 4405
• 4/28/09

2
Definition

• Metaheuristic similar to genetic algorithms,
  simulated annealing etc.
• Flexible enough to be applied to combinatorial
  optimization problems.

3
Inspiration

• Foraging behavior of real ants
• Blind ants communicate through stigmergy
• Leave pheromone trails to make a certain path
  more likely to be traversed by other ants

4
Two-bridge Experiment
FOOD
NEST
5
Two-bridge Experiment
FOOD
NEST
6
Problem Representation

• (S, f, ?)
• S set of candidate solution
• f objective function of s ? S
• ? set of constraints
• Set C c1, c2 cN where N is the number of
  components
• Problem states are defined as x ( ci, cj ch)
• We call ? the set of all states

7
Problem Representation

• Nonempty set S of optimal solutions
• GC (C,L) whose nodes are the components.
• Artificial ants then build solutions by
  performing walks on the complete graph
• Like in the two-bridge experiment, arcs (trails)
  that have more pheromone will have a higher
  probability of being chosen.

8
Scheduling Applications

• JmCmax
• We use Ant System algorithm
• GC (C,L) consists of all the operations and two
  additional nodes for a source and sink node.
• Our constraints ? are simply the precedence
  constraints.

9
Scheduling Applications

• Pheromone trail tij on the arc (i,j) indicates
  the desirability of choosing operation j directly
  after operation i.
• heuristic information associated with that
  operation ?j

10
Scheduling Applications

• At each iteration of the construction procedure,
  m ants concurrently build solutions
• After each iteration, pheromone evaporation will
  be applied on all arcs

Where the parameter ? ? (0,1)
11
Scheduling Applications

• The better Cmax is for the solution constructed
  by a particular ant k, the more pheromone there
  will be to the arcs corresponding to that
  solution

12
Scheduling Applications

• Any ant at node i will choose node j with
  probability

• Where Nk is the set of feasible operations
• nj is the heuristic value proportional to the
  amount of work remaining corresponding to the job
  of the operation considered

13
Scheduling Applications

• 1STjwj
• We use the Ant Colony System algorithm
• Same as AS but with differences in pheromone
  updates and ant decision rule
• For our construction graph, we have for our node
  the n positions and n jobs
• Pheromone trail tij indicate the desirability of
  scheduling job j to position i
• heuristic information ?j inversely proportional
  to job js deadline

14
Scheduling Applications

• Main differences
• Pheromone update (global) Only the best-so-far
  solution increases in pheromone

For all (i,j) in sbs (best-so-far solution) and
where
15
Scheduling Applications

• Pheromone update (local) applied during the
  iteration to the arcs (i,j) that were traversed

16
Scheduling Applications

• Now, in choosing the next job j to schedule the
  probability of choosing job j is

Where J is the random variable that will equal j
with probability
17
Thank You!