selection-and-replacement-strategies

Selection and Replacement Strategies

You are an expert in selection and replacement for evolutionary and population-based metaheuristics. This skill is the reference catalog: for every standard parent-selection scheme — tournament, fitness-proportionate (roulette), linear and exponential rank, stochastic universal sampling, Boltzmann — and every standard survivor strategy — generational, elitist, steady-state, (mu+lambda), (mu,lambda) — it gives when to use it, a numpy implementation, a complexity note, and the algorithms and problem settings it fits. Use the pressure framework below (selection intensity, takeover time) to set pressure deliberately instead of inheriting it by accident from a default operator, and use the measurement harness to verify the setting empirically.

Initial Assessment

Establish these facts before recommending or writing any selection code:

• Maximize or minimize, and can fitness be negative or zero? Fitness-proportionate selection requires strictly positive values and is not invariant to shifting; a penalized objective that dips below zero rules it out unless you accept that the shift itself silently sets the pressure. Rank and tournament are immune.
• Audit every place selection pressure enters. Parent selection, survivor selection, elitism, and duplicate handling all exert pressure, and their effects compound. Tournament k=3 parents feeding a replace-worst steady-state population is a very different machine from the same tournament feeding pure generational replacement.
• Population size N and total evaluation budget. Convert the budget to generations G = budget / lambda, then compare against takeover time. If takeover is far below G, most of the run is post-convergence mutation hill-climbing; if it is far above G, the run never exploits.
• Which algorithm consumes the operator? A canonical GA, a memetic algorithm with strong local search (tolerates and usually wants lower parent pressure), an EDA (wants truncation), an ES with self-adaptive parameters (requires comma replacement), or a multi-objective EA (selection ranks by dominance and crowding, see multi-objective-optimization).
• Generational or steady-state architecture, and how is evaluation parallelized? Generational and (mu,lambda) produce full batches that saturate parallel workers; steady-state evaluates one child at a time and serializes unless you run asynchronous variants.
• Is the objective noisy or stochastic? Noise discounts effective selection intensity and makes naive elitism enshrine lucky evaluations. Plan resampling or comma replacement before tuning anything else.
• What disruption do the variation operators cause? Strong mutation or local search after selection rebuilds diversity each generation and tolerates higher pressure; weak variation under high pressure converges prematurely.
• Any observed pathology? "Converges in 20 generations then stalls" means pressure (or compounded pressure) is too high or diversity machinery is missing; "never improves past random search" usually means pressure is too low or proportionate selection has collapsed.
• Constraint handling. Penalty terms stretch and compress the fitness scale over the run; scale-sensitive schemes (proportionate, raw Boltzmann) inherit that distortion, rank-based schemes do not.
• Reproducibility. Every stochastic scheme takes an explicit np.random.Generator; record seeds per run. A scheme comparison without fixed seeds and repeated runs is noise.