EA*A Hybrid Approach

EA*A Hybrid Approach

Robbie HansonRobbie Hanson

What is it?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.

MotivationMotivation

Poor EA performanceLocal maxima/minima traps!Balancing exploration with exploitation.

When to terminate?

Poor EA performanceLocal maxima/minima traps!Balancing exploration with exploitation.

When to terminate?

The General IdeaThe General Idea

Partition the search spaceExplore each partitionContinue exploration on “promising” partitions

Partition the search spaceExplore each partitionContinue exploration on “promising” partitions

Motivation (cont)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*Intro to A*

Branch and bound techniqueExtension of best-first search of a tree

Uses heuristic to determine fitness of nodes

Branch and bound techniqueExtension of best-first search of a tree

Uses heuristic to determine fitness of nodes

Example TreeExample Tree

Problems with A*Problems with A*

A* relies on a good heuristicWithout 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 heuristicWithout 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

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)! / 210-city: 181,000 solutions20-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)! / 210-city: 181,000 solutions20-city: 10,000,000,000,000,000 solutions

TSPlib contains many real world examples

ExampleExample

ExampleExample

ExampleExample

ExampleExample

EA DetailsEA 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

Representation and Fitness

Selection and SurvivalSelection and Survival

Tournament SelectionSelection size specified in parameter file

(µ + λ) survival strategy

Tournament SelectionSelection size specified in parameter file

(µ + λ) survival strategy

Recombination/MutationRecombination/Mutation

Single parent mutation most popular

Two popular methods

Single parent mutation most popular

Two popular methods

EA* specificEA* 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?”

PerformancePerformance

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)

ProblemsProblems

Large TSP problemsLucky first guesses

Large TSP problemsLucky first guesses

Future ResearchFuture 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?Questions?