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DriP PSO- A fast and inexpensive PSO for drifting problem spaces
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DriP PSO- A fast and inexpensive PSO for drifting problem spaces

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Particle Swarm Optimization is a class of stochastic, population based optimization techniques which are mostly suitable for static problems. However, real world optimization problems are time …

Particle Swarm Optimization is a class of stochastic, population based optimization techniques which are mostly suitable for static problems. However, real world optimization problems are time variant, i.e., the problem space changes over time. Several researches have been done to address this dynamic optimization problem using Particle Swarms. In this paper we probe the issues of tracking and optimizing Particle Swarms in a dynamic system where the problem-space drifts in a particular direction. Our assumption is that the approximate amount of drift is known, but the direction of the drift is unknown. We propose a Drift Predictive PSO (DriP-PSO) model which does not incur high computation cost, and is very fast and accurate. The main idea behind this technique is to use a few stagnant particles to determine the approximate direction in which the problem-space is drifting so that the particle velocities may be adjusted accordingly in the subsequent iteration of the algorithm.

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  • The first papers on the topic, by Kennedy and Eberhart, were presented in 1995; since then more than ten thousand articles and papers have been published on particle swarms.Kennedy also worked as a professional musician for twenty years and currently plays in a band called The Colliders!
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    • 1. Zubin BhuyanSourav HazarikaTezpur University,Assam, INDIAInternational Conf. on Science, Engineering &Technology- 2012, Trichy, IndiaFull paper: http://zubinb.com/papers/T1_EC-346.pdf
    • 2. Outline PSO basics The PSO Algorithm Dynamic systems Proposed PSO Models Drift Predictive PSO Experimental Results Conclusion and Future Work
    • 3. Swarm Intelligence Swarm intelligence collective behavior of simple rule-following agents overall behavior of the entire system appearsintelligent In Nature such behavior is seen in bird flocks,fish schools, ant colonies and animal herds Particle Swarm Optimization is a class ofstochastic, population based optimizationtechniques
    • 4. PSO Basics PSO was developed in 1995 by JamesKennedy (social-psychologist) and RussellEberhart (electrical engineer). † PSO is inspired from the concept of socialinteraction and is used for problem solving. A swarm of n agents or particles flies aroundin the search space looking for the bestsolution Particles communicate directly or indirectly with oneanother to determine its search direction.† Kennedy, J. and Eberhart, R. (1995). “Particle Swarm Optimization”, Proceedingsof the 1995 IEEE International Conference on Neural Networks, pp. 1942-1948,IEEE Press.
    • 5. PSO Basics pBest: Best value obtained so far by anindividual particle Each particle has its own pBest gBest: Best of all pBest The basic concept of PSO is to accelerateeach particle toward its own pBest, AND the gBest locations Usually with a random weighted acceleration at eachtime step
    • 6. PSO Basicsᵵskvkvpbestvgbestsk+1vk+1skvkvpbestvgbestsk+1vk+1Concept of modification of a searching point by PSOxysk : current searching point.sk+1: modified searching point.vk: current velocity.vk+1: modified velocity.vpbest : velocity based on pbest.vgbest : velocity based on gbestᵵSlide taken from Varadarajan Komanduri, Research Assistant, ECE Dept.,Villanova Universityhttp://www23.homepage.villanova.edu/varadarajan.komanduri/PSO_meander-line.ppt
    • 7. PSO topologies
    • 8. PSO Algorithm1. Initialize a population of particles randomly over a problem spacewith random velocities.2. Evaluate fitness of each particle.3. If current fitness of particle is better than pbest, then set pbestvalue equal to current fitness. Set pbest location to currentlocation.4. If current fitness is better than gbest, reset gbest to current fitnessvalue. Set new gbest location to current location.5. Change velocity according to the equation:vvid = w *vid + c1 * rand() * (pid -xid) + c2 * rand() * (pgd -xid)6. Change the position according to equation:xid = xid + vidHere w is inertia weight, c1 and c2 are acceleration constants, andrand() is a random number generator function.7. Loop back to Step 2 until end criterion is satisfied, or maximumnumber of iterations is completed.
    • 9. PSO Algorithm vid = w *vid+ c1 * rand() * (pid -xid)+ c2 * rand() * (pgd -xid)w: Inertia weight of current velocityc1 : Acceleration component of cognitive partc2 : Acceleration component of social part xid = xid + vid
    • 10. Dynamic Systems
    • 11. Dynamic Systems Practical/Real world problems are time-varyingor dynamic Problem space changing its state over time Optima changes continuously Changes may occur: periodically in some predefined sequence continuously in random fashion
    • 12. Dynamic Systems ‡ Hu, et al, defines in [2] three types of basicdynamic systems:The location of the optimum value canchangeThe location can remain constant but theoptimum value may varyBoth the location and the value of theoptimum can vary ‡ X. Hu, and R. C. Eberhart, “Adaptive Particle Swarm Optimization:Response to Dynamic Systems” Proceedings of the 2002 Congress onEvolutionary Computation, 2002.
