Page 137 - Innovations in Intelligent Machines

128 A. Pongpunwattana and R. Rysdyk
In ECoPS, the fitness function is a complex function designed to capture
the dynamics and uncertainties in the system. The fitness value of a candidate
path is defined as the inverse of the loss function given by

J ˜
L
L = α 1 − (32)
α F
sum
˜
L
where J is the objective function given in Equation 16. α is a scaling factor,
and α F is defined by
sum
N T
F
F
α sum = α i,max (33)
i=1
and
F
α F = max{α (k),k =0, 1,... ,N} (34)
i
i,max
F
where α (k) is time-dependent score weighting function of task i at time step
i
k. If there is no assigned task or all the tasks are completed, the loss function
is given by

J ˜
L
L = α 1 − (35)
α V
where α V is the vehicle cost weighting factor.
Mutation Mechanisms
Mutation mechanisms are essential for the evolution process to improve the
fitness of the candidate path generated in each generation and to eventually
converge to an optimal solution. A mutation has the effect of randomly moving
a candidate solution from one point in the search space to another. Therefore,
an effective set of mutation mechanisms must be able to move a candidate
solution from one point to any point in the search space by applying a series of
these mutation mechanisms. Work by Rudolph [23] shows that this property of
mutation mechanisms is necessary for an evolutionary algorithm to converge.
The selection of the types of mutation mechanisms depends on the pop-
ulation representation. For example, in the representation using waypoints,
mutation can be done by randomly perturbing the physical location of vari-
ous points in the waypoint sequence. Therefore, the mutation of the i th trial
solution can be expressed as
i+µ i i
x = x + G(0,σ ), k = {1, 2,... ,c} (36)
k k
i
where x is the k th waypoint in the original sequence, x i+µ is the k th waypoint
k k
in the mutated sequence, µ is the number of parents in the population, and
i
G(0,σ ) presents a Gaussian random variable with zero mean and standard
i
deviation of σ . This perturbation is applied only to c waypoints chosen at
random where c ∈{0, 1,... ,l i } and l i is the length of the waypoint sequence.