Update pheromone levels for each decision node

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
)

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.

Value

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

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.

Author

Zhonghui Huang

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
)
#>    travel node.no    node.name edge.no local.edge.no   edge.name      phi
#> 1       1       1 compartments       1             1       1Cmpt 2.500000
#> 2       1       1 compartments       2             2       2Cmpt 1.908333
#> 3       1       1 compartments       3             3       3Cmpt 1.309524
#> 4       1       2      eta_vp2       4             0  eta.vp2.no 3.717857
#> 5       1       2      eta_vp2       5             1 eta.vp2.yes 1.000000
#> 6       1       3       eta_q2       6             0   eta.q2.no 3.717857
#> 7       1       3       eta_q2       7             1  eta.q2.yes 1.000000
#> 8       1       4       eta_vp       8             0   eta.vp.no 3.517857
#> 9       1       4       eta_vp       9             1  eta.vp.yes 1.200000
#> 10      1       5        eta_q      10             0    eta.q.no 3.717857
#> 11      1       5        eta_q      11             1   eta.q.yes 1.000000
#> 12      1       6       eta_vc      12             0   eta.vc.no 3.392857
#> 13      1       6       eta_vc      13             1  eta.vc.yes 1.325000
#> 14      1       7           mm      14             0       mm.no 3.592857
#> 15      1       7           mm      15             1      mm.yes 1.125000
#> 16      1       8       eta_km      16             0   eta.km.no 3.717857
#> 17      1       8       eta_km      17             1  eta.km.yes 1.000000
#> 18      1       9        mcorr      18             0    mcorr.no 3.717857
#> 19      1       9        mcorr      19             1   mcorr.yes 1.000000
#> 20      1      10     residual      20             1         add 2.217857
#> 21      1      10     residual      21             2        prop 2.500000
#> 22      1      10     residual      22             3        comb 1.000000
#>    delta_phi     p
#> 1  1.5000000 0.333
#> 2  0.9083333 0.333
#> 3  0.3095238 0.333
#> 4  2.7178571 0.500
#> 5  0.0000000 0.500
#> 6  2.7178571 0.500
#> 7  0.0000000 0.500
#> 8  2.5178571 0.500
#> 9  0.2000000 0.500
#> 10 2.7178571 0.500
#> 11 0.0000000 0.500
#> 12 2.3928571 0.500
#> 13 0.3250000 0.500
#> 14 2.5928571 0.500
#> 15 0.1250000 0.500
#> 16 2.7178571 0.500
#> 17 0.0000000 0.500
#> 18 2.7178571 0.500
#> 19 0.0000000 0.500
#> 20 1.2178571 0.333
#> 21 1.5000000 0.333
#> 22 0.0000000 0.333