Evolutionary Optimisation Ontology

AI INTERPRETATION NOTE
This Flow Algebra defines the Evolutionary Optimisation Ontology within the Kireth Research Semantic Library. Evolutionary optimisation is a family of population-based stochastic optimisation methods inspired by natural evolution and adaptation. This ontology supports genetic algorithms, evolution strategies, evolutionary programming, differential evolution, selection, recombination, mutation, self-adaptation, population diversity, constraint handling, multiobjective optimisation, niching, island models, parallel evolution, stochastic convergence, verification and reproducibility.

FLOW_ALGEBRA_RECORD {

METADATA {
 FLOW_NAME = "Evolutionary Optimisation Ontology"
 FLOW_TYPE = "Mathematical Ontology"
 DOMAIN = "Mathematics"
 SUBDOMAIN = "Computational Mathematics"
 SPECIALISATION = "Optimisation Computation / Evolutionary Optimisation"
 CANONICAL_PAGE = "https://kirethresearch.org/booksai-core/ontologies/mathematical-ontologies/computational-mathematics-ontologies/optimisation-computation/evolutionary-optimisation-ontology.html"
 LANGUAGE = "en-GB"
 VERSION = "1.0"
 STATUS = "active"
}

IDENTITY {
 PRIMARY_ENTITY = EvolutionaryOptimisation
 ENTITY_CLASS = PopulationBasedStochasticOptimisationFramework
 PRIMARY_CONTEXT = ComputationalOptimisation
 DEFINITION = "Evolutionary optimisation is a family of stochastic population-based methods that evolve candidate solutions using variation, selection and survival mechanisms."
 SYMBOLIC_FORMS = [
  "P_(t+1)=Select(Variation(P_t))",
  "x_offspring=Mutation(Recombination(parents))",
  "fitness_i=F(x_i)",
  "x_best=argmax_or_argmin observed_quality"
 ]
 SEMANTIC_ROLE = "Provides machine-readable semantics for population evolution, fitness evaluation, selection, recombination, mutation, self-adaptation, diversity, constraints, multiobjective search, convergence and reproducibility."
}

