Optimal Collective Decision-Making through Social Influence and Different Action Execution Times

by Marco A. Montes de Oca, Eliseo Ferrante, Nithin Mathews, Mauro Birattari and Marco Dorigo
July 2009

Paper Abstract

In nature, there are examples of large groups of animals that are capable of making optimal collective-level decisions without the need for global control or information. Understanding the underlying mechanisms of such decentralized decision-making processes may help us to design artificial systems that exhibit some of the desirable properties, like scalability or fault tolerance, that are usually observed in these natural systems.

In this paper, we show how a simple social influence mechanism, based on the binary particle swarm optimization algorithm, can make a whole population of agents achieve consensus on one of two possible choices in a completely decentralized way. Furthermore, we show that, if the conditions for achieving consensus are met and each choice is bound to an action that takes time to perform, the population converges to the choice associated with the shortest execution time. We illustrate the applicability of the decision-making mechanism presented in this paper on an example scenario in swarm robotics.

Keywords: Particle Swarm Optimization, Swarm Intelligence, Swarm Robotics, Social Learning.

Results with no delays

The following are the results with no delay

Effect of the constriction factor

Parameters: n = 100, c_1 = 0.0, c_2 = 0.0
Probabilities	Actions

Parameters: n = 100, c_1 = 0.0, c_2 = 1.0
Probabilities	Actions

Parameters: n = 100, c_1 = 1.0, c_2 = 0.0
Probabilities	Actions

Parameters: n = 100, c_1 = 1.0, c_2 = 1.0
Probabilities	Actions

Parameters: n = 100, c_1 = 0.0, c_2 = 0.0
Probabilities	Actions

Parameters: n = 100, c_1 = 0.0, c_2 = 1.0
Probabilities	Actions

Parameters: n = 100, c_1 = 1.0, c_2 = 0.0
Probabilities	Actions

Parameters: n = 100, c_1 = 1.0, c_2 = 1.0
Probabilities	Actions

Parameters: n = 100, c_1 = 0.0, c_2 = 0.0
Probabilities	Actions

Parameters: n = 100, c_1 = 0.0, c_2 = 1.0
Probabilities	Actions

Parameters: n = 100, c_1 = 1.0, c_2 = 0.0
Probabilities	Actions

Parameters: n = 100, c_1 = 1.0, c_2 = 1.0
Probabilities	Actions

Effect of the acceleration components

Parameters: n = 100, chi = 0.729
Probabilities	Actions

Parameters: n = 100, chi = 0.729
Probabilities	Actions

Parameters: n = 100, chi = 0.729
Probabilities	Actions

Parameters: n = 100, chi = 0.729
Probabilities	Actions

Parameters: n = 100, chi = 1.0
Probabilities	Actions

Parameters: n = 100, chi = 1.0
Probabilities	Actions

Parameters: n = 100, chi = 1.0
Probabilities	Actions

Parameters: n = 100, chi = 1.0
Probabilities	Actions

Parameters: n = 100, chi = 1.3717
Probabilities	Actions

Parameters: n = 100, chi = 1.3717
Probabilities	Actions

Parameters: n = 100, chi = 1.3717
Probabilities	Actions

Parameters: n = 100, chi = 1.3717
Probabilities	Actions

Results with delays

The following are the results with time delays associated to actions

Effect of the population size

Parameters: c_1 = 0.0, c_2 = 0.0, mu = 1.0, sigma = 1, k = 0.0
Probabilities	Actions

Parameters: c_1 = 0.0, c_2 = 0.0, mu = 1.0, sigma = 1, k = 0.5
Probabilities	Actions

Parameters: c_1 = 0.0, c_2 = 0.0, mu = 1.0, sigma = 1, k = 0.75
Probabilities	Actions

Parameters: c_1 = 0.0, c_2 = 0.0, mu = 1.0, sigma = 1, k = 1.0
Probabilities	Actions

Parameters: c_1 = 0.0, c_2 = 0.0, mu = 1.0, sigma = 4, k = 0.0
Probabilities	Actions

Parameters: c_1 = 0.0, c_2 = 0.0, mu = 1.0, sigma = 4, k = 0.5
Probabilities	Actions

Parameters: c_1 = 0.0, c_2 = 0.0, mu = 1.0, sigma = 4, k = 0.75
Probabilities	Actions

Parameters: c_1 = 0.0, c_2 = 0.0, mu = 1.0, sigma = 4, k = 1.0
Probabilities	Actions

Parameters: c_1 = 0.0, c_2 = 0.0, mu = 1.0, sigma = 8, k = 0.0
Probabilities	Actions

Parameters: c_1 = 0.0, c_2 = 0.0, mu = 1.0, sigma = 8, k = 0.5
Probabilities	Actions

Parameters: c_1 = 0.0, c_2 = 0.0, mu = 1.0, sigma = 8, k = 0.75
Probabilities	Actions

Parameters: c_1 = 0.0, c_2 = 0.0, mu = 1.0, sigma = 8, k = 1.0
Probabilities	Actions

Parameters: c_1 = 0.0, c_2 = 0.0, mu = 2.0, sigma = 1, k = 0.0
Probabilities	Actions

Parameters: c_1 = 0.0, c_2 = 0.0, mu = 2.0, sigma = 1, k = 0.5
Probabilities	Actions

Parameters: c_1 = 0.0, c_2 = 0.0, mu = 2.0, sigma = 1, k = 0.75
Probabilities	Actions

Parameters: c_1 = 0.0, c_2 = 0.0, mu = 2.0, sigma = 1, k = 1.0
Probabilities	Actions

Parameters: c_1 = 0.0, c_2 = 0.0, mu = 2.0, sigma = 4, k = 0.0
Probabilities	Actions

Parameters: c_1 = 0.0, c_2 = 0.0, mu = 2.0, sigma = 4, k = 0.5
Probabilities	Actions

Parameters: c_1 = 0.0, c_2 = 0.0, mu = 2.0, sigma = 4, k = 0.75
Probabilities	Actions

Parameters: c_1 = 0.0, c_2 = 0.0, mu = 2.0, sigma = 4, k = 1.0
Probabilities	Actions

Parameters: c_1 = 0.0, c_2 = 0.0, mu = 2.0, sigma = 8, k = 0.0
Probabilities	Actions

Parameters: c_1 = 0.0, c_2 = 0.0, mu = 2.0, sigma = 8, k = 0.5
Probabilities	Actions

Parameters: c_1 = 0.0, c_2 = 0.0, mu = 2.0, sigma = 8, k = 0.75
Probabilities	Actions

Parameters: c_1 = 0.0, c_2 = 0.0, mu = 2.0, sigma = 8, k = 1.0
Probabilities	Actions

Parameters: c_1 = 0.0, c_2 = 0.0, mu = 4.0, sigma = 1, k = 0.0
Probabilities	Actions

Parameters: c_1 = 0.0, c_2 = 0.0, mu = 4.0, sigma = 1, k = 0.5
Probabilities	Actions

Parameters: c_1 = 0.0, c_2 = 0.0, mu = 4.0, sigma = 1, k = 0.75
Probabilities	Actions

Parameters: c_1 = 0.0, c_2 = 0.0, mu = 4.0, sigma = 1, k = 1.0
Probabilities	Actions

Parameters: c_1 = 0.0, c_2 = 0.0, mu = 4.0, sigma = 4, k = 0.0
Probabilities	Actions

Parameters: c_1 = 0.0, c_2 = 0.0, mu = 4.0, sigma = 4, k = 0.5
Probabilities	Actions

Parameters: c_1 = 0.0, c_2 = 0.0, mu = 4.0, sigma = 4, k = 0.75
Probabilities	Actions

Parameters: c_1 = 0.0, c_2 = 0.0, mu = 4.0, sigma = 4, k = 1.0
Probabilities	Actions

Parameters: c_1 = 0.0, c_2 = 0.0, mu = 4.0, sigma = 8, k = 0.0
Probabilities	Actions

Parameters: c_1 = 0.0, c_2 = 0.0, mu = 4.0, sigma = 8, k = 0.5
Probabilities	Actions

Parameters: c_1 = 0.0, c_2 = 0.0, mu = 4.0, sigma = 8, k = 0.75
Probabilities	Actions

Parameters: c_1 = 0.0, c_2 = 0.0, mu = 4.0, sigma = 8, k = 1.0
Probabilities	Actions

Parameters: c_1 = 0.0, c_2 = 1.0, mu = 1.0, sigma = 1, k = 0.0
Probabilities	Actions

Parameters: c_1 = 0.0, c_2 = 1.0, mu = 1.0, sigma = 1, k = 0.5
Probabilities	Actions

Parameters: c_1 = 0.0, c_2 = 1.0, mu = 1.0, sigma = 1, k = 0.75
Probabilities	Actions

Parameters: c_1 = 0.0, c_2 = 1.0, mu = 1.0, sigma = 1, k = 1.0
Probabilities	Actions

Parameters: c_1 = 0.0, c_2 = 1.0, mu = 1.0, sigma = 4, k = 0.0
Probabilities	Actions

