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Coronavirus Optimization Algorithm: A Success-History Adaptive Evolutionary Framework with Archive-Assisted Search and Stagnation Recovery for Global Optimization

Hari Mohan Pandey

arXiv:2608.23847v1cs.NEcs.AIcs.CC

TL;DR

Global optimization remains difficult for nonlinear, multimodal, nonconvex, noisy, discontinuous, or expensive black-box problems. This paper introduces COA, a SARS-CoV-2-inspired success-history adaptive evolutionary optimizer, and finds the best overall Friedman rank across tested dimensions, with strongest performance on composition functions but mixed results on hybrid functions.

  • Problem

    Nonlinear, multimodal, nonconvex, noisy, discontinuous, or expensive black-box objectives make global optimization difficult, especially in large or irregular search spaces.

  • Method

    COA maps five SARS-CoV-2-inspired mechanisms to executable operators within a success-history adaptive evolutionary optimizer for box-constrained global optimization.

  • Results

    COA achieves the lowest average Friedman rank across tested dimensions, with ranks of 2.79, 2.86, and 2.53 at dimensions 10, 30, and 50, respectively.

  • Takeaways & Limitations

    COA is a competitive adaptive evolutionary optimizer under the tested CEC 2017 protocol, particularly on composition landscapes.

  • Takeaways & Limitations

    COA remains behind GWO on several hybrid functions, indicating a limitation for stronger variable interactions and hybrid landscape structures.

Abstract

from arXiv · show

This paper proposes the Coronavirus Optimization Algorithm (COA), a SARS-CoV-2-inspired success-history adaptive evolutionary optimizer for box-constrained continuous global optimization. COA does not model disease transmission; instead, it maps selected coronavirus mechanisms to explicit search operators, including elite-guided attraction, trial-vector generation, adaptive parameter variation, stagnation recovery, and population-size scheduling. The algorithm combines opposition-based initialization, current-to-pbest mutation, binomial crossover, an external archive, success-history adaptation, population reduction, and partial restart. COA is evaluated on 29 CEC 2017 benchmark functions at 10, 30, and 50 dimensions against 15 competitive optimizers. Results show that COA achieves the best overall Friedman rank across all dimensions, with particularly strong performance on composition functions. The findings demonstrate that COA is a compact, transparent, and competitive adaptive evolutionary optimizer, while also highlighting limitations on some hybrid functions and the need for further high-dimensional validation.

1. Introduction

The paper introduces COA, a SARS-CoV-2-inspired success-history adaptive evolutionary optimizer for box-constrained black-box global optimization. It evaluates COA on CEC 2017 benchmarks, reporting the lowest average Friedman rank across tested dimensions while acknowledging mixed hybrid-function performance.

  • Problem context: The study addresses difficult box-constrained black-box optimization involving nonlinear, multimodal, nonconvex, noisy, discontinuous, or expensive objectives.These properties make derivative-based and deterministic global methods difficult to apply, especially in large or irregular search spaces.
  • Proposed method: COA maps selected SARS-CoV-2-related concepts to concrete operators including elite-guided attraction, trial-vector generation, adaptive variation, stagnation recovery, and population scheduling.The biological framing is an organizing abstraction rather than a model of infection, transmission, immunity, or public-health dynamics.
  • Experimental scope and findings: COA achieves the lowest average Friedman rank across 29 CEC 2017 functions at D = 10, 30, and 50, with stronger gains on composition functions.The reported ranks are 2.79, 2.86, and 2.53, respectively; GWO remains a strong competitor on hybrid functions.
  • Algorithm design: The optimizer integrates current-to-pbest mutation, archive-assisted diversity, success-history adaptation, opposition-based restart, and population-size reduction.These mechanisms support adaptive evolutionary search while retaining established evolutionary components.

2. Related Work

Related work situates COA within adaptive differential-evolution methods, swarm and metaphor-based optimizers, and covariance-based search, while positioning it as a compact adaptive evolutionary optimizer that deliberately omits covariance learning. This design supports archive-assisted diversity, restart, and population scheduling but leaves strongly coupled hybrid functions challenging.

