CSM6120 Introduction to Intelligent Systems Other evolutionary algorithms

Today  Other evolutionary algorithms  Genetic programming  Ant colony optimization  Particle swarm optimization  Knowledge representation  Several approaches

The GA cycle selectionselection populationpopulation evaluationevaluation modificationmodification discarddiscard deleted members deleted members parents children modified children modified children evaluated children recombinationrecombination chosen parents chosen parents

Genetic programming  Devised by John KozaJohn Koza  36 Human-Competitive Results Produced by Genetic Programming 

Genetic programming √ * B * AA

 Trees consist of functions and terminals  Choose a set of functions and terminals, e.g { +, -, *, /, √}; {A,B}  Generate random programs (trees) which are syntactically correct  Follow a GA-like procedure  Evaluate fitness, select parents  Apply crossover and mutation Koza’s algorithm

/ A/ // AAAA * A- *√ AAA / A/ // √AAA * A- *A AA X A Crossover

Examples  Symbolic regression (function finding)    Moon lander! 

Other bio-inspired approaches  Simulated annealing  Ant colony optimization (ACO)  Particle swarm optimization (PSO) ...

Ant Colony Optimization  Nature: unsupervised complex problem solving  Simple agents working locally, displaying global intelligence  Ants are capable of finding the shortest route between food source and nest  Also react to changes in environment (obstructions etc) nest food source

Ant Colony Optimization  Shortest path is discovered via pheromone trails  Each ant moves ‘randomly’  Pheromone is deposited on path  Ants detect lead ant’s path, inclined to follow  More pheromone on path increases probability of path being followed nest food source

 Problem formulation for ACO  Graph representation (nodes and edges)  Heuristic desirability of edges  Construction of feasible solutions  Pheromone update rule (pheromone attached to edges)  Also we need a probabilistic transition rule  This evaluates the next step for an ant and considers both the heuristic desirability of an edge and the amount of pheromone deposited on the edge  The edge with the highest value of this combination is chosen by the artificial ant Ant Colony Optimization

ACO algorithm  Key idea: virtual pheromone accumulated on path edges  Algorithm for one ant:  Select starting node at random  While not-finished  Evaluate all edges from this node  Select the best-looking edge via probabilistic transition rule  Deposit artificial pheromone on the chosen edge  Finished path is a potential solution, analysed for optimality

Evaluate position Choose next node Generate Gather solutions Evaluate position continue stop Begin Update pheromone ants Return best solution continue stop (transition rule) Ants ACO algorithm

ACO: TSP Demo of ACO applied to large(ish) dynamic TSP (where cities are moved after a number of iterations)  d/ProjectV1-6/Project/tsp2.html d/ProjectV1-6/Project/tsp2.html  Performs well!  Combines heuristic knowledge with discovered knowledge

Particle Swarm Optimization  Based on the flocking/swarming behaviour of birds/insects

The basic idea  Each particle is searching for the optimum and encodes a solution (like the GA approach)  Each particle is moving (can’t search otherwise!), and hence has a velocity  Each particle remembers the position it was in where it had its best result so far (its personal best)  But this would not be much good on its own; particles need help in figuring out where to search

The basic idea  The particles in the swarm co-operate  They exchange information about what they’ve discovered in the places they have visited  The co-operation need only be very simple; in basic PSO it is like this:  A particle has a neighbourhood associated with it  A particle knows the fitnesses of those in its neighbourhood, and uses the position of the one with best fitness  This position is simply used to adjust the particle’s velocity

Initialization: Positions and velocities

What a particle does  In each time-step, a particle has to move to a new position  It does this by adjusting its velocity via:  The current velocity +  A weighted random portion in the direction of its personal best +  A weighted random portion in the direction of the neighbourhood best +  A weighted random portion in the direction of the global best  Having worked out a new velocity, its position is simply its old position plus the new velocity

PSO search

Neighbourhoods geographical social

Neighbourhoods Global

 PSO visualisation   More info on PSO 

Multi-objective optimisation  Sometimes we're searching for an answer which has to be optimal in several aspects  For example:  Finding the quickest and cheapest flight  Finding the lightest and strongest construction material  Finding the game strategy that will maximise trade profit, cities explored/conquered and health of your character.  Evolutionary algorithms can search the multi-objective space of solutions  Fitness function needs to combine the scores for the different objectives

Summary  What we looked at:  Genetic algorithms  Genetic programming  Other bio-inspired techniques  These are often applied to search/optimisation problems that are very challenging  Free (GNU licsensed) book: Global Optimization Algorithms – Thomas Weise 