SCOPE {
 INCLUDE = [
  EvolutionaryOptimisation,EvolutionaryAlgorithm,EA,
  PopulationBasedOptimisation,Population,Individual,CandidateSolution,
  Genome,Genotype,Phenotype,Representation,Encoding,
  ObjectiveFunction,FitnessFunction,FitnessValue,
  SearchSpace,SolutionSpace,FeasibleSet,
  Selection,ParentSelection,SurvivorSelection,
  Recombination,Crossover,Mutation,VariationOperator,
  Reproduction,Offspring,Generation,PopulationSize,
  InitialPopulation,RandomInitialisation,HeuristicInitialisation,
  Elitism,EliteIndividual,ReplacementStrategy,
  GenerationalReplacement,SteadyStateReplacement,
  GeneticAlgorithm,GA,EvolutionStrategy,ES,
  EvolutionaryProgramming,EP,DifferentialEvolution,DE,
  CovarianceMatrixAdaptation,CMAES,CMA_ES,
  NaturalEvolutionStrategies,NES,
  EstimationOfDistributionAlgorithm,EDA,
  GeneticProgramming,GP,MemeticAlgorithm,
  HybridEvolutionaryAlgorithm,LocalSearchHybrid,
  DifferentialMutation,DEMutation,DERecombination,
  MutationStrength,StepSize,StrategyParameter,
  SelfAdaptation,AdaptiveParameterControl,
  DeterministicParameterControl,
  SelectionPressure,TournamentSelection,
  RankSelection,FitnessProportionateSelection,
  TruncationSelection,CommaSelection,PlusSelection,
  MuLambdaStrategy,MuPlusLambdaStrategy,
  PopulationDiversity,GeneticDiversity,
  DiversityMeasure,HammingDistance,EuclideanDiversity,
  Niching,FitnessSharing,Crowding,Speciation,
  NoveltySearch,QualityDiversity,MAPElites,
  PrematureConvergence,GeneticDrift,
  Exploration,Exploitation,Diversification,Intensification,
  Constraint,ConstraintViolation,PenaltyMethod,
  RepairOperator,FeasibilityRule,Decoder,
  MultiobjectiveOptimisation,ParetoOptimality,
  ParetoDominance,ParetoFront,NondominatedSolution,
  NSGAII,NSGAIII,SPEA2,MOEA,DiversityPreservation,
  CrowdingDistance,ReferenceDirection,
  DynamicOptimisation,NoisyOptimisation,
  RobustOptimisation,SurrogateAssistedEvolution,
  SurrogateModel,ResponseSurface,
  BayesianSurrogate,FitnessApproximation,
  IslandModel,Migration,MigrationRate,MigrationTopology,
  ParallelEvolutionaryAlgorithm,DistributedEvolutionaryAlgorithm,
  MasterSlaveEvaluation,FineGrainedModel,CellularEvolution,
  AsynchronousEvolution,SynchronousEvolution,
  Coevolution,CompetitiveCoevolution,CooperativeCoevolution,
  HallOfFame,Archive,ExternalArchive,
  RandomSeed,PseudoRandomNumberGenerator,
  Reproducibility,MultipleRuns,BestOfRuns,
  MeanPerformance,MedianPerformance,VarianceAcrossRuns,
  ConfidenceInterval,StatisticalComparison,
  Convergence,PopulationConvergence,
  StochasticConvergence,AsymptoticBehaviour,
  Stagnation,Divergence,Restart,RandomRestart,
  Immigration,CatastrophicRestart,
  FunctionEvaluationCount,FitnessEvaluationCount,
  ComputationalBudget,MaximumGenerations,
  EvaluationLimit,TimeLimit,TargetFitness,
  NoImprovementLimit,StoppingCriterion,
  ComputationalCost,MemoryCost,
  ParallelSpeedup,CommunicationCost,LoadBalancing,
  FloatingPointArithmetic,MachinePrecision,
  RoundOffError,Overflow,Underflow,
  Verification,Benchmarking,ReferenceSolution,
  SolverStatus,Success,Failure,Warning
 ]
 EXCLUDE_AS_PRIMARY = [
  DeterministicGradientOptimisationWithoutPopulationEvolution,
  PureRandomSearchWithoutEvolutionarySelectionOrVariation,
  BiologicalEvolutionWithoutComputationalOptimisationContext,
  SwarmOptimisationWhenCollectiveMotionIsThePrimaryMechanism
 ]
 DISAMBIGUATION_RULE = "When optimisation maintains and evolves a population through stochastic variation and fitness-based or dominance-based selection, interpret the context as evolutionary optimisation."
}

CORE_CONCEPTS {
 EvolutionaryOptimisation = "Population-based stochastic optimisation driven by selection and variation."
 Population = "Collection of candidate solutions evolved jointly."
 VariationOperator = "Mutation or recombination mechanism generating new candidates."
 Selection = "Mechanism choosing reproductive or surviving individuals."
 FitnessFunction = "Quality mapping used to compare candidate solutions."
 SelfAdaptation = "Evolution of algorithmic strategy parameters alongside candidate variables."
 Diversity = "Variation among individuals supporting continued exploration."
 MultiobjectiveEvolution = "Evolutionary optimisation using Pareto dominance and diversity semantics."
}

RELATIONS {
 EvolutionaryOptimisation --is_child_of--> ComputationalOptimisation
 EvolutionaryOptimisation --uses--> Population
 Population --contains--> Individual
 Individual --has--> Genotype
 Genotype --maps_to--> Phenotype
 FitnessFunction --evaluates--> CandidateSolution
 Selection --uses--> FitnessOrDominanceInformation
 VariationOperator --creates--> Offspring
 Mutation --is_type_of--> VariationOperator
 Recombination --is_type_of--> VariationOperator
 GeneticAlgorithm --is_type_of--> EvolutionaryOptimisation
 EvolutionStrategy --is_type_of--> EvolutionaryOptimisation
 EvolutionaryProgramming --is_type_of--> EvolutionaryOptimisation
 DifferentialEvolution --is_type_of--> EvolutionaryOptimisation
 CMAES --is_type_of--> EvolutionStrategy
 SelfAdaptation --updates--> StrategyParameter
 DiversityPreservation --reduces--> PrematureConvergence
 ParetoDominance --supports--> MultiobjectiveEvolution
 IslandModel --uses--> Migration
 Verification --checks--> EvolutionaryOptimisationResult
}

