Tuesday AM: more discussion work …

• 2006 IEEE Congress on Evolutionary Computation
• A Distributed Particle Swarm Optimization Algorithm for Swarm Robotic Applications
• James M. Hereford, Member, IEEE
• In summary, the advantages of the PSO over other algorithms are that (a) it is computationally simple and efficient; (b) each agent only needs to know its own local information and the global best to compute the new position, so there is a minimal amount of data transfer among the agents; and (c) the results from all agents in the population are not required to form the next generation, so a centralized processor is not required.
• A New Optimizer Using Particle Swarm Theory
• Russell Eberhart  James Kennedy
• Particle swarm optimization can be used to solve many of the same kinds of problems as genetic algorithms (GAS) [6]. This optimization technique does not scffer, however, from some of GA’s difficulties; interaction in the group enhances rather than detracts from progress toward the solution. Further, a particle swarm system has memory, which the genetic algorithm does not have. Change in genetic populations results in destruction of previous knowledge of the problem, except when elitism is employed, in which case usually one or a small number of individuals retain their iidentities.” In particle swarm optimization, individuals who fly past optima are tugged to return toward them; knowledge of good solutions is retained by all particles.
• (Millonas comment) First is the proximity principle: the population should be ablc to carry out simple space and time computations.  Second is the quality principle: the population should be able to respond to quality factors in the environment.  Third is the principle of diverse response: the population should not commit its activities along excessively narrow channels Fourth is the principle of stability: the popularion should not change its mode of behavior every time the environment changes. Fifth is the principle of adaptability. the population must be able to change behavior mode when it’s worth the computational price.  Note that principles four and five are the opposite sides of the same coin. 
• The particle swarm optimization concept and paradigm presented in this paper seem to adhere to all five principles. Basic to the paradigm are n-dimensional space calculations carried out over a series of time steps. The population is responding to the quality factors pbest and gbest/lbset The allocation of responses between pbest and gbest/lbest ensures a diversity of response. The population changes its state (mode of behavior) only when gbest/lbest changes, thus adhering to the principle of stability. The population is adaptive because it does change when gbest/lbest changes.
• The neural-net application described in Section 3, for instance, showed that the particle swarm optimizer could train NN weights as effectively as the usual error backpropagation method.  The particle swarm optimizer has also been used to train a neural network to classify the Fisher Iris Data Set [3].  Again, the optimizer trained the weights as effectively as the backpropagation method 
• The particle swarm optimizer was compared to a benchmark for genetic algorithms in Davis [2]: the extremely nonlinear Schaffer f6 function. This function is very difficult to optimize, as the highly discontinuous data surface features many local optima. The particle swarm paradigm found the global optimum each run, and appears to approximate the results reported for elementary genetic algorithms in Chapter 2 of [2] in terms of the number of evaluations required to reach certain performance levels [6].
• Conceptually, it seems to lie somewhere between genetic algorithms and evolutionary programming. It is highly dependent on stochastic processes, like evolutionary programming. The adjustment toward pbest and gbest by the particle swarm oplirnizer is conceptually similar to the crossover operation utilized by genetic algorithms. It uses the concept of fitness, as do all evolutionary computation paradigms.
• Unique to the concept of particle swarm optimization is flying potential solutions through hyperspace, accelerating toward “better” solutions. Other evolutionary computation schemes operate directly on potential solutions which are represented as locations in hypcrspace. Much of the success of particle swarms seems to lie in the agents’ tendency to hurtle past their target. Holland’s chapter on the “optimum allocation of trials” [5] reveals the delicate balance between conscrvativc testing of known regions versus risky exploration of the unknown. It appears that the current version of the paradigm allocates trials nearly optimally
• The stochastic factors allow thorough search of spaces between regions that have been found to be relatively good, and the momentum effect caused by modifying the extant velocities rather than replacing them results in overshooting, or exploration of unknown regions of the problem domain.
• [2] L. Davis, Ed., Handbook of Genetic Algorithms.  Van Nostrand Reinhold, New York, NY, 1991.
• [3] R. A. Fisher, “The use of multiple measurements in taxonomic problems.” Annals of Eugenics, 7: 179-188, 1936. 
• [5] J. H. Holland, Adaptation in Natural and Artificial Systems, MIT Press, Cambridge, MA., 1992.
• [6] J. Kennedy and R. Eberhart, Particle swarm optimization.” Proc. IEEE International Conf. on Neural Networks (Perth, Australia), IEEE Service Center, Piscataway, NJ, 1995 (in press).
• Proceedings of the 2007 IEEE Swarm Intelligence Symposium (SIS 2007)
• An Investigation of Grinding Process Optimization via Evolutionary Algorithms
• T.S. Lee1, T.O. Ting2 and Y.J. Lin3
• Similar to GA, a PSO consists of a population refining its knowledge of the given search space.
• Each particle keeps track of its coordinates in the search space, which are associated with the best solution it has achieved so far. This value is known as pbest.
• In this work, three prominent evolution algorithms namely GA, DE and PSO are investigated for the grinding process optimization with the objective of maximizing the Maximum Removal Rate, MRR subject to some operating constraints. The similar constraints handling are applied to all the algorithms. From the numerical results, PSO methodology is superior in comparison with other optimization algorithms such as DE (Differential Evolution) or GA.