Parameters: c_1 = 0.0, c_2 = 1.0, mu = 1.0, sigma = 4, k = 0.5
Probabilities	Actions

Parameters: c_1 = 0.0, c_2 = 1.0, mu = 1.0, sigma = 4, k = 0.75
Probabilities	Actions

Parameters: c_1 = 0.0, c_2 = 1.0, mu = 1.0, sigma = 4, k = 1.0
Probabilities	Actions

Parameters: c_1 = 0.0, c_2 = 1.0, mu = 1.0, sigma = 8, k = 0.0
Probabilities	Actions

Parameters: c_1 = 0.0, c_2 = 1.0, mu = 1.0, sigma = 8, k = 0.5
Probabilities	Actions

Parameters: c_1 = 0.0, c_2 = 1.0, mu = 1.0, sigma = 8, k = 0.75
Probabilities	Actions

Parameters: c_1 = 0.0, c_2 = 1.0, mu = 1.0, sigma = 8, k = 1.0
Probabilities	Actions

Parameters: c_1 = 0.0, c_2 = 1.0, mu = 2.0, sigma = 1, k = 0.0
Probabilities	Actions

Parameters: c_1 = 0.0, c_2 = 1.0, mu = 2.0, sigma = 1, k = 0.5
Probabilities	Actions

Parameters: c_1 = 0.0, c_2 = 1.0, mu = 2.0, sigma = 1, k = 0.75
Probabilities	Actions

Parameters: c_1 = 0.0, c_2 = 1.0, mu = 2.0, sigma = 1, k = 1.0
Probabilities	Actions

Parameters: c_1 = 0.0, c_2 = 1.0, mu = 2.0, sigma = 4, k = 0.0
Probabilities	Actions

Parameters: c_1 = 0.0, c_2 = 1.0, mu = 2.0, sigma = 4, k = 0.5
Probabilities	Actions

Parameters: c_1 = 0.0, c_2 = 1.0, mu = 2.0, sigma = 4, k = 0.75
Probabilities	Actions

Parameters: c_1 = 0.0, c_2 = 1.0, mu = 2.0, sigma = 4, k = 1.0
Probabilities	Actions

Parameters: c_1 = 0.0, c_2 = 1.0, mu = 2.0, sigma = 8, k = 0.0
Probabilities	Actions

Parameters: c_1 = 0.0, c_2 = 1.0, mu = 2.0, sigma = 8, k = 0.5
Probabilities	Actions

Parameters: c_1 = 0.0, c_2 = 1.0, mu = 2.0, sigma = 8, k = 0.75
Probabilities	Actions

Parameters: c_1 = 0.0, c_2 = 1.0, mu = 2.0, sigma = 8, k = 1.0
Probabilities	Actions

Parameters: c_1 = 0.0, c_2 = 1.0, mu = 4.0, sigma = 1, k = 0.0
Probabilities	Actions

Parameters: c_1 = 0.0, c_2 = 1.0, mu = 4.0, sigma = 1, k = 0.5
Probabilities	Actions

Parameters: c_1 = 0.0, c_2 = 1.0, mu = 4.0, sigma = 1, k = 0.75
Probabilities	Actions

Parameters: c_1 = 0.0, c_2 = 1.0, mu = 4.0, sigma = 1, k = 1.0
Probabilities	Actions

Parameters: c_1 = 0.0, c_2 = 1.0, mu = 4.0, sigma = 4, k = 0.0
Probabilities	Actions

Parameters: c_1 = 0.0, c_2 = 1.0, mu = 4.0, sigma = 4, k = 0.5
Probabilities	Actions

Parameters: c_1 = 0.0, c_2 = 1.0, mu = 4.0, sigma = 4, k = 0.75
Probabilities	Actions

Parameters: c_1 = 0.0, c_2 = 1.0, mu = 4.0, sigma = 4, k = 1.0
Probabilities	Actions

Parameters: c_1 = 0.0, c_2 = 1.0, mu = 4.0, sigma = 8, k = 0.0
Probabilities	Actions

Parameters: c_1 = 0.0, c_2 = 1.0, mu = 4.0, sigma = 8, k = 0.5
Probabilities	Actions

Parameters: c_1 = 0.0, c_2 = 1.0, mu = 4.0, sigma = 8, k = 0.75
Probabilities	Actions

Parameters: c_1 = 0.0, c_2 = 1.0, mu = 4.0, sigma = 8, k = 1.0
Probabilities	Actions

Parameters: c_1 = 1.0, c_2 = 0.0, mu = 1.0, sigma = 1, k = 0.0
Probabilities	Actions

Parameters: c_1 = 1.0, c_2 = 0.0, mu = 1.0, sigma = 1, k = 0.5
Probabilities	Actions

Parameters: c_1 = 1.0, c_2 = 0.0, mu = 1.0, sigma = 1, k = 0.75
Probabilities	Actions

Parameters: c_1 = 1.0, c_2 = 0.0, mu = 1.0, sigma = 1, k = 1.0
Probabilities	Actions

Parameters: c_1 = 1.0, c_2 = 0.0, mu = 1.0, sigma = 4, k = 0.0
Probabilities	Actions

Parameters: c_1 = 1.0, c_2 = 0.0, mu = 1.0, sigma = 4, k = 0.5
Probabilities	Actions

Parameters: c_1 = 1.0, c_2 = 0.0, mu = 1.0, sigma = 4, k = 0.75
Probabilities	Actions

Parameters: c_1 = 1.0, c_2 = 0.0, mu = 1.0, sigma = 4, k = 1.0
Probabilities	Actions

Parameters: c_1 = 1.0, c_2 = 0.0, mu = 1.0, sigma = 8, k = 0.0
Probabilities	Actions

Parameters: c_1 = 1.0, c_2 = 0.0, mu = 1.0, sigma = 8, k = 0.5
Probabilities	Actions

Parameters: c_1 = 1.0, c_2 = 0.0, mu = 1.0, sigma = 8, k = 0.75
Probabilities	Actions

Parameters: c_1 = 1.0, c_2 = 0.0, mu = 1.0, sigma = 8, k = 1.0
Probabilities	Actions

Parameters: c_1 = 1.0, c_2 = 0.0, mu = 2.0, sigma = 1, k = 0.0
Probabilities	Actions

Parameters: c_1 = 1.0, c_2 = 0.0, mu = 2.0, sigma = 1, k = 0.5
Probabilities	Actions

Parameters: c_1 = 1.0, c_2 = 0.0, mu = 2.0, sigma = 1, k = 0.75
Probabilities	Actions

Parameters: c_1 = 1.0, c_2 = 0.0, mu = 2.0, sigma = 1, k = 1.0
Probabilities	Actions

Parameters: c_1 = 1.0, c_2 = 0.0, mu = 2.0, sigma = 4, k = 0.0
Probabilities	Actions

Parameters: c_1 = 1.0, c_2 = 0.0, mu = 2.0, sigma = 4, k = 0.5
Probabilities	Actions

Parameters: c_1 = 1.0, c_2 = 0.0, mu = 2.0, sigma = 4, k = 0.75
Probabilities	Actions

Parameters: c_1 = 1.0, c_2 = 0.0, mu = 2.0, sigma = 4, k = 1.0
Probabilities	Actions

Parameters: c_1 = 1.0, c_2 = 0.0, mu = 2.0, sigma = 8, k = 0.0
Probabilities	Actions

Parameters: c_1 = 1.0, c_2 = 0.0, mu = 2.0, sigma = 8, k = 0.5
Probabilities	Actions

Parameters: c_1 = 1.0, c_2 = 0.0, mu = 2.0, sigma = 8, k = 0.75
Probabilities	Actions

Parameters: c_1 = 1.0, c_2 = 0.0, mu = 2.0, sigma = 8, k = 1.0
Probabilities	Actions

Parameters: c_1 = 1.0, c_2 = 0.0, mu = 4.0, sigma = 1, k = 0.0
Probabilities	Actions

Parameters: c_1 = 1.0, c_2 = 0.0, mu = 4.0, sigma = 1, k = 0.5
Probabilities	Actions

Parameters: c_1 = 1.0, c_2 = 0.0, mu = 4.0, sigma = 1, k = 0.75
Probabilities	Actions

Parameters: c_1 = 1.0, c_2 = 0.0, mu = 4.0, sigma = 1, k = 1.0
Probabilities	Actions

Parameters: c_1 = 1.0, c_2 = 0.0, mu = 4.0, sigma = 4, k = 0.0
Probabilities	Actions

Parameters: c_1 = 1.0, c_2 = 0.0, mu = 4.0, sigma = 4, k = 0.5
Probabilities	Actions

Parameters: c_1 = 1.0, c_2 = 0.0, mu = 4.0, sigma = 4, k = 0.75
Probabilities	Actions

Parameters: c_1 = 1.0, c_2 = 0.0, mu = 4.0, sigma = 4, k = 1.0
Probabilities	Actions

