The state of a system s(t) is defined as the logarithm base 10 of the binary vectors selleck products of the agents. A turned-on agent was represented with 1 while a shut-down agent will be represented with 0. The representation of the state of the system is shown Inhibitors,Modulators,Libraries in Equation (1):s(t)=log(s)(1)where s(t) is the state of the system at time t, and s is base-10 representation of the binary number of the state of the system.3.?Optimization Algorithms3.1. Particle Swarm OptimizationThe Particle Swarm Optimization (PSO) algorithm was proposed by Kennedy and Everhart [8,9]. It is based on the choreography of a flock of birds [8�C13], wing a social metaphor [14] where each individual brings their knowledge to get a better solution.
There are three factors that influence the change of the particle state or behavior:Knowledge of the environment or adaptation is the importance given to past experiences.Experience or local memory is the local importance given to best result found.The experience of its neighbors or neighborhood memory is Inhibitors,Modulators,Libraries the importance given to the best result achieved by their neighbors.The basic PSO algorithm [9] uses two equations. Equation (2), which is used to find the velocity, describes the size and direction of the step that will be taken by the particles and is based on the knowledge achieved until that moment.vi=wvi+c1r1(l Besti?xi)+c2r2(g Best?xi)(2)where:vi is the velocity Inhibitors,Modulators,Libraries of the i-th particle, i = 1, 2 ��, N,N is the number of the population,w is the environment adjustment factor,c1 is the memory factor of neighborhood,c2 is memory factor,r1 and r2 are random numbers in range [0, 1],lBest is the best local particle founded for the i-th particle,gBest is the best general particle founded until that moment for all particles.
Equation (3) updates the current position of the particle to the new position using the result of the velocity Inhibitors,Modulators,Libraries equation.xi=xi+vi(3)where xi is the position of the i-th particle.The PSO algorithm [9] is shown in the Algorithm 1:Algorithm 1 PSO Algorithm.Data:P [3, 6] (number of particles), c1 R, c2 R, w [0, 1], G (maximum allowed function evaluations).Result:GBest (best solution found)Initialize particles ‘ position and velocity randomly;For g = 1 to G doRecalculate best particles position gBestSelect the local best Dacomitinib position lBestFor each Xig, i = 1, ��, P doRecalculate particle speedRecalculate particle position3.2.
Binary PSOBinary PSO [13,14] was designed to work in binary spaces. Binary PSO select the lBest and gBest particles in the http://www.selleckchem.com/products/Perifosine.html same way as PSO. The main difference between binary PSO and normal PSO are the equations that are used to update the particle velocity and position. The equation for updating the velocity is based on probabilities but these probabilities must be in the range [0, 1]. A mapping is established for all real values of velocity to the range [0, 1]. The normalization Equation (4) used here is a sigmoid function.