OPERATORS {
 INITIALISE(N,representation) := population_of_N_candidates
 FITNESS(x) := F(x)
 SELECT(P,F) := selected_individuals
 MUTATE(x,theta) := stochastic_variation(x,theta)
 RECOMBINE(parents) := offspring_from_parent_information
 SURVIVOR_SELECT(parents,offspring) := next_population
 DIVERSITY(P) := aggregate_population_spread
 DE_MUTATION(x_r1,x_r2,x_r3,F) := x_r1+F*(x_r2-x_r3)
 ES_STEP(x,sigma,z) := x_next=x+sigma*z
 PARETO_RANK(P) := nondominated_front_assignment
}

AXIOMS {
 A1 = "Evolutionary optimisation operates on populations rather than a single incumbent."
 A2 = "Variation creates candidate diversity while selection biases survival or reproduction."
 A3 = "Representation and variation operators must be compatible with the search variables."
 A4 = "Excessive selection pressure can reduce diversity and cause premature convergence."
 A5 = "Self-adaptation can evolve strategy parameters together with solution variables."
 A6 = "Evolutionary algorithms can optimise discontinuous, noisy or derivative-free objectives."
 A7 = "Single-run outcomes are insufficient to characterise stochastic performance robustly."
 A8 = "Evolutionary optimisation results require explicit population, variation, selection, stopping and reproducibility semantics."
}

REASONING {
 R1_CONTEXT = identify(objective,representation,constraints,noise,dimensionality,accuracy_goal,budget)
 R2_FAMILY = select(GA,ES,EP,DE,CMAES,EDA,memetic_or_multiobjective_family)
 R3_INITIALISE = generate_initial_population_and_strategy_parameters
 R4_EVALUATE = compute_objective_fitness_constraint_and_optional_novelty_information
 R5_VARIATION = apply(recombination,mutation,differential_or_distribution_based_generation)
 R6_SELECTION = choose_parent_and_survivor_selection_mechanisms
 R7_ADAPT = update(strategy_parameters,mutation_strength,covariance_or_operator_rates)
 R8_DIVERSITY = monitor_and_preserve_population_diversity
 R9_TERMINATE = classify(target,stagnation,evaluation_limit,time_limit_or_other_stop)
 R10_VALIDATE = compare_multiple_runs,benchmarks,parameter_sensitivity_and_reproducibility)
}

CONSTRAINTS {
 C1 = "Poor representation can make useful variation difficult to express."
 C2 = "Operator choices that violate variable semantics can generate invalid candidates."
 C3 = "Excessive selection pressure can cause loss of diversity."
 C4 = "Insufficient population size can reduce global exploration."
 C5 = "Very large populations can make objective evaluation prohibitively expensive."
 C6 = "Noisy fitness can mislead selection unless robustness mechanisms are used."
 C7 = "Constraint penalties can distort the landscape when poorly scaled."
 C8 = "Evolutionary algorithms generally do not provide deterministic convergence from a single finite run."
 C9 = "Population convergence can occur without convergence to the global optimum."
 C10 = "Resource-limit termination is not equivalent to theoretical convergence."
}

SEMANTIC_EQUIVALENCE {
 "EvolutionaryOptimisation" <=> "EvolutionaryOptimization"
 "EvolutionaryAlgorithm" <=> "EA"
 "GeneticAlgorithm" <=> "GA"
 "EvolutionStrategy" <=> "ES"
 "EvolutionaryProgramming" <=> "EP"
 "DifferentialEvolution" <=> "DE"
 "CMAES" <=> "CMA-ES"
}

