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Paper · 2601.11499 · 2026

On the Probability of First Success in Differential Evolution: Hazard Identities and Tail Bounds

A Preprint, Dimitar Pilev

arXiv · PDF · Open in the Atlas

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We lifted 11 functions out of this paper's own repositories and ran 0 of them in a sandbox. "Ran" means the function executed on a synthesized input and returned a value. It is not a reproduction of the paper's results.

RepositoryRoleRan
snenovgmailcom/lshade_hazard_project canonical 0 of 11
FunctionStatusWhere it lives
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cec_wrap Not yet run snenovgmailcom/lshade_hazard_project/benchmarks/benchmark.py
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convert_history_for_pickle Not yet run snenovgmailcom/lshade_hazard_project/benchmarks/benchmark.py
code served (permissive licence) · get_code("e0493e1857cb2f34")
extract_best_curve Not yet run snenovgmailcom/lshade_hazard_project/analysis/plot_quasi_morse.py
code served (permissive licence) · get_code("5b12c12c0233990b")
extract_timeslice Not yet run snenovgmailcom/lshade_hazard_project/analysis/gamma0_validate.py
code served (permissive licence) · get_code("1c75367c4528a8f8")
gamma0_comb Not yet run snenovgmailcom/lshade_hazard_project/analysis/gamma0_validate.py
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gamma0_full Not yet run snenovgmailcom/lshade_hazard_project/analysis/gamma0_validate.py
code served (permissive licence) · get_code("5de918d2712e468c")
get_f_star_cec2017 Not yet run snenovgmailcom/lshade_hazard_project/analysis/plot_quasi_morse.py
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load_runs Not yet run snenovgmailcom/lshade_hazard_project/analysis/plot_quasi_morse.py
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pad_and_envelope Not yet run snenovgmailcom/lshade_hazard_project/benchmarks/benchmark.py
code served (permissive licence) · get_code("18c9355e7acae597")
ts Not yet run snenovgmailcom/lshade_hazard_project/analysis/validate_quasi_morse.py
code served (permissive licence) · get_code("7e213629171c1cf7")

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Abstract

We study first-hitting times in Differential Evolution (DE) through a conditional hazard framework. Instead of analyzing convergence via Markov-chain transition kernels or drift arguments, we express the survival probability of a measurable target set A as a product of conditional first-hit probabilities (hazards) p t = P(E t | F t-1 ). This yields distribution-free identities for survival and explicit tail bounds whenever deterministic lower bounds on the hazard hold on the survival event. For the L-SHADE algorithm with current-to-pbest/1 mutation, we construct a checkable algorithmic witness event L t under which the conditional hazard admits an explicit lower bound depending only on sampling rules, population size, and crossover statistics. This separates theoretical constants from empirical event frequencies and explains why worst-case constant-hazard bounds are typically conservative. We complement the theory with a Kaplan-Meier survival analysis on the CEC2017 benchmark suite. Across functions and budgets, we identify three distinct empirical regimes: (i) strongly clustered success, where hitting times concentrate in short bursts; (ii) approximately geometric tails, where a constant-hazard model is accurate; and (iii) intractable cases with no observed hits within the evaluation horizon. The results show that while constant-hazard bounds provide valid tail envelopes, the practical behavior of L-SHADE is governed by burst-like transitions rather than homogeneous per-generation success probabilities.

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