Parameters: c_1 = 1.0, c_2 = 0.0, mu = 4.0, sigma = 8, k = 0.0
Probabilities	Actions

Parameters: c_1 = 1.0, c_2 = 0.0, mu = 4.0, sigma = 8, k = 0.5
Probabilities	Actions

Parameters: c_1 = 1.0, c_2 = 0.0, mu = 4.0, sigma = 8, k = 0.75
Probabilities	Actions

Parameters: c_1 = 1.0, c_2 = 0.0, mu = 4.0, sigma = 8, k = 1.0
Probabilities	Actions

Parameters: c_1 = 1.0, c_2 = 1.0, mu = 1.0, sigma = 1, k = 0.0
Probabilities	Actions

Parameters: c_1 = 1.0, c_2 = 1.0, mu = 1.0, sigma = 1, k = 0.5
Probabilities	Actions

Parameters: c_1 = 1.0, c_2 = 1.0, mu = 1.0, sigma = 1, k = 0.75
Probabilities	Actions

Parameters: c_1 = 1.0, c_2 = 1.0, mu = 1.0, sigma = 1, k = 1.0
Probabilities	Actions

Parameters: c_1 = 1.0, c_2 = 1.0, mu = 1.0, sigma = 4, k = 0.0
Probabilities	Actions

Parameters: c_1 = 1.0, c_2 = 1.0, mu = 1.0, sigma = 4, k = 0.5
Probabilities	Actions

Parameters: c_1 = 1.0, c_2 = 1.0, mu = 1.0, sigma = 4, k = 0.75
Probabilities	Actions

Parameters: c_1 = 1.0, c_2 = 1.0, mu = 1.0, sigma = 4, k = 1.0
Probabilities	Actions

Parameters: c_1 = 1.0, c_2 = 1.0, mu = 1.0, sigma = 8, k = 0.0
Probabilities	Actions

Parameters: c_1 = 1.0, c_2 = 1.0, mu = 1.0, sigma = 8, k = 0.5
Probabilities	Actions

Parameters: c_1 = 1.0, c_2 = 1.0, mu = 1.0, sigma = 8, k = 0.75
Probabilities	Actions

Parameters: c_1 = 1.0, c_2 = 1.0, mu = 1.0, sigma = 8, k = 1.0
Probabilities	Actions

Parameters: c_1 = 1.0, c_2 = 1.0, mu = 2.0, sigma = 1, k = 0.0
Probabilities	Actions

Parameters: c_1 = 1.0, c_2 = 1.0, mu = 2.0, sigma = 1, k = 0.5
Probabilities	Actions

Parameters: c_1 = 1.0, c_2 = 1.0, mu = 2.0, sigma = 1, k = 0.75
Probabilities	Actions

Parameters: c_1 = 1.0, c_2 = 1.0, mu = 2.0, sigma = 1, k = 1.0
Probabilities	Actions

Parameters: c_1 = 1.0, c_2 = 1.0, mu = 2.0, sigma = 4, k = 0.0
Probabilities	Actions

Parameters: c_1 = 1.0, c_2 = 1.0, mu = 2.0, sigma = 4, k = 0.5
Probabilities	Actions

Parameters: c_1 = 1.0, c_2 = 1.0, mu = 2.0, sigma = 4, k = 0.75
Probabilities	Actions

Parameters: c_1 = 1.0, c_2 = 1.0, mu = 2.0, sigma = 4, k = 1.0
Probabilities	Actions

Parameters: c_1 = 1.0, c_2 = 1.0, mu = 2.0, sigma = 8, k = 0.0
Probabilities	Actions

Parameters: c_1 = 1.0, c_2 = 1.0, mu = 2.0, sigma = 8, k = 0.5
Probabilities	Actions

Parameters: c_1 = 1.0, c_2 = 1.0, mu = 2.0, sigma = 8, k = 0.75
Probabilities	Actions

Parameters: c_1 = 1.0, c_2 = 1.0, mu = 2.0, sigma = 8, k = 1.0
Probabilities	Actions

Parameters: c_1 = 1.0, c_2 = 1.0, mu = 4.0, sigma = 1, k = 0.0
Probabilities	Actions

Parameters: c_1 = 1.0, c_2 = 1.0, mu = 4.0, sigma = 1, k = 0.5
Probabilities	Actions

Parameters: c_1 = 1.0, c_2 = 1.0, mu = 4.0, sigma = 1, k = 0.75
Probabilities	Actions

Parameters: c_1 = 1.0, c_2 = 1.0, mu = 4.0, sigma = 1, k = 1.0
Probabilities	Actions

Parameters: c_1 = 1.0, c_2 = 1.0, mu = 4.0, sigma = 4, k = 0.0
Probabilities	Actions

Parameters: c_1 = 1.0, c_2 = 1.0, mu = 4.0, sigma = 4, k = 0.5
Probabilities	Actions

Parameters: c_1 = 1.0, c_2 = 1.0, mu = 4.0, sigma = 4, k = 0.75
Probabilities	Actions

Parameters: c_1 = 1.0, c_2 = 1.0, mu = 4.0, sigma = 4, k = 1.0
Probabilities	Actions

Parameters: c_1 = 1.0, c_2 = 1.0, mu = 4.0, sigma = 8, k = 0.0
Probabilities	Actions

Parameters: c_1 = 1.0, c_2 = 1.0, mu = 4.0, sigma = 8, k = 0.5
Probabilities	Actions

Parameters: c_1 = 1.0, c_2 = 1.0, mu = 4.0, sigma = 8, k = 0.75
Probabilities	Actions

Parameters: c_1 = 1.0, c_2 = 1.0, mu = 4.0, sigma = 8, k = 1.0
Probabilities	Actions

Parameters: c_1 = 0.0, c_2 = 0.0, mu = 1.0, sigma = 1, k = 0.0
Probabilities	Actions

Parameters: c_1 = 0.0, c_2 = 0.0, mu = 1.0, sigma = 1, k = 0.5
Probabilities	Actions

Parameters: c_1 = 0.0, c_2 = 0.0, mu = 1.0, sigma = 1, k = 0.75
Probabilities	Actions

Parameters: c_1 = 0.0, c_2 = 0.0, mu = 1.0, sigma = 1, k = 1.0
Probabilities	Actions

Parameters: c_1 = 0.0, c_2 = 0.0, mu = 1.0, sigma = 4, k = 0.0
Probabilities	Actions

Parameters: c_1 = 0.0, c_2 = 0.0, mu = 1.0, sigma = 4, k = 0.5
Probabilities	Actions

Parameters: c_1 = 0.0, c_2 = 0.0, mu = 1.0, sigma = 4, k = 0.75
Probabilities	Actions

Parameters: c_1 = 0.0, c_2 = 0.0, mu = 1.0, sigma = 4, k = 1.0
Probabilities	Actions

Parameters: c_1 = 0.0, c_2 = 0.0, mu = 1.0, sigma = 8, k = 0.0
Probabilities	Actions

Parameters: c_1 = 0.0, c_2 = 0.0, mu = 1.0, sigma = 8, k = 0.5
Probabilities	Actions

Parameters: c_1 = 0.0, c_2 = 0.0, mu = 1.0, sigma = 8, k = 0.75
Probabilities	Actions

Parameters: c_1 = 0.0, c_2 = 0.0, mu = 1.0, sigma = 8, k = 1.0
Probabilities	Actions

Parameters: c_1 = 0.0, c_2 = 0.0, mu = 2.0, sigma = 1, k = 0.0
Probabilities	Actions

Parameters: c_1 = 0.0, c_2 = 0.0, mu = 2.0, sigma = 1, k = 0.5
Probabilities	Actions

Parameters: c_1 = 0.0, c_2 = 0.0, mu = 2.0, sigma = 1, k = 0.75
Probabilities	Actions

Parameters: c_1 = 0.0, c_2 = 0.0, mu = 2.0, sigma = 1, k = 1.0
Probabilities	Actions

Parameters: c_1 = 0.0, c_2 = 0.0, mu = 2.0, sigma = 4, k = 0.0
Probabilities	Actions

Parameters: c_1 = 0.0, c_2 = 0.0, mu = 2.0, sigma = 4, k = 0.5
Probabilities	Actions

Parameters: c_1 = 0.0, c_2 = 0.0, mu = 2.0, sigma = 4, k = 0.75
Probabilities	Actions

Parameters: c_1 = 0.0, c_2 = 0.0, mu = 2.0, sigma = 4, k = 1.0
Probabilities	Actions

Parameters: c_1 = 0.0, c_2 = 0.0, mu = 2.0, sigma = 8, k = 0.0
Probabilities	Actions

Parameters: c_1 = 0.0, c_2 = 0.0, mu = 2.0, sigma = 8, k = 0.5
Probabilities	Actions

Parameters: c_1 = 0.0, c_2 = 0.0, mu = 2.0, sigma = 8, k = 0.75
Probabilities	Actions

Parameters: c_1 = 0.0, c_2 = 0.0, mu = 2.0, sigma = 8, k = 1.0
Probabilities	Actions