    • 13. Dynamic Systems Particles might lose its global explorationability Redundant pBest, gBest Leads to unsatisfactory, unacceptable andsub-optimal results
    • 14. PSO for Dynamic Systems Several propositions Eberhart and Hu, 2002 “fixed gBest-value method” : If these two valuesdo not change for certain number of iterationsthen a possible optimum change is declared increase the accuracy and prevent false alarms Charged-PSO: Blackwell and Bentley, 2002 Main idea: good balance between exploration andexploitation results in continuous search for better solution
    • 15. PSO for Dynamic Systems Cooperative split PSO: Rakitianskaia, et al, 2008 modified the charged-PSO search space is divided into smaller subspaces, witheach subspace being optimised by a separate swarm Cellular PSO: Hashemi , et al, 2009 hybrid model of particle swarm optimization andcellular automata population of particles is split into different groupsacross cells of cellular automata by imposing arestriction on number of particles in each cell further modified by introducing temporary quantamparticles
    • 16. DRIFT PREDICTIVE PSO MODELFull paper:http://zubinb.com/papers/T1_EC-346.pdf
    • 17. Drip-PSO Specifically designed for the scenario where theproblem-space drifts in an unknown direction ASSUMPTION: Amount of drift is assumed to begradual Most practical transitions are “not abrupt” Change can be determined by LOCALITY searching AIM: To determines the approximate direction inwhich the problem-space is drifting Adjust particle velocities accordingly in thesubsequent iteration of the algorithm
    • 18. Drip-PSO Idea: Add “Adjustment” to the velocity of each particle.
    • 19. Drip-PSO: Detecting the driftdirection In each iteration a small number of stagnantparticles are selected They do not change their positions for thatparticular round If a change is detected by them, Generate 4 sub-particles resting ona circular orbit of radius ρ the sub-particles will be placed atright angle to one another
    • 20. Drip-PSO Pi has been selected as a stagnant particle. It detects change in its fitness (despite the factthat its position did not change) Pi expands its sub-particle orbit Two sub-particles, are selected suchthat previous fitness of the Pi lies between the fitnessvalues of the two selected sub-particles
    • 21. Drip-PSO: Calculating the Drift The approximate direction of drift, i.e. thedirection in which the adjustment is required,is given by
    • 22. Drip-PSO: Calculating the Drift The approximate direction of drift, i.e. the directionin which the adjustment is required, is given by is the angle representing the direction of adjustment of α is the previous fitness value of Pi α ∊ [ Sk, Pi, Sj,Pi ] are the angles at whichthe selected sub-particles are orientedare fitness values
    • 23. Drip-PSO: Calculating the Drift is calculated by all stagnant particles. Weighted average of all ξ is taken and added asan extra term to the velocity equation as shown Weight for a particular ξ is calculated using is the number of times the value occurs, n is the total number of stagnant particles.
    • 24. Drip-PSO: Adjusting the Drift Adding “Adjustment” component to the velocity
    • 25. Experimental Setup Test tool for the the proposed model was implemented in C# WPF(.Net Framework 4.0) Functions used for testing: Sphere, Step, Rastrigin, Rosenbrockand an arbitrary peak functionScreen shot of PSOTest Tool
    • 26. Experimental SetupSphere functionf(x, y) = x2+ y2Arbitrary Peaks functionf(x, y) = 1 – [3(1-x)2e-x2–(y+1)2+ 10(x/5 – x3– y5)e-(x2+y2)– 1/3e-(x+1)2-y2Step functionf(x, y) = |x| + |y| Test tool for the the proposed model was implemented in C#WPF (.Net Framework 4.0) Functions used for testing: Sphere, Step, Rastrigin,Rosenbrock and an arbitrary peak function
    • 27.  We simulate a dynamic system the test tool driftsthe problem space in any direction, by applying anoffset, λ, in every dimensionft+1 = ft(x - λ, y - λ) Offset is varied in the range [0.01, 0.09] The range of x and y is [-3, 3] c1 and c2 are set at 1.49618. Swarm size = 25 and 35Experimental Setup
    • 28. Experimental ResultsPercent error in finding globalminimaFunction Standard PSODrift PredictivePSOSphere 6.799% 2.571%Step 9.847% 2.091%Rastrigin 29.900% 9.143%Rosenbrock 24.616% 3.592%Arbitrary Peaks 27.629% 5.126%RESULTS OF DRIP-PSO IN DYNAMIC SCENARIO USING 25PARTICLES
    • 29. Experimental ResultsRESULTS OF DRIP-PSO IN DYNAMIC SCENARIO USING 35PARTICLESPercent error in finding globalminimaFunctionStandardPSODrift PredictivePSOSphere 5.021% 1.871%Step 8.268% 1.438%Rastrigin 25.728% 7.895%Rosenbrock 21.616% 2.332%Arbitrary Peaks 25.744% 4.661%
    • 30. Conclusion Drip-PSO gives more accurate result fordynamic systems Less computational cost Only few particles need to perform extracalculation Implemented in Atmega32
    • 31. Future Work Can be modified to detect several probablelocal optima then explore by splitting the entire swarm intosub-swarms Comparison with other PSOs
    • 32. Acknowledgement Gunther Maurice Helped us in designing the class structure Tuhin Bhuyan, JEC, Assam Gave us the idea of making the test tool multi-threaded by using .Net Framework ThreadPool
    • 33. Thank You!Full paper: http://zubinb.com/papers/T1_EC-346.pdf

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