Differential Evolution (SciPy)

Population-based Global Optimization

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Differential Evolution (Storn & Price 1997) is a population-based evolutionary algorithm that mutates trial vectors using scaled differences of population members. HumpDay's DifferentialEvolution matches scipy's defaults: the best/1/bin mutation strategy, dither F drawn per-generation in [0.5, 1.0], recombination probability CR = 0.7, and an L-BFGS-B polish from the best DE point at the end. The polish is what closes the residual gap to scipy on Rosenbrock at modest budgets.

HumpDay's DE at a glance

  • Budget split: 50% DE exploration, 50% L-BFGS-B polish. Tuned to match scipy.differential_evolution on Rosenbrock.
  • Mutation: best/1/bin — base point is the current population best, perturbed by F·(donor1 − donor2).
  • Dither F: sampled uniformly per generation from [0.5, 1.0] (scipy's mutation=(0.5, 1) default).
  • Crossover: binomial with CR = 0.7 and one guaranteed coordinate.
  • Population: pop_size = max(10, min(20, de_budget // 5)).

Interactive 3D Visualization

See Differential Evolution in action on 3D optimization surfaces:

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Requires WebGL support

Instructions: Choose a test function and algorithm, then click Start to watch the step-by-step optimization process.

Auto-selection metadata. Consulted by humpday.minimize() when picking a default algorithm.
  • Overhead tier 1: light (~100µs/iter). Eligible when measured eval_time ≥ 10 µs.
  • Dimensional cap: no cap — linear-in-dim or better.
  • Minimum trials: 10 — baseline minimum.

Implementation Details

Component Details Links
Original Algorithm Rainer Storn & Kenneth Price
Evolutionary algorithm using vector differences
Population-based with mutation, crossover, and selection
Published: 1997 		Paper
Reference Implementation scipy.optimize.differential_evolution
Reference scipy implementation with polish=True (L-BFGS-B finishing step).
Package: scipy 		SciPy Docs Source
HumpDay Python HumpDay DifferentialEvolution
best/1/bin mutation, dither F ∈ [0.5, 1.0], CR = 0.7, then L-BFGS-B polish from the best DE point.
Pure Python; no required dependencies.
File: humpday/optimizers/evolutionary_algorithms.py 		Source
HumpDay JavaScript Browser DifferentialEvolution
Mirrors the Python port: best/1/bin + dither F + L-BFGS-B polish.
Class: DifferentialEvolution 		JS Port

Performance characteristics

  • Best for: Global optimization on multimodal continuous objectives. The combination of population exploration and L-BFGS-B polish is one of the most reliable defaults in HumpDay.
  • Worst for: Tiny budgets where DE can't form a useful population — in those regimes prefer NelderMead or PRIMA.
  • Per generation: pop_size trial vectors are proposed and evaluated.
  • Relative to scipy.differential_evolution at n_trials=200, n_dim=2: HumpDay wins on sphere by a wide margin and on Ackley; a small gap on Rosenbrock (scipy's L-BFGS-B polish is unbudgeted). See SOTA status for the live numbers.

Educational Resources

Algorithm Overview

Differential Evolution uses a simple yet powerful strategy:

  • Population: Maintains multiple candidate solutions
  • Mutation: Creates trial vectors using differences between population members
  • Crossover: Combines target and trial vectors
  • Selection: Keeps the better of target vs. trial

Classic DE/rand/1/bin strategy:

Trial = X_a + F × (X_b - X_c)

Where X_a, X_b, X_c are random population members and F is the scaling factor.