Parameters: c_1 = 0.0, c_2 = 0.0, mu = 4.0, sigma = 1, k = 0.0
Probabilities	Actions

Parameters: c_1 = 0.0, c_2 = 0.0, mu = 4.0, sigma = 1, k = 0.5
Probabilities	Actions

Parameters: c_1 = 0.0, c_2 = 0.0, mu = 4.0, sigma = 1, k = 0.75
Probabilities	Actions

Parameters: c_1 = 0.0, c_2 = 0.0, mu = 4.0, sigma = 1, k = 1.0
Probabilities	Actions

Parameters: c_1 = 0.0, c_2 = 0.0, mu = 4.0, sigma = 4, k = 0.0
Probabilities	Actions

Parameters: c_1 = 0.0, c_2 = 0.0, mu = 4.0, sigma = 4, k = 0.5
Probabilities	Actions

Parameters: c_1 = 0.0, c_2 = 0.0, mu = 4.0, sigma = 4, k = 0.75
Probabilities	Actions

Parameters: c_1 = 0.0, c_2 = 0.0, mu = 4.0, sigma = 4, k = 1.0
Probabilities	Actions

Parameters: c_1 = 0.0, c_2 = 0.0, mu = 4.0, sigma = 8, k = 0.0
Probabilities	Actions

Parameters: c_1 = 0.0, c_2 = 0.0, mu = 4.0, sigma = 8, k = 0.5
Probabilities	Actions

Parameters: c_1 = 0.0, c_2 = 0.0, mu = 4.0, sigma = 8, k = 0.75
Probabilities	Actions

Parameters: c_1 = 0.0, c_2 = 0.0, mu = 4.0, sigma = 8, k = 1.0
Probabilities	Actions

Parameters: c_1 = 0.0, c_2 = 1.0, mu = 1.0, sigma = 1, k = 0.0
Probabilities	Actions

Parameters: c_1 = 0.0, c_2 = 1.0, mu = 1.0, sigma = 1, k = 0.5
Probabilities	Actions

Parameters: c_1 = 0.0, c_2 = 1.0, mu = 1.0, sigma = 1, k = 0.75
Probabilities	Actions

Parameters: c_1 = 0.0, c_2 = 1.0, mu = 1.0, sigma = 1, k = 1.0
Probabilities	Actions

Parameters: c_1 = 0.0, c_2 = 1.0, mu = 1.0, sigma = 4, k = 0.0
Probabilities	Actions

Parameters: c_1 = 0.0, c_2 = 1.0, mu = 1.0, sigma = 4, k = 0.5
Probabilities	Actions

Parameters: c_1 = 0.0, c_2 = 1.0, mu = 1.0, sigma = 4, k = 0.75
Probabilities	Actions

Parameters: c_1 = 0.0, c_2 = 1.0, mu = 1.0, sigma = 4, k = 1.0
Probabilities	Actions

Parameters: c_1 = 0.0, c_2 = 1.0, mu = 1.0, sigma = 8, k = 0.0
Probabilities	Actions

Parameters: c_1 = 0.0, c_2 = 1.0, mu = 1.0, sigma = 8, k = 0.5
Probabilities	Actions

Parameters: c_1 = 0.0, c_2 = 1.0, mu = 1.0, sigma = 8, k = 0.75
Probabilities	Actions

Parameters: c_1 = 0.0, c_2 = 1.0, mu = 1.0, sigma = 8, k = 1.0
Probabilities	Actions

Parameters: c_1 = 0.0, c_2 = 1.0, mu = 2.0, sigma = 1, k = 0.0
Probabilities	Actions

Parameters: c_1 = 0.0, c_2 = 1.0, mu = 2.0, sigma = 1, k = 0.5
Probabilities	Actions

Parameters: c_1 = 0.0, c_2 = 1.0, mu = 2.0, sigma = 1, k = 0.75
Probabilities	Actions

Parameters: c_1 = 0.0, c_2 = 1.0, mu = 2.0, sigma = 1, k = 1.0
Probabilities	Actions

Parameters: c_1 = 0.0, c_2 = 1.0, mu = 2.0, sigma = 4, k = 0.0
Probabilities	Actions

Parameters: c_1 = 0.0, c_2 = 1.0, mu = 2.0, sigma = 4, k = 0.5
Probabilities	Actions

Parameters: c_1 = 0.0, c_2 = 1.0, mu = 2.0, sigma = 4, k = 0.75
Probabilities	Actions

Parameters: c_1 = 0.0, c_2 = 1.0, mu = 2.0, sigma = 4, k = 1.0
Probabilities	Actions

Parameters: c_1 = 0.0, c_2 = 1.0, mu = 2.0, sigma = 8, k = 0.0
Probabilities	Actions

Parameters: c_1 = 0.0, c_2 = 1.0, mu = 2.0, sigma = 8, k = 0.5
Probabilities	Actions

Parameters: c_1 = 0.0, c_2 = 1.0, mu = 2.0, sigma = 8, k = 0.75
Probabilities	Actions

Parameters: c_1 = 0.0, c_2 = 1.0, mu = 2.0, sigma = 8, k = 1.0
Probabilities	Actions

Parameters: c_1 = 0.0, c_2 = 1.0, mu = 4.0, sigma = 1, k = 0.0
Probabilities	Actions

Parameters: c_1 = 0.0, c_2 = 1.0, mu = 4.0, sigma = 1, k = 0.5
Probabilities	Actions

Parameters: c_1 = 0.0, c_2 = 1.0, mu = 4.0, sigma = 1, k = 0.75
Probabilities	Actions

Parameters: c_1 = 0.0, c_2 = 1.0, mu = 4.0, sigma = 1, k = 1.0
Probabilities	Actions

Parameters: c_1 = 0.0, c_2 = 1.0, mu = 4.0, sigma = 4, k = 0.0
Probabilities	Actions

Parameters: c_1 = 0.0, c_2 = 1.0, mu = 4.0, sigma = 4, k = 0.5
Probabilities	Actions

Parameters: c_1 = 0.0, c_2 = 1.0, mu = 4.0, sigma = 4, k = 0.75
Probabilities	Actions

Parameters: c_1 = 0.0, c_2 = 1.0, mu = 4.0, sigma = 4, k = 1.0
Probabilities	Actions

Parameters: c_1 = 0.0, c_2 = 1.0, mu = 4.0, sigma = 8, k = 0.0
Probabilities	Actions

Parameters: c_1 = 0.0, c_2 = 1.0, mu = 4.0, sigma = 8, k = 0.5
Probabilities	Actions

Parameters: c_1 = 0.0, c_2 = 1.0, mu = 4.0, sigma = 8, k = 0.75
Probabilities	Actions

Parameters: c_1 = 0.0, c_2 = 1.0, mu = 4.0, sigma = 8, k = 1.0
Probabilities	Actions

Parameters: c_1 = 1.0, c_2 = 0.0, mu = 1.0, sigma = 1, k = 0.0
Probabilities	Actions

Parameters: c_1 = 1.0, c_2 = 0.0, mu = 1.0, sigma = 1, k = 0.5
Probabilities	Actions

Parameters: c_1 = 1.0, c_2 = 0.0, mu = 1.0, sigma = 1, k = 0.75
Probabilities	Actions

Parameters: c_1 = 1.0, c_2 = 0.0, mu = 1.0, sigma = 1, k = 1.0
Probabilities	Actions

Parameters: c_1 = 1.0, c_2 = 0.0, mu = 1.0, sigma = 4, k = 0.0
Probabilities	Actions

Parameters: c_1 = 1.0, c_2 = 0.0, mu = 1.0, sigma = 4, k = 0.5
Probabilities	Actions

Parameters: c_1 = 1.0, c_2 = 0.0, mu = 1.0, sigma = 4, k = 0.75
Probabilities	Actions

Parameters: c_1 = 1.0, c_2 = 0.0, mu = 1.0, sigma = 4, k = 1.0
Probabilities	Actions

Parameters: c_1 = 1.0, c_2 = 0.0, mu = 1.0, sigma = 8, k = 0.0
Probabilities	Actions

Parameters: c_1 = 1.0, c_2 = 0.0, mu = 1.0, sigma = 8, k = 0.5
Probabilities	Actions

Parameters: c_1 = 1.0, c_2 = 0.0, mu = 1.0, sigma = 8, k = 0.75
Probabilities	Actions

Parameters: c_1 = 1.0, c_2 = 0.0, mu = 1.0, sigma = 8, k = 1.0
Probabilities	Actions

Parameters: c_1 = 1.0, c_2 = 0.0, mu = 2.0, sigma = 1, k = 0.0
Probabilities	Actions

Parameters: c_1 = 1.0, c_2 = 0.0, mu = 2.0, sigma = 1, k = 0.5
Probabilities	Actions

Parameters: c_1 = 1.0, c_2 = 0.0, mu = 2.0, sigma = 1, k = 0.75
Probabilities	Actions

