arXiv subjects

Dimitar Pilev

Publications and source records attributed to Dimitar Pilev.

2 recordsLinked to original sources

arXiv2026

MSC-CMA-ES: Structure-Aware Restarts for CMA-ES via Cyclic Nearest-Better Basin Discovery

CMA-ES behaves, per restart, primarily as a local optimizer; multimodal search relies on restart strategies such as IPOP and BIPOP, which draw every restart uniformly and reuse no information from previous evaluations. Multi-Start Clustering CMA-ES (MSC-CMA-ES) makes restarts structure-aware: in alternating cycles, a Sobol pre-sample is partitioned into approximate basins of attraction by nearest-better clustering, restarts are seeded basin by basin with locally scaled step-sizes and population sizes, redundant basin visits are detected and excluded, and the remaining budget is spent on a budget-bounded, tolerance-disabled local refinement of the best-so-far solution. We evaluate the method on the four CEC suites (2014, 2017, 2020, and 2022) at their official budgets, across ten (suite, dimension) cells with dimensions 5--30, with 51 runs per function, and compare it with BIPOP-CMA-ES and five differential-evolution algorithms (ARRDE, jSO, j2020, NL-SHADE-RSP, and L-SRTDE). Read per function class over the $D\leq 20$ cells, the results split three ways. On composition functions MSC-CMA-ES attains the best value on all aggregate measures, with $2.7\times$ the fixed-budget target coverage of BIPOP-CMA-ES -- the highest composition coverage of any algorithm evaluated -- and leads in most suites, dimensions, and budgets. On unimodal and simple-multimodal functions it attains the best median error in aggregate but the lowest deep-target coverage, with orderings varying by suite and dimension. On hybrid functions both CMA algorithms trail the leading DE algorithms. All results and scripts are publicly available.

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arXiv2026

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

We study first-hitting times in Differential Evolution (DE) through a conditional hazard frame work. Instead of analyzing convergence via Markov-chain transition kernels or drift arguments, we ex press the survival probability of a measurable target set $A$ as a product of conditional first-hit probabilities (hazards) $p_t=\Prob(E_t\mid\mathcal F_{t-1})$. 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-$p$best/1 mutation, we construct a checkable algorithmic witness event $\mathcal L_t$ 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-generati on success probabilities.

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