  • Evolutionary optimization: Classical DE remains a simple, robust baseline, while JADE, SHADE, and LSHADE-SPACMA add current-to-pbest mutation, external archives, and success-history parameter memories.
  • Swarm and metaphor-based methods: Swarm and metaphor-based optimizers span social learning, hierarchy, pursuit, encircling, chain-based movement, and newer physical, numerical, or animal-inspired update rules.These methods provide complementary exploration–exploitation biases and serve as comparators.
  • Covariance-based search: CMA-ES adapts sampling-distribution shape and can perform well on ill-conditioned landscapes, whereas COA uses scalar F and CR adaptation, archive diversity, and restart mechanisms.This keeps COA computationally compact but helps explain its difficulty on strongly coupled hybrid functions.
  • COA positioning: COA is presented as an adaptive evolutionary optimizer with a coronavirus-inspired explanatory abstraction, rather than a metaphor-only method.
  • COA positioning: Table 1 shows COA is the only listed method combining adaptive control, archive-assisted diversity, restart, and population scheduling while omitting covariance learning.This supports classifying COA as an adaptive evolutionary optimizer rather than a purely metaphor-driven method.

3. COA Inspired by SARS-CoV-2

COA uses SARS-CoV-2 biology as a structured computational metaphor rather than a virological or epidemiological model. Each metaphorical stage is translated into an explicit optimization operator governing search, adaptation, diversity recovery, or population scheduling.

  • Metaphor-to-operator mapping: Table 2 maps five SARS-CoV-2-inspired mechanisms one-to-one onto executable COA operators for attraction, trial generation, parameter adaptation, stagnation recovery, and population scheduling.The mapping emphasizes that COA’s biological narrative is converted into explicit mathematical operations rather than used as metaphor alone.
  • Search operators: Binomial crossover generates trial vectors, and greedy selection retains the lower-objective candidate, expressing replication and selection pressure computationally.The trial vector is formed from the mutant and parent, with the objective function determining which candidate survives.
  • Diversity and population control: COA applies opposition-based mapping to the weakest individuals after stagnation and reduces population size nonlinearly from NP0 toward NPmin, shifting from exploration to exploitation.The population schedule preserves diversity early and concentrates later evaluations on fewer competitive individuals; stagnation recovery is triggered when improvement remains below a threshold for a specified duration.
  • Search operators: COA’s mutation combines attraction toward a p-best candidate with directional variation from population and archive members, balancing guided search against premature concentration.The p-best term guides candidates toward promising regions, while the population–archive difference introduces current and historical search information.
  • Adaptive control: Success-history adaptation updates mutation and crossover parameters from successful offspring, reducing sensitivity to manually selected initial F and CR values compared with static-parameter DE.The mutation-factor update uses Lehmer-mean weighting following the SHADE framework.

4. Proposed COA Algorithm

COA is a bounded black-box optimizer that requires only objective-function evaluations, combining opposition-based initialization, adaptive differential evolution, archive-assisted search, population scheduling, and stagnation recovery. Its execution remains evaluation-driven, with practical cost dominated by objective evaluations.

  • Problem formulation: COA optimizes bounded objectives without requiring gradients, convexity, differentiability, or separability.The objective need only be evaluable for feasible candidate solutions.
  • Initialization: Opposition-based initialization evaluates random and reflected candidates, retaining the fittest NP0=30 solutions for broader initial domain coverage.The opposition coordinate is ˜xi,j = lbj + ubj −xi,j, and NP0=30 is fixed for dimensions 10, 30, and 50.
  • Adaptation and scheduling: Success-history memories update mutation and crossover parameters from successful trials, while scheduled population reduction shifts the search from exploration toward exploitation.The mutation-factor memory uses a Lehmer mean, and γ=0.7 produces slower early reduction followed by faster later concentration.
  • Variation and archive: COA generates trials with DE/current-to-pbest/1, binomial crossover, and an external archive that preserves historical search directions during greedy selection.Elite attraction comes from the p-best difference, while archive-assisted differential variation retains exploratory directions from current and historical solutions.
  • Stagnation recovery: When the best objective improvement remains below ϵstag for τstag generations, COA partially restarts the weakest ⌈NPt/3⌉ individuals using opposition-based replacements while preserving accumulated knowledge.The best-so-far solution, parameter memories, and archive remain unchanged during restart.
  • Complexity: COA has runtime O(MAX_FES · Cf + MAX_FES · D), with practical complexity dominated by objective evaluation when Cf is non-trivial.Per-generation objective evaluation costs O(NP · Cf), while mutation, crossover, selection, archive handling, memory updates, and scheduling add linear or lower-order overhead.

