Samples

This section provides additional sample files for the HeuristicLab 3.3 Optimizer some of which are included as demo samples in the Optimizer.

Travelling Salesman

• Genetic Algorithm - TSP: A genetic algorithm which solves rge "ch130" travelling salesman problem (imported from TSPLIB)
• Island Genetic Algorithm - TSP: An island genetic algorithm which solves the "ch130" traveling salesman problem (imported from TSPLIB)
• Tabu Search - TSP: A tabu search algorithm that solves the "ch130" TSP (imported from TSPLIB)

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Genetic Algorithm - TSP

This sample demonstrates how to employ a genetic algorithm to optimize a travelling salesman problem instance, namely "ch130" from the ​TSP Lib.

Algorithm: Genetic Algorithm?

Algorithm Parameters:

• PopulationSize: 100
• Elites: 1
• MutationProbability: 5%
• MaximumGenerations: 1000
• Selector: ProportionalSelector
• Crossover: Crossover2 (cf. Affenzeller, M. et al. 2009. Genetic Algorithms and Genetic Programming - Modern Concepts and Practical Applications. CRC Press. p. 135)
• Mutator: InversionManipulator

Problem: Travelling Salesman Problem?

Problem Parameters:

• BestKnownQuality: 6110
• BestKnownSolution: The best known solution of this TSP instance (cf. TSP Lib)
• Coordinates: The x and y coordinates of the cities
• DistanceMatrix: null
• Evaluator: TSPRoundedEuclideanPathEvaluator?
• Maximization: False
• SolutionCreator: RandomPermutationCreator
• UseDistanceMatrix: True

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Island Genentic Algorithm - TSP

Algorithm: Island Genetic Algorithm

Algorithm Parameters:

• Analyzer: MultiAnalyzer
• Crossover: !OrderCrossover2
• Elites: 1
• EmigrantsSelector: BestSelector
• ImmigrationReplacer: WorstReplacer
• IslandAnalyzer: MultiAnalyzer
• MaximumGenerations: 1000
• MigrationInterval: 50
• MigrationRate: 25%
• Migrator: UnidirectionalRingMigrator
• MutationProbability: 5%
• Mutator: InversionManipulator
• NumberOfIslands: 5
• PopulationSize: 100
• Seed: -
• Selector: ProportionalSelector
• SetSeedRandomly: True

Problem: Travelling Salesman Problem?

Problem Parameters:

• BestKnownQuality: 6110
• BestKnownSolution: The best known solution of this TSP instance (cf. TSP Lib)
• Coordinates: The x and y coordinates of the cities
• DistanceMatrix: null
• Evaluator: !TSPRoundedEuclideanPathEvaluator
• Maximization: False
• SolutionCreator: RandomPermutationCreator
• UseDistanceMatrix: True

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Tabu Search - TSP

Algorithm: Tabu Search

Algorithm Parameters:

• Analyzer: MultiAnalyzer
• MaximumIterations: 1000
• MoveEvaluator: TSPInversionMoveRoundedEuclideanPathEvaluator
• MoveGenerator: StochasticInversionMultiMoveGenerator
• MoveMaker: InversionMoveMaker
• SampleSize: 500
• Seed: -
• SetSeedRandomly: True
• TabuChecker: InversionMoveSoftTabuCriterion
• TabuMaker: InversionMoveTabuMaker
• TabuTenure: 60

Problem: Travelling Salesman Problem?

Problem Parameters:

• BestKnownQuality: 6110
• BestKnownSolution: The best known solution of this TSP instance (cf. TSP Lib)
• Coordinates: The x and y coordinates of the cities
• DistanceMatrix: null
• Evaluator: TSPRoundedEuclideanPathEvaluator
• Maximization: False
• SolutionCreator: RandomPermutationCreator
• UseDistanceMatrix: True

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Real-valued Test Functions

• Evolution Strategy - Griewank: An evolution strategy which solves the 10-dimensional Griewank test function
• Simulated Annealing - Rastrigin: A simulated annealing algorithm that solves the 2-dimensional Rastrigin test function

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Evolution Strategy - Griewank

A pre-defined evolution strategy which solves the 10-dimensional [TestFunctions#GriewankFunction Griewank test function]. HeuristicLab 3 provides a set of real valued test functions for benchmarking purposes. For a full overview please go the [TestFunctions Test Functions] wiki page.

