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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

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## Swarm Intell igence

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**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[i]) + 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.

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