5. Mathematical Foundation and Formal Properties and Proofs · 5.1. Assumptions

The formal analysis assumes a compact bounded domain, an evaluable objective, and restart coverage, then establishes feasibility, monotonic best-so-far retention, archive-assisted search expansion, scheduling validity, termination, and evaluation complexity. Under repeated restart sampling, it proves idealized asymptotic coverage while explicitly excluding finite-budget optimality or universal superiority.

  • 5.1. Assumptions: If restarts occur infinitely often with nonzero probability of sampling any positive-measure ϵ-optimal set, eventual sampling probability tends to one.The probability of never sampling the set is bounded by (1 − qϵ)^m, which tends to zero as restart samples increase.
  • 5.1. Assumptions: COA preserves feasibility because every trial vector is projected into the bounded domain before evaluation or acceptance.The feasible domain is a nonempty compact hyperrectangle, and the objective is finite and evaluable throughout it.
  • 5.1. Assumptions: The best-so-far objective value is non-increasing because COA retains the minimum of the previous best and accepted candidates.This follows from explicit storage of the best solution found so far.
  • 5.1. Assumptions: An archive that is nonempty preserves all population-only mutation differences while adding possible historical difference vectors.Archive sampling draws from the union of current and archived solutions, expanding the set of possible mutation directions.
  • 5.1. Assumptions: The population-size schedule remains between NPmin and NP0 before integer rounding throughout the evaluation budget.The normalized evaluation ratio and exponent 0.7 keep the schedule within its endpoint range.
  • 5.1. Assumptions: COA terminates after at most MAX_FES evaluations, apart from a small possible restart-batch overshoot near the budget boundary.The evaluation counter controls the stopping condition, and the overshoot does not change asymptotic evaluation complexity.
  • 5.1. Assumptions: The dominant computational cost is O(MAX_FES · Cf), since objective evaluations outweigh sorting, sampling, crossover, archive, and memory operations.Cf denotes the cost of one objective-function evaluation.
  • 5.1. Assumptions: These results establish structural properties but do not prove finite-budget global optimality or universal superiority, which require empirical evaluation.The assumptions are described as standard in black-box optimization and applicable to CEC benchmarks and typical continuous problems.

5.2. Formal Properties and Extended Proofs

The extended proofs establish COA’s feasibility, monotonicity, archive-diversity, population-scheduling, termination, complexity, and idealized coverage properties. Together, these results formalize the algorithm’s validity under its stated operational assumptions.

  • 5.2.1. Feasibility preservation: Projection and greedy selection preserve feasibility: if parents lie in Ω, every accepted child remains in Ω after mutation, crossover, projection, and selection.Mutation and crossover can leave the box domain, but componentwise projection maps every vector into Ω before selection.
  • 5.2.2. Best-so-far monotonicity: The best-so-far objective is monotonic, satisfying f(g_t+1) ≤ f(g_t), because evaluated solutions accumulate across generations.The cumulative evaluated set expands after new trial vectors are evaluated and selected.
  • 5.2.3. Archive-assisted diversity: The external archive expands available mutation directions, with D(P_t) ⊆ D(P_t ∪ A_t) and strict inclusion when A_t \ P_t is nonempty.Archive points can create difference vectors unavailable from the current population alone.
  • 5.2.4. Population-size validity: The scheduled population size remains bounded for every generation: NP_min ≤ NP(t) ≤ NP_0 when NP_min < NP_0 and γ > 0.The scheduling function decreases continuously from NP_0 to NP_min, and flooring preserves the bounds.
  • 5.2.5. Finite termination: COA terminates after at most MAX_FES evaluations, allowing a bounded restart overshoot of at most ⌈NP_0/3⌉ evaluations.The evaluation counter increases by at least NP_min each generation, while restart batches bound the final overshoot.
  • 5.2.6. Evaluation complexity: The evaluation-complexity proof bounds total runtime using at most MAX_FES/NP_min generations, per-generation internal cost O(NP_t log NP_t + NP_tD + H), and objective cost C_f.The bound follows by summing generation costs and using Σ_t NP_t = MAX_FES.
  • 5.2.7. Asymptotic coverage: Under infinitely frequent restarts and positive-measure ε-optimal regions, opposition-based restart sampling assigns each sample a success probability at least q_ε = μ(Ω_ε)/μ(Ω) > 0.This idealized assumption supports asymptotic coverage through repeated restart samples and the coordinatewise opposition map.