Algorithm: Evolution Strategy?

Algorithm Parameters:

• Population Size: 20
• Children: 500
• MaximumGenerations: 200
• ParentsPerChild: 5
• PlusSelection: False (Comma Selection)
• Recombinator: AverageCrossover
• Mutator: NormalAllPositionsManipulator

Problem: Single Objective Test Function

Problem Parameters:

• BestKnownQuality: 0
• BestKnownSolution: [0;0;0;0;0;0;0;0;0;0]
• Bounds: [-600, 600]
• Evaluator: GriewankEvaluator
• Maximization: False
• ProblemSize: 10
• SolutionCreator: UniformRandomRealVectorCreator

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Simulated Annealing - Rastrigin

Algorithm: Simulated Annealing

Algorithm Parameters:

• Analyzer: MultiAnalyzer
• AnnealingOperator: ExponentialDiscreteDoubleValueModifier
• EndTemperature: 1E-06
• InnerIterations: 50
• MaximumIterations: 1000
• MoveEvaluator: RastriginAdditiveMoveEvaluator
• MoveGenerator: StochasticNormalMultiMoveGenerator
• MoveMaker: AdditiveMoveMaker
• Seed: -
• SetSeedRandomly: True
• StartTemperature: 1

Problem: Single Objective Test Function

Problem Parameters:

• BestKnownQuality: 0
• BestKnownSolution: [0;0]
• Bounds: ([-5, 12], [-5,12])
• Evaluator: RastriginEvaluator
• Maximization: False
• ProblemSize: 2
• SolutionCreator: UniformRandomRealVectorCreator

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Genetic Programming

• Genetic Programming - Artificial Ant Problem: A standard genetic programming algorithm to solve an artificial ant problem (Santa-Fe ant trail)
• Genetic Programming - Symbolic Regression (Boston Housing): A standard genetic programming algorithm to solve a symbolic regression problem (Boston Housing dataset)
• Genetic Programming - Symbolic Regression (Tower): A genetic programming algorithm to solve a symbolic regression problem (Tower dataset)
• Genetic Programming - Symbolic Regression (Mackey-Glass): A genetic programming algorithm to create a one-step prediction model for a chaotic time series (Mackey-Glass time series)
• Genetic Programming - Symbolic Classification (Wisconsin): A genetic programming algorithm to solve a symbolic classification problem (Wisconsin Diagnostic Breast Cancer dataset)
• Genetic Programming - Symbolic Classification (Mammography): A genetic programming algorithm to solve a symbolic classification problem (Mammography dataset)
• Genetic Programming - Even Parity (4 inputs): A genetic programming algorithm to synthesize the boolean even parity function with 4 binary inputs
• Genetic Programming - Multiplexer (11 inputs): A genetic programming algorithm to synthesize the boolean multiplexer function with 11 binary inputs

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Genetic programming - Artificial Ant Problem

SGP_SantaFe.hl

Algorithm: Genetic Algorithm?

Algorithm Parameters:

• Analyzer: MultiAnalyzer
• Crossover: SubtreeCrossover - An operator which performs subtree swapping crossover
• Elites: 1
• MaximumGenerations: 100
• MutationProbability: 15%
• Mutator: MultiSymbolicExpressionTreeManipulator
• Population Size: 500
• Seed: -
• Selector: TournamentSelector
• SetSeedRandomly: True

Problem: Artificial Ant Problem?

