Psychological Preference-based Optimization Framework: An evolutionary computation approach for...
-
Upload
pearl-kelly -
Category
Documents
-
view
229 -
download
0
Transcript of Psychological Preference-based Optimization Framework: An evolutionary computation approach for...
NTUTEIL
Psychological Preference-based Optimization Framework:
An evolutionary computation approach for constrained problems involving human preference
You, Ying-ShiuanAdvisor: Yu, Tian-Li
11-JUN-2010
NTUTEIL
2
Agenda
• Introductions• Psychological Preference-based Optimization
Framework• Case Study 1: Nurse Scheduling Problem• Case Study 2 : Space Layout Problem• Contributions & Conclusions
NTUTEIL
3
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.
NTUTEIL
4
Constraint-handling Techniques in ECs
• Penalty function
• Repair algorithm
• Decoder
Coello-Coello, 2002
)()()( xhrxfx jj
repair
Decoder
InfeasibleSolution
FeasibleSolution
GuidanceFeasibleSolution
NTUTEIL
5
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.
NTUTEIL
6
Goal of this Thesis
• To solve the problem which is constrained, human preference-based, and no handmade objective function by the researcher.
NTUTEIL
7
Agenda
• Introductions• Psychological Preference-based Optimization
Framework• Case study 1: Nurse Scheduling Problem• Case study 2 : Space Layout Problem• Contributions & Conclusions
NTUTEIL
8
Psychological Preference-based Optimization Framework
NTUTEIL
9
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
NTUTEIL
10
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.
NTUTEIL
11
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.
NTUTEIL
12
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
NTUTEIL
13
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
NTUTEIL
14
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.
NTUTEIL
15
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
NTUTEIL
16
Psychological Preference-based Optimization Framework
NTUTEIL
17
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.
NTUTEIL
18
Agenda
• Introduction• Psychological Preference-based Optimization
Framework• Case study 1: Nurse Scheduling Problem• Case study 2 : Space Layout Problem• Contributions & Conclusions
NTUTEIL
19
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.
NTUTEIL
20
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.
NTUTEIL
21
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”.
minj
ij Ff
conAj
jkika 0
jj
ij Ra
jj
iji RSas
off-day requestedPriority ,,1 jifij
AaNaaa jijijiij 1,1, and if,0
NTUTEIL
22
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.
NTUTEIL
23
PPOF in NSPGFSSFS
→ Hill-climbing decoderPartial ordering + ε-SVR
ECM Compact GA→→
(Llorà, 2005)
NTUTEIL
24
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
NTUTEIL
25
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
NTUTEIL
Experiments: Linear Fitness
• 14C
26hbhbOAOOAOcococwcw fwfwfwfwF
Agent A Agent B
NTUTEIL
27
Experiments: Linear Fitness (cont’d)
• 07A
hbhbOAOOAOcococwcw fwfwfwfwF
Agent A Agent B
NTUTEIL
28
Experiments: Non-linear Fitness
22
2221
213
4
12
1
122
111
)44()1.24(
,242
,
,362
,
xxxxxxxF
xxffx
xxffx
hbOAO
cocw
14C 07A
(Dixon, 1978)
NTUTEIL
29
Agenda
• Introductions• Psychological Preference-based Optimization
Framework• Case study 1: Nurse Scheduling Problem• Case study 2 : Space Layout Problem• Contributions & Conclusions
NTUTEIL
30
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).
NTUTEIL
31
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.
NTUTEIL
32
PPOF in SLPGFS
SFS
→ Backtracking search decoder(BSD)Partial ordering + ε-SVR
ECM Compact GA→→
NTUTEIL
33
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
NTUTEIL
34
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.
NTUTEIL
35
Agenda
• Introductions• Psychological Preference-based Optimization
Framework• Case study 1: Nurse Scheduling Problem• Case study 2 : Space Layout Problem• Contributions & Conclusions
NTUTEIL
36
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
NTUTEIL
37
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.
NTUTEIL
38
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.
NTUTEIL
39
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.
NTUTEIL
40
QUESTIONSThe End