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Psychological Preference-based Optimization Framework:

An evolutionary computation approach for constrained problems involving human preference

You, Ying-ShiuanAdvisor: Yu, Tian-Li

11-JUN-2010

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Agenda

• Introductions• Psychological Preference-based Optimization

Framework• Case Study 1: Nurse Scheduling Problem• Case Study 2 : Space Layout Problem• Contributions & Conclusions

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Real-world Problems in ECs

• Evolutionary computations (ECs) have been applied to many real-world problems.

• Issues about real-world problems in ECs– Constraints.– Objective functions.

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Constraint-handling Techniques in ECs

• Penalty function

• Repair algorithm

• Decoder

Coello-Coello, 2002

)()()( xhrxfx jj

repair

Decoder

InfeasibleSolution

FeasibleSolution

GuidanceFeasibleSolution

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Objective Functions Design in ECs

• Some are relatively easy to define.– Well studied scientific theories or mathematical

models.

• Some are difficult to define.– Involving human preference. – Two approaches:

• Interactive ECs.• Handmade objective functions.

A strong assumption: The handmade objective function is close to human preference.

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Goal of this Thesis

• To solve the problem which is constrained, human preference-based, and no handmade objective function by the researcher.

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Agenda

• Introductions• Psychological Preference-based Optimization

Framework• Case study 1: Nurse Scheduling Problem• Case study 2 : Space Layout Problem• Contributions & Conclusions

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Psychological Preference-based Optimization Framework

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Guidable Fast Search (GFS)

• Objective: Handling constraints -> Decoder

• Three characteristics:– Acceptable time performance– Guidable objective function– Search space mapping

GFSGuidance Potential feasible sol.

input output

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GFS: Acceptable Time Performance • Objective: Prevent the influence of human fatigue.– Fatigue affects the quality of human evaluations. (Takagi,

2001)

• “Acceptable”: Waiting time should be short enough so that the user doesn’t feel tired or bored.

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GFS: Guidable Objective Function

• Objective: Optimize solutions by guidance from ECM.

• “Guidable”: GFS is able to search solutions in different directions by guidance from ECM.

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GFS: Search Space Mapping

• Reduction from a constrained search space of potential solutions to a constraint-less one of guidance.

• Thinking: constrained to constrained?– The user has to evaluate infeasible solutions

• Increasing the burden of evaluations

GFS

infeasible, feasible

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Surrogate Fitness Synthesizer (SFS)

• Objective: Reduce human fatigue -> Fitness inheritance

• Two characteristics:– Sampling (e.g., random, uniform, adaptive) – Modeling (e.g., neuron network, regression)

SFSUser’s evaluations Surrogate fitness

func.

inputoutput

Evaluated guidance

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SFS: Assumptions

• User’s evaluations can be transformed into numerical values.– The user has corresponding values of evaluated solutions. – An essential assumption of preference-based optimization

algorithms.

• User’s evaluations are consistent.– The waiting time is “acceptable”.

• Preference can be simulated with mathematical models (explicit or implicit).– An essential assumption of preference-based optimization

algorithms.

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Evolutionary Computation Method (ECM)

• Objective: Find the optimal individuals as the guidance for GFS.

• “ECM”: an algorithm implementation rather than a class of algorithms based on the evolutionary concept.

ECMSurrogate fitness func. Optimal guidance

input output

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Psychological Preference-based Optimization Framework

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Why Decoder?

• Penalty function– Handmade: Violate the objective, “no handmade objective func.”– Synthetic: Evaluating infeasible solutions is needed.

• Repair algorithm (individuals -> solutions)– Every infeasible individual in ECM needs repair. – More difficult to achieve acceptable time performance

requirement.

• Decoder (individuals -> guidance)– Most evaluations are from the surrogate fitness function. – The decoder only processes some of the best guidance.

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Agenda

• Introduction• Psychological Preference-based Optimization

Framework• Case study 1: Nurse Scheduling Problem• Case study 2 : Space Layout Problem• Contributions & Conclusions

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Case Study 1: Nurse Scheduling Problem (NSP)

• Practical problem arisen from the National Taiwan University Hospital.

• Objectives: – Supply manpower needs.– Balance the workload.– Increase employee satisfaction.– Improve efficiency.

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Problem Definition

• Three-shift working system– day (A), evening (E), night (N)

• Senior and junior nurses.– The senior can cover the junior’s work, but not vice versa.

• Requested day-off.– Priority requested day-off.

• Must be granted.