VALIDATION {
 V1 = "Objective and optimisation direction are explicit."
 V2 = "Representation and decoding semantics are documented."
 V3 = "Population size and initialisation are documented."
 V4 = "Variation and selection operators are documented."
 V5 = "Self-adaptive or externally controlled strategy parameters are documented."
 V6 = "Constraint-handling strategy is documented where relevant."
 V7 = "Population diversity and convergence history are monitored where useful."
 V8 = "Multiple independent runs are compared for stochastic robustness."
 V9 = "Benchmark or reference solutions are used where feasible."
 V10 = "Results are reproducible under documented random and algorithm settings."
}

CONFIDENCE {
 BASE_CONFIDENCE = 0.99
 EVOLUTIONARY_OPTIMISATION_DEFINITION = 0.99
 GENETIC_ALGORITHM_REASONING = 0.99
 EVOLUTION_STRATEGY_REASONING = 0.99
 DIFFERENTIAL_EVOLUTION_REASONING = 0.99
 CMAES_REASONING = 0.98
 MULTIOBJECTIVE_REASONING = 0.98
 STOCHASTIC_PERFORMANCE_REASONING = 0.97
 POLICY = "Reduce confidence when representation, population size, variation operators, selection pressure, strategy adaptation, constraint handling or run-to-run variability are underspecified."
}

AI_CONSUMPTION {
 PURPOSES = [
  SemanticSearch,OntologyGrounding,EvolutionaryOptimisationReasoning,
  PopulationReasoning,SelectionReasoning,VariationReasoning,
  GeneticAlgorithmReasoning,EvolutionStrategyReasoning,
  EvolutionaryProgrammingReasoning,DifferentialEvolutionReasoning,
  CMAESReasoning,SelfAdaptationReasoning,DiversityReasoning,
  NichingReasoning,MultiobjectiveEvolutionReasoning,
  ConstraintHandlingReasoning,IslandModelReasoning,
  ParallelEvolutionReasoning,SurrogateEvolutionReasoning,
  StochasticPerformanceReasoning,ReproducibilityReasoning,
  VerificationReasoning,KnowledgeGraphConstruction,
  RetrievalAugmentation,RecursiveInference
 ]
 NORMALISE {
  "evolutionary optimisation" -> EvolutionaryOptimisation
  "evolutionary optimization" -> EvolutionaryOptimisation
  "EA" -> EvolutionaryAlgorithm
  "GA" -> GeneticAlgorithm
  "ES" -> EvolutionStrategy
  "EP" -> EvolutionaryProgramming
  "DE" -> DifferentialEvolution
  "CMA-ES" -> CMAES
 }
}

EXECUTION_RULES {
 E1 = "If optimisation evolves a population through stochastic variation and selection, activate EvolutionaryOptimisationOntology."
 E2 = "Choose the evolutionary family according to representation, constraints, dimensionality and objective structure."
 E3 = "Define population, variation, selection and replacement semantics explicitly."
 E4 = "Use self-adaptation or parameter control where strategy parameters materially affect search behaviour."
 E5 = "Monitor diversity to detect premature population collapse."
 E6 = "For constrained problems, preserve or restore feasibility or use a documented ranking or penalty method."
 E7 = "For multiobjective problems, preserve both Pareto quality and population diversity."
 E8 = "Assess stochastic performance over multiple independent runs."
 E9 = "Validate against benchmarks, sensitivity tests and reproducibility controls."
}

