Particle Swarm Optimization in .NET framework

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Messerschmidt and Engelbrecht [580], and Franken and Engelbrecht [283, 284, 285] used the gbest, lbest and Von Neumann PSO algorithms as well as the GCPSO to coevolve neural networks to approximate the evaluation function of leaf nodes in game trees No target values were available; therefore NNs compete in game tournaments against groups of opponents in order to determine a score or tness for each NN During the coevolutionary training process, weights are adjusted using PSO algorithms to have NNs (particles) move towards the best game player The coevolutionary training process has been applied successfully to the games of tick-tack-toe, checkers, bao, the iterated prisoner s dilemma, and a probabilistic version of tick-tack-toe For more information, refer to Section 1523
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Zhang and Shao [949, 950] proposed a PSO model to simultaneously optimize NN weights and architecture Two swarms are maintained: one swarm optimizes the architecture, and the other optimizes weights Particles in the architecture swarm are two-dimensional, with each particle representing the number of hidden units used and the connection density The rst step of the algorithm randomly initializes these architecture particles within prede ned ranges The second swarm s particles represent actual weight vectors For each architecture particle, a swarm of particles is created by randomly initializing weights to correspond with the number of hidden units and the connection density speci ed by the architecture particle Each of these swarms is evolved using a PSO, where the tness function is the MSE computed from the training set After convergence of each NN weights swarm, the best weight vector is identi ed from each swarm (note that the selected weight vectors are of di erent architectures) The tness of these NNs are then evaluated using a validation set containing patterns not used for training The obtained tness values are used to quantify the performance of the di erent architecture speci cations given by the corresponding particles of the architecture swarm Using these tness values, the architecture swarm is further optimized using PSO This process continues until a termination criterion is satis ed, at which point the global best particle is one with an optimized architecture and weight values
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Messerschmidt and Engelbrecht [580] developed a PSO approach to train NNs in a coevolutionary mechanism to approximate the evaluation function of leaf nodes in a game tree as described in Section 1523 The initial model was applied to the simple game of tick-tack-toe As mentioned in Section 1523 the training process is not supervised No target evaluation of board states is provided The lack of desired outputs for the NN necessitates a coevolutionary training mechanism, where NN agents compete against other agents, and all inferior NNs strive to beat superior NNs For the PSO coevolutionary training
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algorithm, summarized in Algorithm 1617, a swarm of particles is randomly created, where each particle represents a single NN Each NN plays in a tournament against a group of randomly selected opponents, selected from a competition pool (usually consisting of all the current particles of the swarm and all personal best positions) After each NN has played against a group of opponents, it is assigned a score based on the number of wins, losses and draws achieved These scores are then used to determine personal best and neighborhood best solutions Weights are adjusted using the position and velocity updates of any PSO algorithm Algorithm 1617 PSO Coevolutionary Game Training Algorithm Create and randomly initialize a swarm of NNs; repeat Add each personal best position to the competition pool; Add each particle to the competition pool; for each particle (or NN) do Randomly select a group of opponents from the competition pool; for each opponent do Play a game (using game trees to determine next moves) against the opponents, playing as rst player; Record if game was won, lost or drawn; Play a game against same opponent, but as the second player; Record if game was won, lost or drawn; end Determine a score for each particle; Compute new personal best positions based on scores; end Compute neighbor best positions; Update particle velocities; Update particle positions; until stopping condition is true; Return global best particle as game-playing agent; The basic algorithm as given in Algorithm 1617 has been applied successfully to the zero-sum games of tick-tack-toe [283, 580], checkers [284], and bao [156] Franken and Engelbrecht also applied the approach to the non-zero-sum game, the iterated prisoner s dilemma [285] A variant of the approach, using two competing swarms has recently been used to train agents for a probabilistic version of tick-tac-toe [654]
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