– Normal requested day-off.• Better to be granted.

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Problem Definition – Hard ConstraintsDescription Mathematical Description

HC-1 Minimum days off in a mouth.

HC-2 Maximum consecutive working days.

HC-3 Minimum working nurses.

HC-4 Minimum working senior nurses.

HC-5 Priority requested day-off must be met.

HC-6 No “NA”.

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conAj

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jj

ij Ra

jj

iji RSas

off-day requestedPriority ,,1 jifij

AaNaaa jijijiij 1,1, and if,0

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Problem Definition – Soft Constraints

Description

SC-1 Longer consecutive working days, better in Apr days.

SC-2 Consecutive days off are Fpr days.

SC-3 Avoiding “OAO”.

SC-4 Balance workload on official holidays.

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PPOF in NSPGFSSFS

→ Hill-climbing decoderPartial ordering + ε-SVR

ECM Compact GA→→

(Llorà, 2005)

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Input parameters Influence value of corresponding SC

SC-1

SC-2

SC-3

SC-4

Case Study 1: Input of HCD• Four parameters

cw

co

OAO

hb

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Experiments

• Data from two wards: 14C & 07A

• Agents simulate chief nurses.

• Evaluation fitness– Linear– Non-linear

PreferenceA Consecutive working and offB Uncomfortable to “OAO”

Agents simulate two type of chief nurses in linear fitness

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Experiments: Linear Fitness

• 14C

26hbhbOAOOAOcococwcw fwfwfwfwF

Agent A Agent B

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Experiments: Linear Fitness (cont’d)

• 07A

hbhbOAOOAOcococwcw fwfwfwfwF

Agent A Agent B

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Experiments: Non-linear Fitness

22

2221

213

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12

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122

111

)44()1.24(

,242

,

,362

,

xxxxxxxF

xxffx

xxffx

hbOAO

cocw

14C 07A

(Dixon, 1978)

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Agenda

• Introductions• Psychological Preference-based Optimization

Framework• Case study 1: Nurse Scheduling Problem• Case study 2 : Space Layout Problem• Contributions & Conclusions

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Case Study 2: Space Layout Problem (SLP)

• Handmade problem to test the applicability of PPOF

• Objective– Find optimal arrangements of a set of discrete and

interdependent designing units (DUs).

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Problem Definition

• 3x3 discrete subspaces.• DUs: table, sofa, television, and door.– Each DU occupies one subspace– Orientations are not considered

DescriptionHC-1 Door is built on the wall.

HC-2 Table is placed in front of sofa.

HC-3 DUs’ location is all different.

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PPOF in SLPGFS

SFS

→ Backtracking search decoder(BSD)Partial ordering + ε-SVR

ECM Compact GA→→

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Input of BSD

• Four parameters

Parameters Description

Preferred location of table

Preferred location of sofa

Preferred location of television

Preferred location of door

tablep

sofaptvp

doorp

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Case Study 2: Experiments

• Agent’s evaluation guidelines– Agent can see door while sitting on sofa.– Agent can see television while sitting on sofa.– Door does not face sofa.– Backside of sofa attaches to walls.

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Agenda

• Introductions• Psychological Preference-based Optimization

Framework• Case study 1: Nurse Scheduling Problem• Case study 2 : Space Layout Problem• Contributions & Conclusions

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Contributions

• Propose PPOF.

• Discuss the characteristics of elements of PPOF.

• Implement on two cases: NSP & SLP.– GFS: Hill-climbing decoder (NSP) & Backtracking search

decoder (SLP)– SFS: Partial ordering + ε-SVR – ECM: Compact GA

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Conclusions

• PPOF consists of three components.– GFS: Handling constraints.– SFS: Modeling human preference.– ECM: Searching optimal guidance for GFS.

• GFS has three characteristics.– Acceptable time performance -> Prevent human fatigue– Guidable objective function -> Search different solutions– Search space mapping -> Reduce from a constrained one

to a constraint-less one.

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Conclusions (cont’d)

• SFS has three assumptions behind it.– User’s evaluations can be transformed into numeric values.– User’s evaluations are consistency.– Preference can be simulated with mathematical models.

• The decoder is the most proper approach to handle constraints in PPOF.

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Conclusions (cont’d)

• Experiments– The implementations of PPOF has the ability to optimize

solutions by human preference in a NSP and an SLP.– SFS could speed up the optimization.

• We believe that PPOF works on other problems with constraints and human interactive nature.

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QUESTIONSThe End