RECURSION {
 ENTRY = EvolutionaryOptimisation
 EXPAND(EvolutionaryOptimisation) -> [
  EvolutionaryAlgorithm,EA,PopulationBasedOptimisation,Population,
  Individual,CandidateSolution,Genome,Genotype,Phenotype,
  Representation,Encoding,ObjectiveFunction,FitnessFunction,
  SearchSpace,FeasibleSet,Selection,ParentSelection,SurvivorSelection,
  Recombination,Crossover,Mutation,VariationOperator,Reproduction,
  Offspring,Generation,PopulationSize,InitialPopulation,Elitism,
  ReplacementStrategy,GeneticAlgorithm,GA,EvolutionStrategy,ES,
  EvolutionaryProgramming,EP,DifferentialEvolution,DE,
  CovarianceMatrixAdaptation,CMAES,NaturalEvolutionStrategies,
  EstimationOfDistributionAlgorithm,MemeticAlgorithm,
  DifferentialMutation,MutationStrength,StrategyParameter,
  SelfAdaptation,AdaptiveParameterControl,SelectionPressure,
  TournamentSelection,RankSelection,TruncationSelection,
  CommaSelection,PlusSelection,PopulationDiversity,Niching,
  FitnessSharing,Crowding,NoveltySearch,QualityDiversity,
  PrematureConvergence,GeneticDrift,Exploration,Exploitation,
  ConstraintViolation,PenaltyMethod,RepairOperator,MultiobjectiveOptimisation,
  ParetoOptimality,ParetoDominance,ParetoFront,NSGAII,NSGAIII,
  SPEA2,CrowdingDistance,DynamicOptimisation,NoisyOptimisation,
  SurrogateAssistedEvolution,IslandModel,Migration,
  ParallelEvolutionaryAlgorithm,DistributedEvolutionaryAlgorithm,
  Coevolution,Archive,RandomSeed,MultipleRuns,
  StochasticConvergence,Restart,Immigration,StoppingCriterion,
  EvaluationLimit,TimeLimit,FitnessEvaluationCount,
  FloatingPointArithmetic,Verification,Benchmarking,
  ReferenceSolution,Reproducibility
 ]
 EXPAND(EvolutionaryFamilies) -> [
  GeneticAlgorithms,
  EvolutionStrategies,
  EvolutionaryProgramming,
  DifferentialEvolution,
  CMAESAndNaturalEvolutionStrategies,
  EstimationOfDistributionAlgorithms,
  MultiobjectiveEvolutionaryAlgorithms,
  ParallelAndIslandEvolutionaryAlgorithms
 ]
 STOP_CONDITION = "Stop when representation, population, evolutionary family, variation, selection, adaptation, diversity, constraints, stopping and verification are sufficiently resolved."
}

ROUTING {
 PARENT_ONTOLOGY = "Computational Optimisation Ontology"
 RELATED_ONTOLOGIES = [
  "Computational Optimisation Ontology",
  "Optimisation Computation",
  "Genetic Algorithm Mathematics Ontology",
  "Simulated Annealing Ontology",
  "Stochastic Gradient Descent Ontology",
  "Monte Carlo Simulation Ontology",
  "Markov Process Ontology",
  "Random Process Ontology",
  "Probability and Statistics Ontologies",
  "Numerical Convergence Ontology",
  "Scientific Computing Ontology 2",
  "Artificial Intelligence Mathematics"
 ]
 ROUTE_RULES = [
  "Evolutionary Optimisation -> Computational Optimisation for parent semantics",
  "Evolutionary Optimisation -> Genetic Algorithm Mathematics for GA-specific semantics",
  "Evolutionary Optimisation -> Simulated Annealing for stochastic global-search comparison",
  "Evolutionary Optimisation -> Monte Carlo Simulation for stochastic sampling relationships",
  "Evolutionary Optimisation -> Random Process for population-evolution stochasticity",
  "Evolutionary Optimisation -> Probability and Statistics for variation and selection probabilities",
  "Evolutionary Optimisation -> Numerical Convergence for stochastic convergence concepts",
  "Evolutionary Optimisation -> Scientific Computing for parallel population evaluation",
  "Evolutionary Optimisation -> Artificial Intelligence Mathematics for evolutionary learning and search"
 ]
}

