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scipy.optimize.differential_evolution is a stochastic, population-based method for searching for a minimum of a multivariable function within specified bounds. It is useful when a problem is difficult to solve with gradient-based methods, but it does not guarantee that a run will find the true global minimum. You provide an objective function and bounds, then choose settings that balance search effort, evaluation cost, and problem constraints.
What differential evolution does
The SciPy project describes differential_evolution as a function that “finds the global minimum of a multivariate function.” In practice, treat that as the method’s aim, not a guarantee: it is a stochastic global-search technique, and its result depends on the objective, bounds, and run configuration. Unlike gradient-based methods, it does not use derivatives. It can therefore be useful for challenging bounded objectives, but may require substantially more function evaluations than a conventional local optimizer. See the SciPy differential_evolution API reference.
The algorithm maintains a population of candidate points. It mutates population members to generate trial candidates, evaluates those trials, and retains a trial when it improves on its corresponding candidate. SciPy provides built-in strategies, with best1bin identified in the API as a good starting point for many systems; a custom strategy callable is also available. The SciPy implementation provides further detail.
Write the objective and define bounds
The objective must accept a vector of variables and return a scalar value to minimize. Additional fixed parameters can be passed through args. Supply one bound per variable, either as a sequence of lower-and-upper pairs or as a Bounds object. Bounds are part of the problem definition: choose them to reflect the feasible domain rather than using arbitrarily broad ranges.
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import numpy as np
from scipy.optimize import differential_evolution
def objective(x):
# Replace with the scalar cost or error you want to minimize.
return (x[0] - 2)**2 + (x[1] + 1)**2
result = differential_evolution(
objective,
bounds=[(-5, 5), (-5, 5)],
)
print(result.x) # best point found
print(result.fun) # objective value at that point
print(result.success) # whether the configured stopping condition was met
print(result.message) # termination explanationThe call returns an OptimizeResult. Inspect the point and objective value, along with the termination status and message; do not interpret successful termination by itself as proof of a global optimum. SciPy’s optimization tutorial includes examples using Rosenbrock and Ackley functions, among other optimization workflows.
Choose a computation budget before tuning
Population search can make many objective calls. The API gives the following maximum evaluation-count formula when polishing is disabled:
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(maxiter + 1) * popsize * (N - N_equal)
Here, N is the number of variables and N_equal is the number whose lower and upper bounds are equal. This is a budget calculation, not a runtime estimate or accuracy promise. The optional polishing stage can add evaluations.
The default population initialization is Latin hypercube. The API also supports Sobol, Halton, random, and user-supplied populations. Stopping is based on the standard deviation of population energies in relation to the configured absolute and relative tolerances. When tuning a real problem, consider the variables’ bounds, initialization, stopping tolerances, population size, and maximum generations together: tightening one setting does not by itself guarantee a better answer.
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Configure strategy, constraints, and polishing
Strategy and search settings
The API exposes strategy, maximum generations (maxiter), population-size multiplier (popsize), mutation, recombination, relative and absolute tolerances, initialization, and an optional initial point. Begin with a built-in strategy such as best1bin, then change settings in response to the objective and the available evaluation budget. A custom strategy callable is supported, but callable strategies and expanded callback support were added in SciPy 1.12.0; verify the documentation for the version installed in your environment.
Constraints and integer variables
Constraints and an integrality option are supported. Use these when feasibility or discrete-valued variables are part of the actual problem rather than trying to repair an unconstrained result afterward. The precise constraint definitions and accepted option forms are documented in the API reference.
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Polishing
Polishing is enabled by default. For an unconstrained problem, SciPy uses L-BFGS-B; when constraints are present, it uses trust-constr. Polishing seeks a locally improved result after the population search and can incur extra evaluations. A custom polish callable is available starting in SciPy 1.17.0. If you provide one, you are responsible for ensuring it respects bounds, constraints, and integrality. The API also notes workers-related polishing behavior added in SciPy 1.15.0, so check the version-specific reference when relying on that behavior.
Choose immediate, parallel, or vectorized evaluation
With updating='immediate', the best candidate can update during a generation. With updating='deferred', it updates at the end of the generation. The workers and vectorized options are compatible with deferred updating and may override the requested updating mode.
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- Parallel workers: Consider this when objective evaluations are expensive enough to offset process overhead. For inexpensive objectives, parallel execution can be slower.
- Vectorization: Consider this when your objective can evaluate a batch of candidates together; it may reduce interpreter overhead.
- Serial immediate updating: This allows the best candidate to update within the generation, but is not compatible with every execution mode.
Neither parallel nor vectorized execution is universally faster; the useful choice depends on objective cost and how the objective is implemented. SciPy’s examples demonstrate parallel workers and vectorization, but are documentation examples rather than comparative performance tests.
Check your SciPy version and interpret results carefully
The current SciPy reference in the versioned v1.18.0 manual records version-sensitive options: callable strategy customization and expanded callback support in 1.12.0, workers-related polishing behavior in 1.15.0, and callable polishing in 1.17.0. Check the documentation matching your installed SciPy release before using these features, because defaults and available options can change.
The official API does not establish a general-purpose benchmark statistic or a numerical success rate for differential evolution. Its evaluation formula describes a maximum count under specified conditions, not expected speed, reliability, or typical accuracy. The API credits Storn and Price with the method and cites their 1997 paper, “Differential Evolution — a Simple and Efficient Heuristic for Global Optimization over Continuous Spaces.” For an algorithm-focused specialist book rather than a SciPy manual, Springer catalogs Differential Evolution: A Practical Approach to Global Optimization by Kenneth V. Price, Rainer M. Storn, and Jouni A. Lampinen.
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