Fitness Landscape Analysis of Simulation Optimisation Problems in - - PowerPoint PPT Presentation

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 2 EMS 2011, Madrid, Spain

Fitness

• 1. parameter
• 2. parameter

Introduction

• The fitness landscape consists of

– The set of solutions – The fitness function – A distance measure

• 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)

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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

• ptimisation

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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

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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

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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/

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Vehicle Scheduling Problem (1)

• Objective function f is the minimisation of the total idle time Tidle for

all vehicles taking into account the total time of constraint violation (Tc, Tm, To) and an amount of constraints not satisfied (Nol, Not) by a potential solution.

• Decision variables

min

5 4 3 2 1

→ + + + + + = ∑

• t
• l

m c idle

N k N k T k T k T k T f

• Decision variables

– Vehicle numbers assigned to trips – Start time for each trip.

• Soft constraints

– Delivery time constraints (Tm) – Vehicle capacity constraints (Nol) – Trips should not intersect for one vehicle (Tc) – Duration of day (To, Not)

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Vehicle Scheduling Problem (2)

• Simulation model of VSP was

implemented as a plug-in of HeuristicLab

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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

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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

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Fitness Landscape Analysis in HeuristicLab

• Example of statistics obtained in VSP

landscape analysis in HeuristicLab

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Fitness value trail Fitness cloud Information measures

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

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Autocorrelation function in up- down walk Fitness values of best found solutions with evolution strategies

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

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Information content for deterministic (black) and stochastic (green) VSP in random walk Information content for problems evaluated with different number of replications

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

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Autocorrelation for permutation (green) and integer (black) encodings of VSP in neutral walk Fitness values of best found solutions with genetic algorithm for different encodings

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

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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

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• Thank You!

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