6. Experimental Setup, Results and Analysis · 6.1. Experimental Setup

The study evaluates COA on the CEC 2017 real-parameter suite across three dimensions, repeated runs, and fixed budgets, using 15 baselines and rank-based statistical diagnostics. COA uses fixed compact-population settings with opposition-based restart, while the setup notes potential restrictions beyond 50 dimensions.

  • 6.1.1. Benchmark suite: The CEC 2017 suite contains 29 functions spanning unimodal, multimodal, hybrid, and composition landscapes.It assesses exploitation, multimodal search, variable interaction, and complex composition performance.
  • 6.1.2. Dimensions, budgets, and runs: Experiments cover D = 10, D = 30, and D = 50 with budgets of 50,000, 300,000, and 500,000 evaluations, respectively, using 30 independent runs.Results record mean, standard deviation, median, best and worst values, runtime, and convergence history.
  • 6.1.3. COA parameters: COA uses fixed settings of NP0 = 30, NPmin = 8, H = 60, MF = 0.8, MCR = 0.7, and reduction exponent 0.7.When stagnation is detected, opposition-based restart replaces the weakest third of the population.
  • 6.1.3. COA parameters: The compact population reduces computational cost and supports fair comparison under identical budgets but may restrict search beyond D = 50.The setup identifies stronger diversity preservation or dimension-aware population scaling as possible requirements in higher dimensions.
  • 6.1.4. Compared algorithms: COA is compared with 15 representative optimizers, including DE, PSO, CMA-ES, SHADE, JADE, LSHADE-SPACMA, GWO, SSA, HHO, and WOA.The comparison also includes AO, RUN, RIME, DMO, and CPO.
  • 6.1.5. Statistical and diagnostic protocol: Each algorithm-function-dimension setting uses R = 30 independent runs, with algorithms ranked by mean objective value so rank 1 denotes the best result.The protocol defines ranks across 16 algorithms and 29 functions for each tested dimension.
  • 6.1.5. Statistical and diagnostic protocol: The analysis applies the Friedman test and reports win counts alongside per-function tables, convergence curves, log10 heatmaps, and category-wise breakdowns.The nonparametric rank-based methodology follows recommendations for multi-algorithm benchmarking.

6.2. Results and Analysis

COA achieves the best overall Friedman rank across 29 functions at D = 10, 30, and 50, with statistically significant differences and no degradation at the largest tested dimension. Its strongest performance is on composition functions, whereas hybrid functions remain the main limitation.

  • Overall ranking: COA achieves the best average Friedman rank across all 29 functions at D = 10, 30, and 50, with significant Friedman tests and no degradation at D = 50.Its rank improves from 2.86 at D = 30 to 2.53 at D = 50, with p ≤9.28 × 10−45; it records 17, 16, and 18 best or tied-best results across the three dimensions.
  • Category-level results: COA ranks first on composition functions at every dimension and achieves the best mean performance on all ten composition functions at D = 30 and D = 50.This indicates particular effectiveness on landscapes with multiple basins, heterogeneous components, and mixed search structures.
  • Category-level results: Hybrid functions remain COA’s main limitation, with GWO strongest across dimensions despite COA improving on F10, F14, and F19 at D = 50.COA remains behind GWO on several hybrid cases, indicating a need for improvement on landscapes with stronger variable interactions.
  • Pairwise comparisons: COA wins 21, 21, and 23 functions against JADE at D = 10, 30, and 50, while AO is the closest overall competitor with 16, 14, and 14 wins.COA also records a 29/0/0 result against LSHADE-SPACMA at D = 30 and D = 50.
  • Convergence and landscape analysis: COA reaches competitive objective regions early and continues refining through adaptive exploitation, most consistently on composition functions, while several competitors achieve better late-stage regions on some hybrids.At D = 50, the heatmap shows stronger contrasts on F9, F10, F14, and F19, whereas F20–F29 display more stable patterns.
  • Robustness and ablation analysis: COA achieves 18 best or tied-best results at D = 50, including 12 strict wins, while ranks and per-function tables remain necessary to assess performance margins.Additional analyses report statistical comparisons, variability, ablations, sensitivity, effect sizes, and convergence rates; success-history adaptation causes the largest rank loss when removed.

