nlmixr2auto (version 1.0.0)

phi.calculate: Update pheromone levels for each decision node

Description

Compute pheromone increments (delta_phi) for each node in the ant colony optimization search tree and update the global pheromone levels (phi) based on the ants' paths in the current round.

Usage

phi.calculate(
  r,
  search.space = "ivbase",
  fitness_history = NULL,
  nodeslst.hist = NULL,
  Q = 1,
  alpha = 1,
  rho = 0.5,
  diff_tol = 1,
  phi0 = 2,
  phi_min = 1,
  phi_max = Inf
)

Value

A data frame (node list) with updated phi and delta_phi

for each node.

Arguments

r

Integer. Current optimization round.

search.space

Character, one of "ivbase" or "oralbase". Default is "ivbase".

fitness_history

Data frame. History of ants' fitness values and decision variable selections across rounds.

nodeslst.hist

Data frame. History of node-level pheromone values across previous rounds.

Q

A positive numeric value. Pheromone scaling constant controlling the amount of pheromone deposited by high-quality solutions during each iteration. Defaults to 1.

alpha

A non-negative numeric value. Exponent controlling the influence of pheromone values on the probability of selecting a component during solution construction. Defaults to 1.

rho

Numeric in (0, 1). Pheromone evaporation rate. Higher values increase evaporation, encouraging exploration. Defaults to 0.5.

diff_tol

Numeric. Tolerance threshold controlling when differences in fitness values are treated as meaningful during pheromone updates. Defaults to 1.

phi0

A non-negative numeric value. Initial pheromone value assigned to all nodes at the start of the search. Defaults to 2.

phi_min

A non-negative numeric value. Lower bound for pheromone values, preventing premature convergence. Defaults to 1.

phi_max

A non-negative numeric value. Upper bound for pheromone values, limiting excessive reinforcement. Defaults to Inf.

Author

Zhonghui Huang

Details

The update proceeds as follows:

• Initialize the node list for the given search space with \(phi = 0\).

• Subset the ants from the current round in fitness_history.

• Compute rank-based weights so better-performing ants contribute more: $$\Delta \phi \propto 1 / \mathrm{rank}^{\alpha}.$$

• Extract the decision columns and attach the computed weights to form a working table of ant paths and contributions.

• Map local decision indices to global node numbers using node.no and local.edge.no from the node list.

• For each node, sum contributions from ants that selected the node to obtain \(\Delta \phi\), then update pheromone with evaporation: $$\phi_{\mathrm{new}} = (1 - \rho)\,\phi_{\mathrm{prev}} + \Delta \phi.$$

• Clamp updated \(\phi\) to be between phi_min and phi_max.

See Also

initNodeList, rank_new

Examples

# Define search space
search.space <- "ivbase"
# Example fitness_history from round 1
fitness_history <- data.frame(
  round   = rep(1, 8),
  mod.no  = 1:8,
  no.cmpt = c(1, 1, 2, 2, 3, 3, 2, 2),
  eta.km  = c(0, 0, 0, 0, 0, 0, 0, 0),
  eta.vc  = c(0, 0, 0, 0, 0, 0, 1, 1),
  eta.vp  = c(0, 0, 0, 0, 0, 0, 0, 1),
  eta.vp2 = c(0, 0, 0, 0, 0, 0, 0, 0),
  eta.q   = c(0, 0, 0, 0, 0, 0, 0, 0),
  eta.q2  = c(0, 0, 0, 0, 0, 0, 0, 0),
  mm      = c(0, 0, 0, 0, 0, 0, 1, 0),
  mcorr   = c(0, 0, 0, 0, 0, 0, 0, 0),
  rv      = c(1, 2, 1, 2, 1, 2, 1, 1),
  fitness = c(1243.874, 1200.762, 31249.876, 31202.200,
              51259.286, 51204.839, 61032.572, 41031.825),
  allrank = c(2, 1, 4, 3, 7, 6, 8, 5)
)

# Example node list history
nodeslst.hist <- initNodeList(
  search.space = search.space,
  phi0 = 2
)

 phi.calculate(
  r = 1,
  search.space = search.space,
  fitness_history = fitness_history,
  nodeslst.hist = nodeslst.hist
)