Fitness Landscape Analysis of Simulation Optimisation Problems in HeuristicLab Problems in HeuristicLab Vitaly Bolshakov, Riga Technical University Erik Pitzer, Michael Affenzeller, Upper Austrian University of Applied Sciences
Acknowledgements • This work has been supported by the European Social Fund within the project «Support for the implementation of doctoral studies at Riga Technical doctoral studies at Riga Technical University». 2011.11.16 EMS 2011, Madrid, Spain 2
Introduction Fitness • The fitness landscape consists of – The set of solutions – The fitness function – A distance measure 1. parameter 2. parameter 2. parameter • It is proposed, that different structures of fitness landscape affect the optimisation process • Fitness landscape analysis is proposed as a technique for meta-optimisation (e.g. for a selection of suitable optimisation algorithms) 2011.11.16 EMS 2011, Madrid, Spain 3
Motivation • Most fitness landscape analysis techniques are theoretical approaches to estimate measures of problem’s fitness landscape landscape • There are no good methodology to apply results of fitness landscape analysis in optimisation 2011.11.16 EMS 2011, Madrid, Spain 4
Goals • To find significant structures in the fitness landscapes of different vehicle scheduling problems (VSP) • To find in what way these structures affect • To find in what way these structures affect metaheuristic optimisation algorithms • To find in what way stochastic noise in simulation-based evaluation of goal function affects the structures of landscape 2011.11.16 EMS 2011, Madrid, Spain 5
Fitness Landscape Analysis • Ruggedness analysis (Weinberger, 1990) – Autocorrelation function – Correlation length • Information analysis (Vassilev, et al, 2000) – Information content – Information content – Density-basin information – Partial information content – Information stability • Walk types on landscapes – Random walk – Adaptive & Up-Down walk – Neutral walk 2011.11.16 EMS 2011, Madrid, Spain 6
HeuristicLab Optimisation Framework • Powerful framework for heuristic and evolutionary algorithms • Open source optimization environment • Paradigm independent • Developed by members of the HELA (Heuristic • Developed by members of the HELA (Heuristic and Evolutionary Algorithms Laboratory) • http://dev.heuristiclab.com/ 2011.11.16 EMS 2011, Madrid, Spain 7
Vehicle Scheduling Problem (1) Objective function f is the minimisation of the total idle time T idle for • all vehicles taking into account the total time of constraint violation ( T c , T m , T o ) and an amount of constraints not satisfied ( N ol , N ot ) by a potential solution. min f T k T k T k T k N k N = ∑ 1 2 3 0 4 5 idle c m ol ot + + + + + → Decision variables Decision variables • • – Vehicle numbers assigned to trips – Start time for each trip. Soft constraints • – Delivery time constraints ( T m ) – Vehicle capacity constraints ( N ol ) – Trips should not intersect for one vehicle ( T c ) – Duration of day ( T o , N ot ) 2011.11.16 EMS 2011, Madrid, Spain 8
Vehicle Scheduling Problem (2) • Simulation model of VSP was implemented as a plug-in of HeuristicLab 2011.11.16 EMS 2011, Madrid, Spain 9
Vehicle Scheduling Problem (3) • Permutation encoding is proposed for the representation of VSP solution – All trip intersection constraints are satisfied – Idle time is minimized – Idle time is minimized – Application of implemented in HeuristicLab universal operators for permutation encoding 2011.11.16 EMS 2011, Madrid, Spain 10
Fitness Landscape Analysis Experiments • A large grid of landscape analysis experiments was created to compare values between different fitness landscapes. – Different problem instances (real, artificial) – Different types of landscape walks – For existing encoding: different operators – Stochastic vehicle scheduling problems versus deterministic – Comparison between existing and proposed encodings of VSP – Comparison between existing and proposed encodings of VSP • Corresponding grid of optimisation experiments was created to interpret results of landscape analysis – Evolution strategy – Genetic algorithm 2011.11.16 EMS 2011, Madrid, Spain 11
Fitness Landscape Analysis in HeuristicLab • Example of statistics obtained in VSP landscape analysis in HeuristicLab Fitness value trail Fitness cloud Information measures 2011.11.16 EMS 2011, Madrid, Spain 12
Experiments (1) • Experiment series 1: different mutation operators – More effective optimisation operators has higher autocorrelation function of fitness value trail – Artificial VSP instances that have different structure than real-life problems stand out in landscape analysis analysis Autocorrelation function in up- Fitness values of best found down walk solutions with evolution strategies 2011.11.16 EMS 2011, Madrid, Spain 13
Experiments (2) • Experiment series 2: stochastic and deterministic vehicle scheduling problems – Information content is higher for problems with noise – Different problem instances show different impact of noise on the structures of landscape noise on the structures of landscape Information content for deterministic Information content for problems evaluated (black) and stochastic (green) VSP with different number of replications in random walk 2011.11.16 EMS 2011, Madrid, Spain 14
Experiments (3) • Experiment series 3: different representation of solutions chromosome – VSP in permutation encoding has more rugged landscape – Permutation encoding is more effective except for VSP of high dimensionality VSP of high dimensionality Autocorrelation for permutation Fitness values of best found solutions with (green) and integer (black) genetic algorithm for different encodings encodings of VSP in neutral walk 2011.11.16 EMS 2011, Madrid, Spain 15
Conclusions (1) • To make comprehensive analysis different combinations of analysis techniques and landscape walk types should be performed • Problem instances that are different in structure than typical instances can be determined in fitness typical instances can be determined in fitness landscape analysis • The impact of noise and stochastic data in simulation is easily determined – It is possible to see to what extent the stochastic parameters of the simulation model affect specific problem instances 2011.11.16 EMS 2011, Madrid, Spain 16
Conclusions (2) • Optimisation experiment results shows promising relationships between landscape analysis and performance of optimisation algorithms • In future work this topic should be investigated in more detail to provide a methodology to interpret results of landscape analysis for the tuning of meta-heuristic algorithms 2011.11.16 EMS 2011, Madrid, Spain 17
• Thank You! 2011.11.16 EMS 2011, Madrid, Spain 18
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