Parameters: c_1 = 1.0, c_2 = 0.0, mu = 2.0, sigma = 1, k = 1.0
Probabilities	Actions

Parameters: c_1 = 1.0, c_2 = 0.0, mu = 2.0, sigma = 4, k = 0.0
Probabilities	Actions

Parameters: c_1 = 1.0, c_2 = 0.0, mu = 2.0, sigma = 4, k = 0.5
Probabilities	Actions

Parameters: c_1 = 1.0, c_2 = 0.0, mu = 2.0, sigma = 4, k = 0.75
Probabilities	Actions

Parameters: c_1 = 1.0, c_2 = 0.0, mu = 2.0, sigma = 4, k = 1.0
Probabilities	Actions

Parameters: c_1 = 1.0, c_2 = 0.0, mu = 2.0, sigma = 8, k = 0.0
Probabilities	Actions

Parameters: c_1 = 1.0, c_2 = 0.0, mu = 2.0, sigma = 8, k = 0.5
Probabilities	Actions

Parameters: c_1 = 1.0, c_2 = 0.0, mu = 2.0, sigma = 8, k = 0.75
Probabilities	Actions

Parameters: c_1 = 1.0, c_2 = 0.0, mu = 2.0, sigma = 8, k = 1.0
Probabilities	Actions

Parameters: c_1 = 1.0, c_2 = 0.0, mu = 4.0, sigma = 1, k = 0.0
Probabilities	Actions

Parameters: c_1 = 1.0, c_2 = 0.0, mu = 4.0, sigma = 1, k = 0.5
Probabilities	Actions

Parameters: c_1 = 1.0, c_2 = 0.0, mu = 4.0, sigma = 1, k = 0.75
Probabilities	Actions

Parameters: c_1 = 1.0, c_2 = 0.0, mu = 4.0, sigma = 1, k = 1.0
Probabilities	Actions

Parameters: c_1 = 1.0, c_2 = 0.0, mu = 4.0, sigma = 4, k = 0.0
Probabilities	Actions

Parameters: c_1 = 1.0, c_2 = 0.0, mu = 4.0, sigma = 4, k = 0.5
Probabilities	Actions

Parameters: c_1 = 1.0, c_2 = 0.0, mu = 4.0, sigma = 4, k = 0.75
Probabilities	Actions

Parameters: c_1 = 1.0, c_2 = 0.0, mu = 4.0, sigma = 4, k = 1.0
Probabilities	Actions

Parameters: c_1 = 1.0, c_2 = 0.0, mu = 4.0, sigma = 8, k = 0.0
Probabilities	Actions

Parameters: c_1 = 1.0, c_2 = 0.0, mu = 4.0, sigma = 8, k = 0.5
Probabilities	Actions

Parameters: c_1 = 1.0, c_2 = 0.0, mu = 4.0, sigma = 8, k = 0.75
Probabilities	Actions

Parameters: c_1 = 1.0, c_2 = 0.0, mu = 4.0, sigma = 8, k = 1.0
Probabilities	Actions

Parameters: c_1 = 1.0, c_2 = 1.0, mu = 1.0, sigma = 1, k = 0.0
Probabilities	Actions

Parameters: c_1 = 1.0, c_2 = 1.0, mu = 1.0, sigma = 1, k = 0.5
Probabilities	Actions

Parameters: c_1 = 1.0, c_2 = 1.0, mu = 1.0, sigma = 1, k = 0.75
Probabilities	Actions

Parameters: c_1 = 1.0, c_2 = 1.0, mu = 1.0, sigma = 1, k = 1.0
Probabilities	Actions

Parameters: c_1 = 1.0, c_2 = 1.0, mu = 1.0, sigma = 4, k = 0.0
Probabilities	Actions

Parameters: c_1 = 1.0, c_2 = 1.0, mu = 1.0, sigma = 4, k = 0.5
Probabilities	Actions

Parameters: c_1 = 1.0, c_2 = 1.0, mu = 1.0, sigma = 4, k = 0.75
Probabilities	Actions

Parameters: c_1 = 1.0, c_2 = 1.0, mu = 1.0, sigma = 4, k = 1.0
Probabilities	Actions

Parameters: c_1 = 1.0, c_2 = 1.0, mu = 1.0, sigma = 8, k = 0.0
Probabilities	Actions

Parameters: c_1 = 1.0, c_2 = 1.0, mu = 1.0, sigma = 8, k = 0.5
Probabilities	Actions

Parameters: c_1 = 1.0, c_2 = 1.0, mu = 1.0, sigma = 8, k = 0.75
Probabilities	Actions

Parameters: c_1 = 1.0, c_2 = 1.0, mu = 1.0, sigma = 8, k = 1.0
Probabilities	Actions

Parameters: c_1 = 1.0, c_2 = 1.0, mu = 2.0, sigma = 1, k = 0.0
Probabilities	Actions

Parameters: c_1 = 1.0, c_2 = 1.0, mu = 2.0, sigma = 1, k = 0.5
Probabilities	Actions

Parameters: c_1 = 1.0, c_2 = 1.0, mu = 2.0, sigma = 1, k = 0.75
Probabilities	Actions

Parameters: c_1 = 1.0, c_2 = 1.0, mu = 2.0, sigma = 1, k = 1.0
Probabilities	Actions

Parameters: c_1 = 1.0, c_2 = 1.0, mu = 2.0, sigma = 4, k = 0.0
Probabilities	Actions

Parameters: c_1 = 1.0, c_2 = 1.0, mu = 2.0, sigma = 4, k = 0.5
Probabilities	Actions

Parameters: c_1 = 1.0, c_2 = 1.0, mu = 2.0, sigma = 4, k = 0.75
Probabilities	Actions

Parameters: c_1 = 1.0, c_2 = 1.0, mu = 2.0, sigma = 4, k = 1.0
Probabilities	Actions

Parameters: c_1 = 1.0, c_2 = 1.0, mu = 2.0, sigma = 8, k = 0.0
Probabilities	Actions

Parameters: c_1 = 1.0, c_2 = 1.0, mu = 2.0, sigma = 8, k = 0.5
Probabilities	Actions

Parameters: c_1 = 1.0, c_2 = 1.0, mu = 2.0, sigma = 8, k = 0.75
Probabilities	Actions

Parameters: c_1 = 1.0, c_2 = 1.0, mu = 2.0, sigma = 8, k = 1.0
Probabilities	Actions

Parameters: c_1 = 1.0, c_2 = 1.0, mu = 4.0, sigma = 1, k = 0.0
Probabilities	Actions

Parameters: c_1 = 1.0, c_2 = 1.0, mu = 4.0, sigma = 1, k = 0.5
Probabilities	Actions

Parameters: c_1 = 1.0, c_2 = 1.0, mu = 4.0, sigma = 1, k = 0.75
Probabilities	Actions

Parameters: c_1 = 1.0, c_2 = 1.0, mu = 4.0, sigma = 1, k = 1.0
Probabilities	Actions

Parameters: c_1 = 1.0, c_2 = 1.0, mu = 4.0, sigma = 4, k = 0.0
Probabilities	Actions

Parameters: c_1 = 1.0, c_2 = 1.0, mu = 4.0, sigma = 4, k = 0.5
Probabilities	Actions

Parameters: c_1 = 1.0, c_2 = 1.0, mu = 4.0, sigma = 4, k = 0.75
Probabilities	Actions

Parameters: c_1 = 1.0, c_2 = 1.0, mu = 4.0, sigma = 4, k = 1.0
Probabilities	Actions

Parameters: c_1 = 1.0, c_2 = 1.0, mu = 4.0, sigma = 8, k = 0.0
Probabilities	Actions

Parameters: c_1 = 1.0, c_2 = 1.0, mu = 4.0, sigma = 8, k = 0.5
Probabilities	Actions

Parameters: c_1 = 1.0, c_2 = 1.0, mu = 4.0, sigma = 8, k = 0.75
Probabilities	Actions

Parameters: c_1 = 1.0, c_2 = 1.0, mu = 4.0, sigma = 8, k = 1.0
Probabilities	Actions

Parameters: c_1 = 0.0, c_2 = 0.0, mu = 1.0, sigma = 1, k = 0.0
Probabilities	Actions

Parameters: c_1 = 0.0, c_2 = 0.0, mu = 1.0, sigma = 1, k = 0.5
Probabilities	Actions

Parameters: c_1 = 0.0, c_2 = 0.0, mu = 1.0, sigma = 1, k = 0.75
Probabilities	Actions

Parameters: c_1 = 0.0, c_2 = 0.0, mu = 1.0, sigma = 1, k = 1.0
Probabilities	Actions

Parameters: c_1 = 0.0, c_2 = 0.0, mu = 1.0, sigma = 4, k = 0.0
Probabilities	Actions

Parameters: c_1 = 0.0, c_2 = 0.0, mu = 1.0, sigma = 4, k = 0.5
Probabilities	Actions

Parameters: c_1 = 0.0, c_2 = 0.0, mu = 1.0, sigma = 4, k = 0.75
Probabilities	Actions