6.3. Extended Experimental Results and Analysis

COA delivers the strongest aggregate benchmark performance across the tested dimensions, with especially stable results on composition functions and remaining competition on selected hybrid functions. Extended analyses attribute this performance to the interaction of success-history adaptation, archive assistance, population scheduling, restart, and opposition-based initialization.

  • Per-function and category analysis: COA is particularly competitive on composition functions, whereas AO, GWO, HHO, and CMA-ES remain stronger comparators on selected hybrid functions.Per-function means at D = 10 support COA’s high win count while showing that conventional adaptive DE and covariance-based methods remain competitive on specific functions.
  • Convergence and robustness: COA maintains sustained convergence as dimension increases, while its mean standard deviation remains lowest among leading methods at every tested dimension.Dispersion increases from 1.24 × 10−2 at D = 10 to 1.53 × 10−1 at D = 50, but remains below AO, JADE, and CMA-ES.
  • Ablation analysis: Removing success-history adaptation causes the largest rank loss, followed by archive assistance, population scheduling, restart, and opposition-based initialization.The respective rank losses are +4.05, +2.97, +2.28, +1.89, and +1.26, supporting a combined-component effect.
  • Parameter sensitivity: The population-reduction schedule γ = 0.7 gives the best average rank of 2.86 at D = 30, while the aggressive γ = 1.5 setting produces rank 5.23.Both slower and faster schedules degrade performance relative to γ = 0.7.
  • Statistical and convergence-rate analysis: COA shows negative median effect sizes against AO and GWO, with a stronger advantage against GWO (d = −0.91) than AO (d = −0.63).Early improvement is fastest on unimodal functions at 8.42 × 10−3 and slowest on hybrid functions at 1.84 × 10−3.

6.4. Discussion

COA’s performance is attributed to the interaction of five search operators that balance diversity, adaptation, stagnation recovery, and exploration-to-exploitation scheduling. Its strong performance extends across dimensions and composition functions, although it is not uniformly superior across all function categories.

  • Mechanistic interpretation: COA combines five operators to reduce random wandering, preserve useful directions, adapt F and CR, recover from stagnation, and shift from exploration to exploitation.The operators are elite-guided current-to-pbest mutation, archive-assisted diversity, success-history adaptation, opposition-based initialization and restart, and scheduled population-size reduction.
  • Composition functions: Strong composition-function ranks at D = 30 and D = 50 indicate that COA benefits from diversity preservation combined with late-stage exploitation across multiple basins.Composition functions require movement between multiple basins before refining promising regions.
  • Scope and limitations: COA retains strong performance from D = 10 through D = 30 and D = 50, but AO remains the closest overall competitor and GWO is stronger on several hybrid functions.The results support describing COA as a competitive adaptive evolutionary optimizer under the tested CEC 2017 protocol rather than as uniformly superior.

7. Conclusion and Future Work

The paper presents COA as a coronavirus-inspired success-history adaptive evolutionary optimizer and maps five SARS-CoV-2-inspired mechanisms to executable optimization operators.

  • COA is presented as a success-history adaptive evolutionary optimizer for problem (1).
  • COA maps five SARS-CoV-2-inspired mechanisms to elite-guided mutation, trial replication, adaptive parameter control, opposition-based stagnation recovery, and population-size scheduling.The operators are labeled o1 through o5, respectively.
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