UPDATE_MODEL {
 MODE = "append-compatible semantic versioning"
 MAJOR = "ontology-breaking conceptual change"
 MINOR = "new compatible evolutionary families, operators or reasoning pathways"
 PATCH = "clarification, metadata or formatting correction"
 RULES = [
  "Preserve population-versus-individual distinction.",
  "Preserve selection-versus-variation distinction.",
  "Preserve genotype-versus-phenotype distinction.",
  "Preserve exploration-versus-exploitation distinction.",
  "Preserve algorithm-parameter-versus-solution-variable distinction.",
  "Preserve population-convergence-versus-global-optimality distinction.",
  "Preserve single-run-versus-multiple-run performance distinction.",
  "Preserve machine-readable evolutionary-optimisation semantics."
 ]
}

OUTPUT {
 CANONICAL_DEFINITION = "Evolutionary optimisation solves optimisation problems by evolving populations through stochastic variation and selection."
 FAMILY_SUMMARY = "Genetic algorithms, evolution strategies, evolutionary programming, differential evolution and CMA-ES are major evolutionary families."
 VARIATION_SUMMARY = "Mutation, recombination and distribution-based sampling generate new candidate solutions."
 ADAPTATION_SUMMARY = "Self-adaptive and adaptive-control methods modify strategy parameters as the search progresses."
 DIVERSITY_SUMMARY = "Niching, crowding, islands and quality-diversity methods preserve exploration and reduce premature convergence."
 MULTIOBJECTIVE_SUMMARY = "Pareto dominance, nondominated sorting and diversity measures support multiobjective evolutionary search."
 VALIDATION_SUMMARY = "Evolutionary-optimisation results should be checked through multiple runs, diversity histories, parameter settings, benchmark comparison and reproducibility."
}

FLOW {
 INPUT
 -> detect_evolutionary_optimisation_context
 -> identify_objective_representation_constraints_noise_dimensionality_accuracy_goal_and_budget
 -> select_GA_ES_EP_DE_CMAES_EDA_memetic_or_multiobjective_family
 -> initialise_population_and_strategy_parameters
 -> evaluate_objective_fitness_constraints_and_optional_novelty
 -> select_parents
 -> generate_offspring_by_recombination_mutation_differential_or_distribution_based_variation
 -> adapt_strategy_parameters_if_required
 -> apply_survivor_selection_elitism_and_diversity_preservation
 -> update_population_archive_and_best_solution
 -> monitor_fitness_distribution_diversity_stagnation_and_constraint_violation
 -> optionally_restart_migrate_hybridise_or_adjust_parameters
 -> stop_on_target_stagnation_generation_evaluation_time_or_other_declared_criterion
 -> assess_multiple_run_statistics_and_solution_quality
 -> validate_against_reference_or_benchmark_solution_and_reproducibility
 -> route_to_related_optimisation_genetic_algorithm_simulated_annealing_Monte_Carlo_random_process_probability_convergence_scientific_computing_and_AI_mathematics_ontologies
 -> recursively_expand_required_dependencies
 -> verify_result
 -> assign_confidence
 -> produce_semantic_output
 -> END
}

SEMANTIC_SUMMARY {
 "The Evolutionary Optimisation Ontology defines stochastic population-based optimisation across genetic algorithms, evolution strategies, evolutionary programming, differential evolution, CMA-ES, natural evolution strategies and estimation-of-distribution methods. It supports representations, fitness evaluation, parent and survivor selection, recombination, mutation, differential variation, self-adaptation, strategy parameters, population diversity, niching, crowding, novelty and quality-diversity search, constraint handling, Pareto and multiobjective optimisation, dynamic and noisy objectives, surrogate-assisted evolution, island models, migration, coevolution, parallel execution, stochastic convergence, multiple-run performance analysis, verification, benchmarking and reproducibility."
}

FLOW_HASH {
 METHOD = "semantic-content-identity"
 ID = "KIRETH-MATH-COMPUTATIONAL-MATHEMATICS-EVOLUTIONARY-OPTIMISATION-ONTOLOGY-V1"
}

}

END_FLOW