DynDEGA

Generational GAs explore; steady-state GAs exploit. Fixed hybrids make you guess the switch point. DEGA unifies both regimes, and Method 2 is a trigger built from quantities the GA already tracks: when the rolling mean of elite-centroid displacement falls under 2% of its first value and elite fitness variance under 10% of its initial value, the algorithm flips from generational to steady-state, once, and keeps its population. Across XOR, Iris and Wine it fired in all 60 runs, succeeded 20/20 on every benchmark, and matched the best hand-tuned schedule within a standard deviation.

Two ways to replace a population

A generational GA replaces the whole population every iteration. Turnover is high, selection pressure per individual is weak, and the search stays broad. A steady-state GA replaces one or two individuals at a time. Pressure is strong, the population changes slowly, and promising regions get exploited fast, sometimes before the search has seen enough of the landscape.

Neither wins everywhere, and their relative merit changes during a single run. The obvious hybrid, start generational and switch to steady-state at a fixed generation, works, but it moves the problem: now you have to pick the switch point, and a switch point that suits one problem is wrong for the next.

DEGA, and a trigger you don't have to tune

DEGA (Dynamic Evolution with Generational–Steady-State Adaptation) is a single framework that contains both regimes with shared representation, fitness, selection and variation operators. The only thing that changes at the switch is how many individuals are replaced per outer iteration.

Method 2 decides when to switch from quantities the algorithm already tracks:

• the elite centroid, the mean position of the top fraction of the population, and its displacement from one iteration to the next, δ_t;
• the elite fitness variance, v_t.

The trigger fires, once, when the 10-iteration rolling mean of δ_t falls below 2% of the first non-zero displacement and v_t falls below 10% of its initial value, after a minimum number of generational iterations. Both are normalised by their own reference values, so the same thresholds apply across problems without recalibration. The centroid condition says the elite region has stopped moving; the variance condition says the elite set has actually collapsed rather than merely circling a stable mean. The result is denoted DynDEGA-M2.

Evaluation

Three neural-network weight-optimisation problems of increasing dimensionality (XOR, Iris, Wine), 20 matched-seed runs each, against pure GGA, pure SSGA and six fixed-schedule DEGA variants that switch at predetermined quartiles. Paired Wilcoxon signed-rank tests.

	Iris	Wine	XOR
DynDEGA-M2 successes	20 / 20	20 / 20	20 / 20
Mean result	0.9967 acc.	0.9986 acc.	≈ 1.0000 (1 − MSE)
Trigger fired at	12.9% of budget	7.4%	26.6%

On every benchmark the dynamic variant lands within one reported standard deviation of the best fixed-schedule mean, and the trigger fired in all 60 runs without anyone choosing a switch point.

Why I care about this

Most adaptive evolutionary methods tune scalar parameters inside one replacement regime. Switching the regime itself has had far less attention, and the few hybrids that exist make the practitioner pick the moment. A parameter-light, interpretable trigger that reads the search state directly is the kind of tool I want in every optimiser I build, including the ones that schedule physicians.