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Documentation Index

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Differential Evolution (DE) is a population-based optimizer for continuous parameter spaces. dplbnDE applies DE to the space of CPT parameters, using CLL as the fitness function.

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The DE cycle

Each generation, every individual goes through mutation, crossover, constraint repair, and selection.
1

Mutation

A mutant vector is formed by combining existing population members. For DE/best/1:
mutant <- vec(best$.params) + F * (vec(r1$.params) - vec(r2$.params))
best is the current best individual, r1 and r2 are randomly selected, and F is the mutation factor.
2

Crossover

A trial vector mixes the mutant with the current individual. Binomial crossover:
cross_points <- runif(dim) > CR
trial[cross_points] <- mutant[cross_points]
3

Constraint repair

Two repairs enforce the probability constraints:
# Fold out-of-bounds values back into [0, 1]
trial <- reflect(trial)
# Renormalize CPT rows to sum to 1
trial <- keepSumFast(trial, group_indices)
4

Selection

The trial replaces the current individual only if its CLL is strictly better:
if (f > fitness[j]) {
  pop[[j]] <- trial
}

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Mutation strategies

StrategyFormulaUsed by
DE/best/1best + F×(r1 − r2)DEbest (pairs=1)
DE/best/2best + F×(r1−r2+r3−r4)DEbest (pairs=2)
DE/rand/1r0 + F×(r1 − r2)DErand (pairs=1)
DE/rand/2r0 + F×(r1−r2+r3−r4)DErand (pairs=2)
current-to-pbestxi + F×(xp−xi) + F×(r1−r2)JADE, L-SHADE, jSO, NL-SHADE-RSP

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Key parameters

Number of candidate solutions. Minimum enforced is 6. Larger NP explores more broadly but costs more evaluations per generation. Default: 40.
Maximum number of generations. Total evaluations ≈ NP × G for classic variants. Default: 100.
Controls mutation step size. Range [0, 2]. Typical values 0.4–0.9. Adaptive variants update F automatically using a Cauchy distribution. Default: 0.5.
Probability of inheriting a dimension from the mutant. Range [0, 1]. Adaptive variants update CR using a Normal distribution. Default: 0.7.

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Adaptive variants

JADE, L-SHADE, jSO, and NL-SHADE-RSP automatically tune F and CR each generation using success histories:
  • F is sampled from a Cauchy distribution centered on the historical mean of successful F values
  • CR is sampled from a Normal distribution centered on the historical mean of successful CR values
  • Successful values are those that produced an improvement — they are stored in a memory of size H (default 6)
L-SHADE and jSO additionally apply Linear Population Size Reduction (LPSR): the population shrinks linearly from NP to a minimum of 4 over the course of evolution, concentrating evaluations on the most promising individuals.

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