Swarm Intell igence

1. ISE 410 Heuristics in OptimizationParticle Swarm Optimizationhttp://www.particleswarm.info/http://www.swarmintelligence.org/

2. Swarm Intelligence • Origins in Artificial Life (Alife) Research • ALife studies how computational techniques can help when studying biological phenomena • ALife studies how biological techniques can help out with computational problems • Two main Swarm Intelligence based methods • Particle Swarm Optimization (PSO) • Ant Colony Optimization(ACO)

3. Swarm Intelligence • Swarm Intelligence (SI) is the property of a system whereby the collective behaviors of (unsophisticated) agents interacting locally with their environment cause coherent functional global patterns to emerge. • SI provides a basis with which it is possible to explore collective (or distributed) problem solving without centralized control or the provision of a global model. • Leverage the power of complex adaptive systems to solve difficult non-linear stochastic problems

4. Swarm Intelligence • Characteristics of a swarm: • Distributed, no central control or data source; • Limited communication • No (explicit) model of the environment; • Perception of environment (sensing) • Ability to react to environment changes.

5. Swarm Intelligence • Social interactions (locally shared knowledge) provides the basis for unguided problem solving • The efficiency of the effort is related to but not dependent upon the degree or connectedness of the network and the number of interacting agents

6. Swarm Intelligence • Robust exemplars of problem-solving in Nature • Survival in stochastic hostile environment • Social interaction creates complex behaviors • Behaviors modified by dynamic environment. • Emergent behavior observed in: • Bacteria, immune system, ants, birds • And other social animals

7. Particle Swarm Optimization(PSO) • History • Main idea and Algorithm • Comparisons with GA • Advantages and Disadvantages • Implementation and Applications

8. Particle Swarm Optimization(PSO) • History • Main idea and Algorithm • Comparisons with GA • Advantages and Disadvantages • Implementation and Applications

9. Origins and Inspiration of PSO • Population based stochastic optimization technique inspired by social behaviour of bird flocking or fish schooling. • Developed by Jim Kennedy, Bureau of Labor Statistics, U.S. Department of Labor and Russ Eberhart, Purdue University • A concept for optimizing nonlinear functions using particle swarm methodology

10. Inspired by simulation social behavior • Related to bird flocking, fish schooling and swarming theory - steer toward the center - match neighbors’ velocity - avoid collisions • Suppose • a group of birds are randomly searching food in an area. • There is only one piece of food in the area being searched. • All the birds do not know where the food is. But they know how far the food is in each iteration. • So what's the best strategy to find the food? The effective one is to follow the bird which is nearest to the food.

11. What is PSO? • In PSO, each single solution is a "bird" in the search space. • Call it "particle". • All of particles have fitness values • which are evaluated by the fitness function to be optimized, and • have velocities • which direct the flying of the particles. • The particles fly through the problem space by following the current optimum particles.

12. PSO Algorithm • Initialize with randomly generated particles. • Update through generations in search for optima • Each particle has a velocity and position • Update for each particle uses two “best” values. • Pbest: best solution (fitness) it has achieved so far. (The fitness value is also stored.) • Gbest: best value, obtained so far by any particle in the population.

13. PSO algorithm is not only a tool for optimization, but also a tool for representing sociocognition of human and artificial agents, based on principles of social psychology. • A PSO system combines local search methods with global search methods, attempting to balance exploration and exploitation.

14. Population-based search procedure in which individuals called particles change their position (state) with time.  individual has position & individual changes velocity

15. Particles fly around in a multidimensional search space. During flight, each particle adjusts its position according to its own experience, and according to the experience of a neighboring particle, making use of the best position encountered by itself and its neighbor.

16. Particle Swarm Optimization (PSO) Process • Initialize population in hyperspace • Evaluate fitness of individual particles • Modify velocities based on previous best and global (or neighborhood) best positions • Terminate on some condition • Go to step 2

17. PSO Algorithm • Update each particle, each generation v[i]= v[i] + c1 * rand() * (pbest[i] - present[i]) + c2 * rand() * (gbest[i] - present[i])and present[i] = persent[i] + v[i] where c1 and c2 are learning factors (weights) a b

18. inertia Personal influence Social (global) influence PSO Algorithm • Update each particle, each generation v[i] = v[i] + c1 * rand() * (pbest[i] - present[]) + c2 * rand() * (gbest[i] - present[i])and present[i] = present[i] + v[i] where c1 and c2 are learning factors (weights) a b

19. PSO Algorithm • Inertia Weight d is the dimension, c1 and c2 are positive constants, rand1and rand2 are random numbers, and w is the inertia weight Velocity can be limited to Vmax

20. Particle Swarm Optimization(PSO) • History • Main idea and Algorithm • Comparisons with GA • Advantages and Disadvantages • Implementation and Applications

21. PSO and GA Comparison • Commonalities • PSO and GA are both population based stochastic optimization • both algorithms start with a group of a randomly generated population, • both have fitness values to evaluate the population. • Both update the population and search for the optimium with random techniques. • Both systems do not guarantee success.