Problem Parameters:

• ArtificialAntExpressionGrammar: IfFoodAhead, Prog2, Prog3, Right, Left, Move
• BestKnownQuality: 89
• Evaluator: ArtificialAntEvaluator
• MaxExpressionDepth: 6
• MaxExpressionLength: 50
• MaxFunctionArguments: 3
• MaxFunctionDefinitions: 3
• Maximization: True
• MaxTimeSteps: 600
• SolutionCreator: ProbabilisticTreeCreator
• World: 32x32 grid, 89 randomly scattered food items

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Genetic programming - Symbolic Regression (Boston Housing)

Algorithm: Genetic Algorithm?

Algorithm Parameters:

Problem: Symbolic Regression Problem

Problem Parameters:

• BestKnownQuality: null
• DataAnalysisProblemData: Data imported from Housing Dataset from UCI Repository (cf. ​http://archive.ics.uci.edu/ml/datasets/Housing)
• Evaluator: SymbolicRegressionScaledMeanSquaredErrorEvaluator
• FunctionTreeGrammar: Addition, Subtraction, Multiplication, Division, Constant, Variable
• LowerEstimationLimit: -289,08968253968254
• MaxExpressionDepth: 10
• MaxExpressionLength: 100
• MaxFunctionArguments: 0
• MaxFunctionDefiningBranches: 0
• Maximization: False
• SolutionCreator: ProbabilisticTreeCreator
• SymbolicExpressionTreeInterpreter: -
• UpperEstimationLimit: 332,91031746031746

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Genetic programming - Symbolic Regression (Tower)

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Genetic programming - Symbolic Regression (Mackey-Glass)

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Genetic programming - Symbolic Classification (Wisconsin)

Example for a simple genetic programming algorithm including the Wisconsin breast cancer dataset from the UCI Machine Learning Repository. The engine uses all available GP manipulation operators, single-point cross-over and squared Pearson's correlation coefficient evaluation.

The engine reaches an accuracy of ~95% on the test set. This engine is supposed to be a demo for GP in HeuristicLab, the aim is not to find high quality models.

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Genetic programming - Symbolic Classification (Mammography)

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Genetic Programming - Even Parity (4 inputs)

SGP_Boolean-Even-Parity-4.hl

A genetic programming algorithm to synthesize the boolean even parity function with 4 binary inputs

• Population size: 4000
• Generations: 100
• Function set: AND, OR, NOT
• Terminal set: D0, D1, D2, D3
• Max. function defining branches: 3
• Max. function arguments: 3

Up to three automatically defined functions (ADF), each with up to three arguments, are allowed.

References

John R. Koza, Genetic Programming - On the Programming of Computers by Means of Natural Selection, MIT Press, 1992

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Genetic Programming - Multiplexer (11 inputs

SGP_Boolean-Multiplexer-11.hl

A genetic programming algorithm to synthesize the boolean multiplexer function with 11 binary inputs

• Population size: 4000
• Generations: 100
• Function set: IF, AND, OR, NOT
• Terminal set: A0, A1, A2, D0, D1, D2, D3, D4, D5, D6, D7

References

John R. Koza, Genetic Programming - On the Programming of Computers by Means of Natural Selection, MIT Press, 1992

Additional

• Local Search - Knapsack: A local search algorithm that solves a randomly generated Knapsack problem

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Local Search - Knapsack

Algorithm: Local Search

Algorithm Parameters:

• Analyzer: MultiAnalyzer
• MaximumIterations: 1000
• MoveEvaluator: KnapsackOneBitflipMoveEvaluator
• MoveGenerator: ExhaustiveBitflipMoveGenerator
• MoveMaker: OneBitflipMoveMaker
• SampleSize: 100
• Seed: -
• SetSeedRandomly: True

Problem: Knapsack Problem?

Problem Parameters:

• BestKnownQuality: 226
• BestKnownSolution: Binary Vector
• Evaluator: KnapsackEvaluator
• KnapsackCapacity: 134
• Maximization: True
• Penalty: 1
• SolutionCreator: RandomBinaryVectorCreator
• Values: The values of the items.
• Weights: The weights of the items.