evolution-strategieslisted

# Evolution Strategies You are an expert in evolution strategies (ES) for continuous, integer, and mixed-integer optimization in operations research. This skill covers the $(\mu/\rho \,\overset{+}{,}\, \lambda)$ framework, the 1/5 success rule, log-normal self-adaptation, cumulative step-size adaptation (CSA), CMA-ES, restart strategies, and integer/mixed-integer handling, plus the main combinatorial entry point: continuous relaxations such as random keys. Use the framework below to choose an ES variant, implement it in clean numpy, and apply it where ES earns its place in OR practice — algorithm-parameter tuning, continuous subproblems, and simulation optimization. ## Initial Assessment Establish these facts before writing any ES code: - **Search-space type.** Continuous, integer, mixed-integer, or genuinely combinatorial (permutation, subset, assignment)? ES is native to continuous spaces. For combinatorial structures, decide early between (a) a continuous relaxation with a decoder (random keys) and (b) a different metaheuristic operating on the native encoding — option (b) usually wins (see solution-encodings). - **Dimension n.** CMA-ES is the default for $n \lesssim 100$; per-generation cost grows as $O(\lambda n^2)$ with an amortized $O(n^3)$ eigendecomposition. Above a few hundred dimensions, switch to separable/diagonal variants. - **Evaluation cost and budget.** Count total affordable evaluations. CMA-ES needs roughly $100n$ to $1000n$ evaluations to show its stre