1 / 70

740 likes | 1.47k Vues

ISE 410 Heuristics in Optimization Particle Swarm Optimization http://www.particleswarm.info/ http://www.swarmintelligence.org/. Swarm Intell igence. Origins in Artificial Life (Alife) Research ALife studies how computational techniques can help when studying biological phenomena

Télécharger la présentation
## ISE 410 Heuristics in Optimization Particle Swarm Optimization http://www.particleswarm.info/ http://www.swarmintelligen

**An Image/Link below is provided (as is) to download presentation**
Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.
Content is provided to you AS IS for your information and personal use only.
Download presentation by click this link.
While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.
During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

**ISE 410 Heuristics in OptimizationParticle Swarm**Optimizationhttp://www.particleswarm.info/http://www.swarmintelligence.org/**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)**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**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.**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**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**Particle Swarm Optimization(PSO)**• History • Main idea and Algorithm • Comparisons with GA • Advantages and Disadvantages • Implementation and Applications**Particle Swarm Optimization(PSO)**• History • Main idea and Algorithm • Comparisons with GA • Advantages and Disadvantages • Implementation and Applications**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**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.**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.**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.**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.**Population-based search procedure in which individuals**called particles change their position (state) with time. individual has position & individual changes velocity**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.**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**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] = persent[i] + v[i] where c1 and c2 are learning factors (weights) a b**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**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**Particle Swarm Optimization(PSO)**• History • Main idea and Algorithm • Comparisons with GA • Advantages and Disadvantages • Implementation and Applications**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.**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**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**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**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**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**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**PSO – Pros and Cons**• Simple in concept • Easy to implement • Computationally efficient • Application to combinatorial problems? Binary PSO**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**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**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**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)**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**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**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**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.**Implementation**• Can be used for both Static and Dynamic Combinatorial optimization problems • Convergence is guaranteed, although the speed is unknown • Value • Solution**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)**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.**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.**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.**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.**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.

More Related