Parameters: c_1 = 0.0, c_2 = 0.0, mu = 1.0, sigma = 4, k = 1.0
Probabilities	Actions

Parameters: c_1 = 0.0, c_2 = 0.0, mu = 1.0, sigma = 8, k = 0.0
Probabilities	Actions

Parameters: c_1 = 0.0, c_2 = 0.0, mu = 1.0, sigma = 8, k = 0.5
Probabilities	Actions

Parameters: c_1 = 0.0, c_2 = 0.0, mu = 1.0, sigma = 8, k = 0.75
Probabilities	Actions

Parameters: c_1 = 0.0, c_2 = 0.0, mu = 1.0, sigma = 8, k = 1.0
Probabilities	Actions

Parameters: c_1 = 0.0, c_2 = 0.0, mu = 2.0, sigma = 1, k = 0.0
Probabilities	Actions

Parameters: c_1 = 0.0, c_2 = 0.0, mu = 2.0, sigma = 1, k = 0.5
Probabilities	Actions

Parameters: c_1 = 0.0, c_2 = 0.0, mu = 2.0, sigma = 1, k = 0.75
Probabilities	Actions

Parameters: c_1 = 0.0, c_2 = 0.0, mu = 2.0, sigma = 1, k = 1.0
Probabilities	Actions

Parameters: c_1 = 0.0, c_2 = 0.0, mu = 2.0, sigma = 4, k = 0.0
Probabilities	Actions

Parameters: c_1 = 0.0, c_2 = 0.0, mu = 2.0, sigma = 4, k = 0.5
Probabilities	Actions

Parameters: c_1 = 0.0, c_2 = 0.0, mu = 2.0, sigma = 4, k = 0.75
Probabilities	Actions

Parameters: c_1 = 0.0, c_2 = 0.0, mu = 2.0, sigma = 4, k = 1.0
Probabilities	Actions

Parameters: c_1 = 0.0, c_2 = 0.0, mu = 2.0, sigma = 8, k = 0.0
Probabilities	Actions

Parameters: c_1 = 0.0, c_2 = 0.0, mu = 2.0, sigma = 8, k = 0.5
Probabilities	Actions

Parameters: c_1 = 0.0, c_2 = 0.0, mu = 2.0, sigma = 8, k = 0.75
Probabilities	Actions

Parameters: c_1 = 0.0, c_2 = 0.0, mu = 2.0, sigma = 8, k = 1.0
Probabilities	Actions

Parameters: c_1 = 0.0, c_2 = 0.0, mu = 4.0, sigma = 1, k = 0.0
Probabilities	Actions

Parameters: c_1 = 0.0, c_2 = 0.0, mu = 4.0, sigma = 1, k = 0.5
Probabilities	Actions

Parameters: c_1 = 0.0, c_2 = 0.0, mu = 4.0, sigma = 1, k = 0.75
Probabilities	Actions

Parameters: c_1 = 0.0, c_2 = 0.0, mu = 4.0, sigma = 1, k = 1.0
Probabilities	Actions

Parameters: c_1 = 0.0, c_2 = 0.0, mu = 4.0, sigma = 4, k = 0.0
Probabilities	Actions

Parameters: c_1 = 0.0, c_2 = 0.0, mu = 4.0, sigma = 4, k = 0.5
Probabilities	Actions

Parameters: c_1 = 0.0, c_2 = 0.0, mu = 4.0, sigma = 4, k = 0.75
Probabilities	Actions

Parameters: c_1 = 0.0, c_2 = 0.0, mu = 4.0, sigma = 4, k = 1.0
Probabilities	Actions

Parameters: c_1 = 0.0, c_2 = 0.0, mu = 4.0, sigma = 8, k = 0.0
Probabilities	Actions

Parameters: c_1 = 0.0, c_2 = 0.0, mu = 4.0, sigma = 8, k = 0.5
Probabilities	Actions

Parameters: c_1 = 0.0, c_2 = 0.0, mu = 4.0, sigma = 8, k = 0.75
Probabilities	Actions

Parameters: c_1 = 0.0, c_2 = 0.0, mu = 4.0, sigma = 8, k = 1.0
Probabilities	Actions

Parameters: c_1 = 0.0, c_2 = 1.0, mu = 1.0, sigma = 1, k = 0.0
Probabilities	Actions

Parameters: c_1 = 0.0, c_2 = 1.0, mu = 1.0, sigma = 1, k = 0.5
Probabilities	Actions

Parameters: c_1 = 0.0, c_2 = 1.0, mu = 1.0, sigma = 1, k = 0.75
Probabilities	Actions

Parameters: c_1 = 0.0, c_2 = 1.0, mu = 1.0, sigma = 1, k = 1.0
Probabilities	Actions

Parameters: c_1 = 0.0, c_2 = 1.0, mu = 1.0, sigma = 4, k = 0.0
Probabilities	Actions

Parameters: c_1 = 0.0, c_2 = 1.0, mu = 1.0, sigma = 4, k = 0.5
Probabilities	Actions

Parameters: c_1 = 0.0, c_2 = 1.0, mu = 1.0, sigma = 4, k = 0.75
Probabilities	Actions

Parameters: c_1 = 0.0, c_2 = 1.0, mu = 1.0, sigma = 4, k = 1.0
Probabilities	Actions

Parameters: c_1 = 0.0, c_2 = 1.0, mu = 1.0, sigma = 8, k = 0.0
Probabilities	Actions

Parameters: c_1 = 0.0, c_2 = 1.0, mu = 1.0, sigma = 8, k = 0.5
Probabilities	Actions

Parameters: c_1 = 0.0, c_2 = 1.0, mu = 1.0, sigma = 8, k = 0.75
Probabilities	Actions

Parameters: c_1 = 0.0, c_2 = 1.0, mu = 1.0, sigma = 8, k = 1.0
Probabilities	Actions

Parameters: c_1 = 0.0, c_2 = 1.0, mu = 2.0, sigma = 1, k = 0.0
Probabilities	Actions

Parameters: c_1 = 0.0, c_2 = 1.0, mu = 2.0, sigma = 1, k = 0.5
Probabilities	Actions

Parameters: c_1 = 0.0, c_2 = 1.0, mu = 2.0, sigma = 1, k = 0.75
Probabilities	Actions

Parameters: c_1 = 0.0, c_2 = 1.0, mu = 2.0, sigma = 1, k = 1.0
Probabilities	Actions

Parameters: c_1 = 0.0, c_2 = 1.0, mu = 2.0, sigma = 4, k = 0.0
Probabilities	Actions

Parameters: c_1 = 0.0, c_2 = 1.0, mu = 2.0, sigma = 4, k = 0.5
Probabilities	Actions

Parameters: c_1 = 0.0, c_2 = 1.0, mu = 2.0, sigma = 4, k = 0.75
Probabilities	Actions

Parameters: c_1 = 0.0, c_2 = 1.0, mu = 2.0, sigma = 4, k = 1.0
Probabilities	Actions

Parameters: c_1 = 0.0, c_2 = 1.0, mu = 2.0, sigma = 8, k = 0.0
Probabilities	Actions

Parameters: c_1 = 0.0, c_2 = 1.0, mu = 2.0, sigma = 8, k = 0.5
Probabilities	Actions

Parameters: c_1 = 0.0, c_2 = 1.0, mu = 2.0, sigma = 8, k = 0.75
Probabilities	Actions

Parameters: c_1 = 0.0, c_2 = 1.0, mu = 2.0, sigma = 8, k = 1.0
Probabilities	Actions

Parameters: c_1 = 0.0, c_2 = 1.0, mu = 4.0, sigma = 1, k = 0.0
Probabilities	Actions

Parameters: c_1 = 0.0, c_2 = 1.0, mu = 4.0, sigma = 1, k = 0.5
Probabilities	Actions

Parameters: c_1 = 0.0, c_2 = 1.0, mu = 4.0, sigma = 1, k = 0.75
Probabilities	Actions

Parameters: c_1 = 0.0, c_2 = 1.0, mu = 4.0, sigma = 1, k = 1.0
Probabilities	Actions

Parameters: c_1 = 0.0, c_2 = 1.0, mu = 4.0, sigma = 4, k = 0.0
Probabilities	Actions

Parameters: c_1 = 0.0, c_2 = 1.0, mu = 4.0, sigma = 4, k = 0.5
Probabilities	Actions

Parameters: c_1 = 0.0, c_2 = 1.0, mu = 4.0, sigma = 4, k = 0.75
Probabilities	Actions

Parameters: c_1 = 0.0, c_2 = 1.0, mu = 4.0, sigma = 4, k = 1.0
Probabilities	Actions

Parameters: c_1 = 0.0, c_2 = 1.0, mu = 4.0, sigma = 8, k = 0.0
Probabilities	Actions

Parameters: c_1 = 0.0, c_2 = 1.0, mu = 4.0, sigma = 8, k = 0.5
Probabilities	Actions

