EA* A Hybrid Approach Robbie Hanson

What is it?  The A* algorithm, using an EA for the heuristic.  An efficient way of partitioning the search space for an EA.  An effective termination technique for EA’s.  The A* algorithm, using an EA for the heuristic.  An efficient way of partitioning the search space for an EA.  An effective termination technique for EA’s.

Motivation  Poor EA performance  Local maxima/minima traps!  Balancing exploration with exploitation.  When to terminate?  Poor EA performance  Local maxima/minima traps!  Balancing exploration with exploitation.  When to terminate?

The General Idea  Partition the search space  Explore each partition  Continue exploration on “promising” partitions  Partition the search space  Explore each partition  Continue exploration on “promising” partitions

Motivation (cont)  Hybridisation… (Chapter 10)  “This category of algorithms is very successful in practice and forms a rapidly growing research area with great potential.”  Hybridisation… (Chapter 10)  “This category of algorithms is very successful in practice and forms a rapidly growing research area with great potential.”

Intro to A*  Branch and bound technique  Extension of best-first search of a tree  Uses heuristic to determine fitness of nodes  Branch and bound technique  Extension of best-first search of a tree  Uses heuristic to determine fitness of nodes

Example Tree

Problems with A*  A* relies on a good heuristic  Without it, it becomes essentially a breadth first search  Some problems are difficult to design standard heuristics for  “For every common sense heuristic you can invent, you can find a pathological case that will make it look very silly.”  (Michalewicz & Fogel: “How to solve it: Modern Heuristics”)  A* relies on a good heuristic  Without it, it becomes essentially a breadth first search  Some problems are difficult to design standard heuristics for  “For every common sense heuristic you can invent, you can find a pathological case that will make it look very silly.”  (Michalewicz & Fogel: “How to solve it: Modern Heuristics”)

Traveling Salesman Problem The traveling salesman must visit every city in his territory exactly once and then return home covering the shortest distance. Search space: (N-1)! / 2 10-city: 181,000 solutions 20-city: 10,000,000,000,000,000 solutions TSPlib contains many real world examples The traveling salesman must visit every city in his territory exactly once and then return home covering the shortest distance. Search space: (N-1)! / 2 10-city: 181,000 solutions 20-city: 10,000,000,000,000,000 solutions TSPlib contains many real world examples

Example

EA Details  Parameter file specifies specifics, such as population size, number of children, etc.  Log file captures output.  This facilitates experimentation of parameter values.  Parameter file specifies specifics, such as population size, number of children, etc.  Log file captures output.  This facilitates experimentation of parameter values.

Representation and Fitness

Selection and Survival  Tournament Selection  Selection size specified in parameter file  (µ + λ) survival strategy  Tournament Selection  Selection size specified in parameter file  (µ + λ) survival strategy

Recombination/Mutation  Single parent mutation most popular  Two popular methods  Single parent mutation most popular  Two popular methods

EA* specific  Number of generations to run EA for each iteration.  How long may a node remain in the “open list?”  Number of generations to run EA for each iteration.  How long may a node remain in the “open list?”

Performance  Final solutions are VERY consistent.  Initial results suggest a lower standard deviation than regular EA.  SO FAR, it averages better solutions. (Very difficult to say)  Final solutions are VERY consistent.  Initial results suggest a lower standard deviation than regular EA.  SO FAR, it averages better solutions. (Very difficult to say)

Problems  Large TSP problems  Lucky first guesses  Large TSP problems  Lucky first guesses

Future Research  EA’s report expected fitness in generations to come.  This could help the EA to overestimate less often, possibly making the heuristic admissible for A*.  Local search techniques in the EA for better performance.  Trivial parallelization. (BOINC?)  EA’s report expected fitness in generations to come.  This could help the EA to overestimate less often, possibly making the heuristic admissible for A*.  Local search techniques in the EA for better performance.  Trivial parallelization. (BOINC?)

Questions?