22. PSO and GA Comparison • Differences • PSO does not have genetic operators like crossover and mutation. Particles update themselves with the internal velocity. • They also have memory, which is important to the algorithm. • Particles do not die • the information sharing mechanism in PSO is significantly different • Info from best to others, GA population moves together

23. PSO has a memory not “what” that best solution was, but “where” that best solution was • Quality: population responds to quality factors pbest and gbest • Diverse response: responses allocated between pbest and gbest • Stability: population changes state only when gbest changes • Adaptability: population does change state when gbest changes

24. There is no selection in PSO all particles survive for the length of the run PSO is the only EA that does not remove candidate population members • In PSO, topology is constant; a neighbor is a neighbor • Population size: Jim 10-20, Russ 30-40

25. PSO Velocity Update Equations • Global version vs Neighborhood version  change pgd to pld . where pgd is the global best position and pld is the neighboring best position

26. Inertia Weight • Large inertia weight facilitates global exploration, small on facilitates local exploration • w must be selected carefully and/or decreased over the run • Inertia weight seems to have attributes of temperature in simulated annealing

27. Vmax • An important parameter in PSO; typically the only one adjusted • Clamps particles velocities on each dimension • Determines “fineness” with which regions are searched if too high, can fly past optimal solutions if too low, can get stuck in local minima

28. PSO – Pros and Cons • Simple in concept • Easy to implement • Computationally efficient • Application to combinatorial problems?  Binary PSO

29. Books and Website • Swarm Intelligence by Kennedy, Eberhart, and Shi, Morgan Kaufmann division of Academic Press, 2001. http://www.engr.iupui.edu/~eberhart/web/PSObook.html • http://www.particleswarm.net/ • http://web.ics.purdue.edu/~hux/PSO.shtml • http://www.cis.syr.edu/~mohan/pso/ • http://clerc.maurice.free.fr/PSO/index.htm • http://users.erols.com/cathyk/jimk.html

30. Ant Colony Optimization

31. ACO Concept • Ants (blind) navigate from nest to food source • Shortest path is discovered via pheromone trails • each ant moves at random • pheromone is deposited on path • ants detect lead ant’s path, inclined to follow • more pheromone on path increases probability of path being followed

32. ACO System • Virtual “trail” accumulated on path segments • Starting node selected at random • Path selected at random • based on amount of “trail” present on possible paths from starting node • higher probability for paths with more “trail” • Ant reaches next node, selects next path • Continues until reaches starting node • Finished “tour” is a solution

33. ACO System, cont. • A completed tour is analyzed for optimality • “Trail” amount adjusted to favor better solutions • better solutions receive more trail • worse solutions receive less trail • higher probability of ant selecting path that is part of a better-performing tour • New cycle is performed • Repeated until most ants select the same tour on every cycle (convergence to solution)

34. ACO System, cont. • Often applied to TSP (Travelling Salesman Problem): shortest path between n nodes • Algorithm in Pseudocode: • Initialize Trail • Do While (Stopping Criteria Not Satisfied) – Cycle Loop • Do Until (Each Ant Completes a Tour) – Tour Loop • Local Trail Update • End Do • Analyze Tours • Global Trail Update • End Do

41. ACO Background • Discrete optimization problems difficult to solve • “Soft computing techniques” developed in past ten years: • Genetic algorithms (GAs) • based on natural selection and genetics • Ant Colony Optimization (ACO) • modeling ant colony behavior

42. ACO Background, cont. • Developed by Marco Dorigo (Milan, Italy), and others in early 1990s • Some common applications: • Quadratic assignment problems • Scheduling problems • Dynamic routing problems in networks • Theoretical analysis difficult • algorithm is based on a series of random decisions (by artificial ants) • probability of decisions changes on each iteration

43. What is ACO as Optimization Tech • Probabilistictechnique for solvingcomputational problems which can be reduced to finding good paths through graphs • They are inspired by the behavior of ants in finding paths from the colonyto food.

44. Implementation • Can be used for both Static and Dynamic Combinatorial optimization problems • Convergence is guaranteed, although the speed is unknown • Value • Solution

45. The Algorithm • Ant Colony Algorithms are typically use to solve minimum cost problems. • We may usually have N nodes and A undirected arcs • There are two working modes for the ants: either forwards or backwards. • Pheromones are only deposited in backward mode. (so that we know how good the path was to update its trail)

46. The Algorithm • The ants memory allows them to retrace the path it has followed while searching for the destination node • Before moving backward on their memorized path, they eliminate any loops from it. While moving backwards, the ants leave pheromones on the arcs they traversed.

47. The Algorithm • The ants evaluate the cost of the paths they have traversed. • The shorter paths will receive a greater deposit of pheromones. An evaporation rule will be tied with the pheromones, which will reduce the chance for poor quality solutions.

48. The ACO Algorithm • At the beginning of the search process, a constant amount of pheromone is assigned to all arcs. When located at a node i an ant k uses the pheromone trail to compute the probability of choosing j as the next node: • where is the neighborhood of ant k when in node i.

49. The Algorithm • When the arc (i,j) is traversed , the pheromone value changes as follows: • By using this rule, the probability increases that forthcoming ants will use this arc.

50. The Algorithm • After each ant k has moved to the next node, the pheromones evaporate by the following equation to all the arcs: • where is a parameter. An iteration is a complete cycle involving ants’ movement, pheromone evaporation, and pheromone deposit.