Parameters: c_1 = 0.0, c_2 = 1.0, mu = 4.0, sigma = 8, k = 0.75
Probabilities	Actions

Parameters: c_1 = 0.0, c_2 = 1.0, mu = 4.0, sigma = 8, k = 1.0
Probabilities	Actions

Parameters: c_1 = 1.0, c_2 = 0.0, mu = 1.0, sigma = 1, k = 0.0
Probabilities	Actions

Parameters: c_1 = 1.0, c_2 = 0.0, mu = 1.0, sigma = 1, k = 0.5
Probabilities	Actions

Parameters: c_1 = 1.0, c_2 = 0.0, mu = 1.0, sigma = 1, k = 0.75
Probabilities	Actions

Parameters: c_1 = 1.0, c_2 = 0.0, mu = 1.0, sigma = 1, k = 1.0
Probabilities	Actions

Parameters: c_1 = 1.0, c_2 = 0.0, mu = 1.0, sigma = 4, k = 0.0
Probabilities	Actions

Parameters: c_1 = 1.0, c_2 = 0.0, mu = 1.0, sigma = 4, k = 0.5
Probabilities	Actions

Parameters: c_1 = 1.0, c_2 = 0.0, mu = 1.0, sigma = 4, k = 0.75
Probabilities	Actions

Parameters: c_1 = 1.0, c_2 = 0.0, mu = 1.0, sigma = 4, k = 1.0
Probabilities	Actions

Parameters: c_1 = 1.0, c_2 = 0.0, mu = 1.0, sigma = 8, k = 0.0
Probabilities	Actions

Parameters: c_1 = 1.0, c_2 = 0.0, mu = 1.0, sigma = 8, k = 0.5
Probabilities	Actions

Parameters: c_1 = 1.0, c_2 = 0.0, mu = 1.0, sigma = 8, k = 0.75
Probabilities	Actions

Parameters: c_1 = 1.0, c_2 = 0.0, mu = 1.0, sigma = 8, k = 1.0
Probabilities	Actions

Parameters: c_1 = 1.0, c_2 = 0.0, mu = 2.0, sigma = 1, k = 0.0
Probabilities	Actions

Parameters: c_1 = 1.0, c_2 = 0.0, mu = 2.0, sigma = 1, k = 0.5
Probabilities	Actions

Parameters: c_1 = 1.0, c_2 = 0.0, mu = 2.0, sigma = 1, k = 0.75
Probabilities	Actions

Parameters: c_1 = 1.0, c_2 = 0.0, mu = 2.0, sigma = 1, k = 1.0
Probabilities	Actions

Parameters: c_1 = 1.0, c_2 = 0.0, mu = 2.0, sigma = 4, k = 0.0
Probabilities	Actions

Parameters: c_1 = 1.0, c_2 = 0.0, mu = 2.0, sigma = 4, k = 0.5
Probabilities	Actions

Parameters: c_1 = 1.0, c_2 = 0.0, mu = 2.0, sigma = 4, k = 0.75
Probabilities	Actions

Parameters: c_1 = 1.0, c_2 = 0.0, mu = 2.0, sigma = 4, k = 1.0
Probabilities	Actions

Parameters: c_1 = 1.0, c_2 = 0.0, mu = 2.0, sigma = 8, k = 0.0
Probabilities	Actions

Parameters: c_1 = 1.0, c_2 = 0.0, mu = 2.0, sigma = 8, k = 0.5
Probabilities	Actions

Parameters: c_1 = 1.0, c_2 = 0.0, mu = 2.0, sigma = 8, k = 0.75
Probabilities	Actions

Parameters: c_1 = 1.0, c_2 = 0.0, mu = 2.0, sigma = 8, k = 1.0
Probabilities	Actions

Parameters: c_1 = 1.0, c_2 = 0.0, mu = 4.0, sigma = 1, k = 0.0
Probabilities	Actions

Parameters: c_1 = 1.0, c_2 = 0.0, mu = 4.0, sigma = 1, k = 0.5
Probabilities	Actions

Parameters: c_1 = 1.0, c_2 = 0.0, mu = 4.0, sigma = 1, k = 0.75
Probabilities	Actions

Parameters: c_1 = 1.0, c_2 = 0.0, mu = 4.0, sigma = 1, k = 1.0
Probabilities	Actions

Parameters: c_1 = 1.0, c_2 = 0.0, mu = 4.0, sigma = 4, k = 0.0
Probabilities	Actions

Parameters: c_1 = 1.0, c_2 = 0.0, mu = 4.0, sigma = 4, k = 0.5
Probabilities	Actions

Parameters: c_1 = 1.0, c_2 = 0.0, mu = 4.0, sigma = 4, k = 0.75
Probabilities	Actions

Parameters: c_1 = 1.0, c_2 = 0.0, mu = 4.0, sigma = 4, k = 1.0
Probabilities	Actions

Parameters: c_1 = 1.0, c_2 = 0.0, mu = 4.0, sigma = 8, k = 0.0
Probabilities	Actions

Parameters: c_1 = 1.0, c_2 = 0.0, mu = 4.0, sigma = 8, k = 0.5
Probabilities	Actions

Parameters: c_1 = 1.0, c_2 = 0.0, mu = 4.0, sigma = 8, k = 0.75
Probabilities	Actions

Parameters: c_1 = 1.0, c_2 = 0.0, mu = 4.0, sigma = 8, k = 1.0
Probabilities	Actions

Parameters: c_1 = 1.0, c_2 = 1.0, mu = 1.0, sigma = 1, k = 0.0
Probabilities	Actions

Parameters: c_1 = 1.0, c_2 = 1.0, mu = 1.0, sigma = 1, k = 0.5
Probabilities	Actions

Parameters: c_1 = 1.0, c_2 = 1.0, mu = 1.0, sigma = 1, k = 0.75
Probabilities	Actions

Parameters: c_1 = 1.0, c_2 = 1.0, mu = 1.0, sigma = 1, k = 1.0
Probabilities	Actions

Parameters: c_1 = 1.0, c_2 = 1.0, mu = 1.0, sigma = 4, k = 0.0
Probabilities	Actions

Parameters: c_1 = 1.0, c_2 = 1.0, mu = 1.0, sigma = 4, k = 0.5
Probabilities	Actions

Parameters: c_1 = 1.0, c_2 = 1.0, mu = 1.0, sigma = 4, k = 0.75
Probabilities	Actions

Parameters: c_1 = 1.0, c_2 = 1.0, mu = 1.0, sigma = 4, k = 1.0
Probabilities	Actions

Parameters: c_1 = 1.0, c_2 = 1.0, mu = 1.0, sigma = 8, k = 0.0
Probabilities	Actions

Parameters: c_1 = 1.0, c_2 = 1.0, mu = 1.0, sigma = 8, k = 0.5
Probabilities	Actions

Parameters: c_1 = 1.0, c_2 = 1.0, mu = 1.0, sigma = 8, k = 0.75
Probabilities	Actions

Parameters: c_1 = 1.0, c_2 = 1.0, mu = 1.0, sigma = 8, k = 1.0
Probabilities	Actions

Parameters: c_1 = 1.0, c_2 = 1.0, mu = 2.0, sigma = 1, k = 0.0
Probabilities	Actions

Parameters: c_1 = 1.0, c_2 = 1.0, mu = 2.0, sigma = 1, k = 0.5
Probabilities	Actions

Parameters: c_1 = 1.0, c_2 = 1.0, mu = 2.0, sigma = 1, k = 0.75
Probabilities	Actions

Parameters: c_1 = 1.0, c_2 = 1.0, mu = 2.0, sigma = 1, k = 1.0
Probabilities	Actions

Parameters: c_1 = 1.0, c_2 = 1.0, mu = 2.0, sigma = 4, k = 0.0
Probabilities	Actions

Parameters: c_1 = 1.0, c_2 = 1.0, mu = 2.0, sigma = 4, k = 0.5
Probabilities	Actions

Parameters: c_1 = 1.0, c_2 = 1.0, mu = 2.0, sigma = 4, k = 0.75
Probabilities	Actions

Parameters: c_1 = 1.0, c_2 = 1.0, mu = 2.0, sigma = 4, k = 1.0
Probabilities	Actions

Parameters: c_1 = 1.0, c_2 = 1.0, mu = 2.0, sigma = 8, k = 0.0
Probabilities	Actions

Parameters: c_1 = 1.0, c_2 = 1.0, mu = 2.0, sigma = 8, k = 0.5
Probabilities	Actions

Parameters: c_1 = 1.0, c_2 = 1.0, mu = 2.0, sigma = 8, k = 0.75
Probabilities	Actions

Parameters: c_1 = 1.0, c_2 = 1.0, mu = 2.0, sigma = 8, k = 1.0
Probabilities	Actions

Parameters: c_1 = 1.0, c_2 = 1.0, mu = 4.0, sigma = 1, k = 0.0
Probabilities	Actions

Parameters: c_1 = 1.0, c_2 = 1.0, mu = 4.0, sigma = 1, k = 0.5
Probabilities	Actions

