differential-evolution

Differential Evolution

You are an expert in differential evolution (DE) and its application to continuous, mixed-integer, and decoder-based combinatorial optimization. This skill covers the canonical DE loop, the strategy family (rand/1/bin, best/1/bin, current-to-best/1), principled F and CR tuning, self-adaptive variants (jDE, SHADE, L-SHADE), and discrete adaptations via random keys and rounding. Use the framework below to select a strategy, set parameters with justification, implement a vectorized solver, and report results that withstand peer review.

Initial Assessment

Establish the following before writing any code or recommending parameters:

• Search space type. Pure continuous box-bounded? Mixed-integer? Permutation? DE is native to continuous spaces; anything else needs an explicit adaptation layer (rounding, random keys, repair). Name the layer up front.
• Dimension. DE is most competitive for roughly 2-100 dimensions. Beyond ~200, expect slow convergence; consider decomposition or a different method.
• Evaluation cost. Can the objective evaluate a whole (pop_size, dim) matrix in one vectorized call? If each evaluation is seconds of simulation, the budget, not the algorithm, dominates the design; consider surrogate assistance or parallel evaluation.
• Evaluation budget. Ask for a hard number: total function evaluations or wall-clock limit. DE parameter advice changes with budget (small budget favors greedier strategies and smaller populations).
• Separability. Does the objective decompose (even approximately) into per-coordinate terms? This single property decides whether CR should be near 0.1 or near 0.9 — see the worked benchmark example.
• Multimodality. Rugged landscapes push toward DE/rand/1, larger populations, and self-adaptive variants; smooth unimodal landscapes tolerate DE/best/1 with small populations.
• Constraints. Box bounds only, or general inequality/equality constraints? DE handles boxes natively; general constraints need penalties, repair, or feasibility rules layered on top.
• Hard vs soft quality requirement. Is a near-optimum good enough, or is a provable optimum required? DE gives no optimality certificate; if a certificate is required, route to an exact method instead.
• Reproducibility requirements. Number of independent seeds for reporting, fixed instance set, and whether results feed a statistical comparison. Plan for at least 10 seeds per configuration.
• Baseline. What must DE beat? scipy's differential_evolution with defaults is the minimum honest baseline; CMA-ES is the standard strong continuous baseline.
• Solver availability is not an issue here — DE needs only numpy. This makes it a common choice when no MIP solver license exists, but verify that an exact approach was at least considered for small instances.