Parameters: c_1 = 1.0, c_2 = 1.0, mu = 4.0, sigma = 1, k = 0.75
Probabilities	Actions

Parameters: c_1 = 1.0, c_2 = 1.0, mu = 4.0, sigma = 1, k = 1.0
Probabilities	Actions

Parameters: c_1 = 1.0, c_2 = 1.0, mu = 4.0, sigma = 4, k = 0.0
Probabilities	Actions

Parameters: c_1 = 1.0, c_2 = 1.0, mu = 4.0, sigma = 4, k = 0.5
Probabilities	Actions

Parameters: c_1 = 1.0, c_2 = 1.0, mu = 4.0, sigma = 4, k = 0.75
Probabilities	Actions

Parameters: c_1 = 1.0, c_2 = 1.0, mu = 4.0, sigma = 4, k = 1.0
Probabilities	Actions

Parameters: c_1 = 1.0, c_2 = 1.0, mu = 4.0, sigma = 8, k = 0.0
Probabilities	Actions

Parameters: c_1 = 1.0, c_2 = 1.0, mu = 4.0, sigma = 8, k = 0.5
Probabilities	Actions

Parameters: c_1 = 1.0, c_2 = 1.0, mu = 4.0, sigma = 8, k = 0.75
Probabilities	Actions

Parameters: c_1 = 1.0, c_2 = 1.0, mu = 4.0, sigma = 8, k = 1.0
Probabilities	Actions

Effect of the acceleration components

Parameters: n = 10, mu = 1.0, sigma = 1, k = 0.0
Probabilities	Actions

Parameters: n = 10, mu = 1.0, sigma = 1, k = 0.5
Probabilities	Actions

Parameters: n = 10, mu = 1.0, sigma = 1, k = 0.75
Probabilities	Actions

Parameters: n = 10, mu = 1.0, sigma = 1, k = 1.0
Probabilities	Actions

Parameters: n = 10, mu = 1.0, sigma = 4, k = 0.0
Probabilities	Actions

Parameters: n = 10, mu = 1.0, sigma = 4, k = 0.5
Probabilities	Actions

Parameters: n = 10, mu = 1.0, sigma = 4, k = 0.75
Probabilities	Actions

Parameters: n = 10, mu = 1.0, sigma = 4, k = 1.0
Probabilities	Actions

Parameters: n = 10, mu = 1.0, sigma = 8, k = 0.0
Probabilities	Actions

Parameters: n = 10, mu = 1.0, sigma = 8, k = 0.5
Probabilities	Actions

Parameters: n = 10, mu = 1.0, sigma = 8, k = 0.75
Probabilities	Actions

Parameters: n = 10, mu = 1.0, sigma = 8, k = 1.0
Probabilities	Actions

Parameters: n = 10, mu = 2.0, sigma = 1, k = 0.0
Probabilities	Actions

Parameters: n = 10, mu = 2.0, sigma = 1, k = 0.5
Probabilities	Actions

Parameters: n = 10, mu = 2.0, sigma = 1, k = 0.75
Probabilities	Actions

Parameters: n = 10, mu = 2.0, sigma = 1, k = 1.0
Probabilities	Actions

Parameters: n = 10, mu = 2.0, sigma = 4, k = 0.0
Probabilities	Actions

Parameters: n = 10, mu = 2.0, sigma = 4, k = 0.5
Probabilities	Actions

Parameters: n = 10, mu = 2.0, sigma = 4, k = 0.75
Probabilities	Actions

Parameters: n = 10, mu = 2.0, sigma = 4, k = 1.0
Probabilities	Actions

Parameters: n = 10, mu = 2.0, sigma = 8, k = 0.0
Probabilities	Actions

Parameters: n = 10, mu = 2.0, sigma = 8, k = 0.5
Probabilities	Actions

Parameters: n = 10, mu = 2.0, sigma = 8, k = 0.75
Probabilities	Actions

Parameters: n = 10, mu = 2.0, sigma = 8, k = 1.0
Probabilities	Actions

Parameters: n = 10, mu = 4.0, sigma = 1, k = 0.0
Probabilities	Actions

Parameters: n = 10, mu = 4.0, sigma = 1, k = 0.5
Probabilities	Actions

Parameters: n = 10, mu = 4.0, sigma = 1, k = 0.75
Probabilities	Actions

Parameters: n = 10, mu = 4.0, sigma = 1, k = 1.0
Probabilities	Actions

Parameters: n = 10, mu = 4.0, sigma = 4, k = 0.0
Probabilities	Actions

Parameters: n = 10, mu = 4.0, sigma = 4, k = 0.5
Probabilities	Actions

Parameters: n = 10, mu = 4.0, sigma = 4, k = 0.75
Probabilities	Actions

Parameters: n = 10, mu = 4.0, sigma = 4, k = 1.0
Probabilities	Actions

Parameters: n = 10, mu = 4.0, sigma = 8, k = 0.0
Probabilities	Actions

Parameters: n = 10, mu = 4.0, sigma = 8, k = 0.5
Probabilities	Actions

Parameters: n = 10, mu = 4.0, sigma = 8, k = 0.75
Probabilities	Actions

Parameters: n = 10, mu = 4.0, sigma = 8, k = 1.0
Probabilities	Actions

Parameters: n = 10, mu = 1.0, sigma = 1, k = 0.0
Probabilities	Actions

Parameters: n = 10, mu = 1.0, sigma = 1, k = 0.5
Probabilities	Actions

Parameters: n = 10, mu = 1.0, sigma = 1, k = 0.75
Probabilities	Actions

Parameters: n = 10, mu = 1.0, sigma = 1, k = 1.0
Probabilities	Actions

Parameters: n = 10, mu = 1.0, sigma = 4, k = 0.0
Probabilities	Actions

Parameters: n = 10, mu = 1.0, sigma = 4, k = 0.5
Probabilities	Actions

Parameters: n = 10, mu = 1.0, sigma = 4, k = 0.75
Probabilities	Actions

Parameters: n = 10, mu = 1.0, sigma = 4, k = 1.0
Probabilities	Actions

Parameters: n = 10, mu = 1.0, sigma = 8, k = 0.0
Probabilities	Actions

Parameters: n = 10, mu = 1.0, sigma = 8, k = 0.5
Probabilities	Actions

Parameters: n = 10, mu = 1.0, sigma = 8, k = 0.75
Probabilities	Actions

Parameters: n = 10, mu = 1.0, sigma = 8, k = 1.0
Probabilities	Actions

Parameters: n = 10, mu = 2.0, sigma = 1, k = 0.0
Probabilities	Actions

Parameters: n = 10, mu = 2.0, sigma = 1, k = 0.5
Probabilities	Actions

Parameters: n = 10, mu = 2.0, sigma = 1, k = 0.75
Probabilities	Actions

Parameters: n = 10, mu = 2.0, sigma = 1, k = 1.0
Probabilities	Actions

Parameters: n = 10, mu = 2.0, sigma = 4, k = 0.0
Probabilities	Actions

Parameters: n = 10, mu = 2.0, sigma = 4, k = 0.5
Probabilities	Actions

Parameters: n = 10, mu = 2.0, sigma = 4, k = 0.75
Probabilities	Actions

Parameters: n = 10, mu = 2.0, sigma = 4, k = 1.0
Probabilities	Actions

Parameters: n = 10, mu = 2.0, sigma = 8, k = 0.0
Probabilities	Actions

Parameters: n = 10, mu = 2.0, sigma = 8, k = 0.5
Probabilities	Actions

Parameters: n = 10, mu = 2.0, sigma = 8, k = 0.75
Probabilities	Actions

Parameters: n = 10, mu = 2.0, sigma = 8, k = 1.0
Probabilities	Actions

Parameters: n = 10, mu = 4.0, sigma = 1, k = 0.0
Probabilities	Actions

Parameters: n = 10, mu = 4.0, sigma = 1, k = 0.5
Probabilities	Actions

Parameters: n = 10, mu = 4.0, sigma = 1, k = 0.75
Probabilities	Actions

Parameters: n = 10, mu = 4.0, sigma = 1, k = 1.0
Probabilities	Actions

Parameters: n = 10, mu = 4.0, sigma = 4, k = 0.0
Probabilities	Actions

Parameters: n = 10, mu = 4.0, sigma = 4, k = 0.5
Probabilities	Actions

Parameters: n = 10, mu = 4.0, sigma = 4, k = 0.75
Probabilities	Actions

Parameters: n = 10, mu = 4.0, sigma = 4, k = 1.0
Probabilities	Actions

Parameters: n = 10, mu = 4.0, sigma = 8, k = 0.0
Probabilities	Actions

Parameters: n = 10, mu = 4.0, sigma = 8, k = 0.5
Probabilities	Actions

Parameters: n = 10, mu = 4.0, sigma = 8, k = 0.75
Probabilities	Actions

Parameters: n = 10, mu = 4.0, sigma = 8, k = 1.0
Probabilities	Actions