Making Choices using
Structure at the Instance Level
within a Case Based Reasoning
Framework
Cormac Gebruers*, Alessio Guerri†,
Brahim Hnich* & Michela Milano†
* Cork Constraint Computation Centre, University College Cork.
† DEIS, University of Bologna.
Overview
•
•
•
•
•
•
Motivation
Objectives
Case Study: The Bid Evaluation Problem
Case Based Reasoning CBR
Indications
Further Work
Motivation
• Sometimes its easy to choose between a CP or
an IP algorithm.
• In many domains, the choice is not so simple.
• Choice is problem instance dependent. How do
we decide?
• Using Structure at the Instance Level?
Objectives
• A methodology to predict whether to use a CP or
IP algorithm for problem instances; Algorithm
portfolio selection.
• Methodology must be
– low knowledge from the end users perspective
• We would also like
– Cheap to compute
– Keep most effort off-line
Case Study
• The Bid Evaluation Problem
• Choice whether to use CP or IP is not clear.
• Two sub-problems
– ‘IP’ subproblem: Winner Determination Problem
– ‘CP’ subproblem: Temporal Feasability
Winner
Determination Problem
• Winner Determination Problem (WDP):
– From a set of bids, choose a subset that covers a set
of required tasks, subject to lowest cost or maximum
revenue.
– e.g. Oil/Gas Field Construction… Oil company tender
for a set of construction jobs & accept optimal lowest
cost set of bids that covers all construction jobs.
• WDP is np-hard. IP represents the technology of
Choice to solve it.
Temporal Feasibility
• Time windows and temporal constraints
introduced into the WDP → BEP
• Interactions within problem makes CP/IP Choice
unclear
• Extending our previous example…
– Oil company tender for a set of construction jobs &
accept optimal lowest cost set of bids that satisfy
delivery date and construction sequencing
constraints.
Algorithms for BEP
• IP based Algorithm:
– IP Model
– Complete Branch and Bound based on Linear Relaxation (LR) of the
problem without temporal constraints.
• CP based Algorithm:
–
–
–
–
CP Model
Limited Discrepancy Search
Fail First variable selection heuristic.
The value selection heuristic chooses the minimum price-for-task value
next.
• Hybrid CP/IP Algorithm (HCP):
– based largely on a CP model & CP algorithm.
– Value Ordering Heuristic decided using IP
Case Based Reasoning
• We explore how well CBR can decide between
IP algorithm and HCP algorithm for the BEP.
• If 2 instances are ‘similar’ then the same
algorithm should apply to both.
• CBR makes a prediction by comparing a new
instance to a store of examples for which the
correct choice is known.
CBR System
Similarity
• Two decisions:
– Choice of problem representation R
– Choice of similarity measure fsim
• In the proceedings, the similarity measure given
is inaccurate. The correct formula takes the
following form:
A Key Challenge
• Find a cheap problem representation R, and a
cheap similarity measure fsim that predicts
whether to use CP, IP or CP/IP based algorithms.
Indications
Prediction of correct Algorithm for BEP
100
90
80
70
60
% correct
prediction
50
40
30
20
10
0
n
io
is
ec
n
io
is
ec
Tr
w
ne
t
es
-B
om
se
n
nd
U
io
a
ss
R
re
d
te
eg
R
gh
ic
ei
t
is
W
)
og
ve
si
lL
ia
en
m
xp
no
(E
Bi
ee
Tr
D
D
BR
BR
C
C
ee
Method
Indications
• Performance of several quite different approaches
suggests that Structure at the Instance Level exists and
can be exploited
• All approaches significantly outperform both “Use-Best”
and “Weighted Random”
• Using quite basic problem representations and cheap
similarity measures, we achieve acceptable prediction
levels
Future Work
• In-depth analysis of data obtained.
• Further domains, richer algorithmic decisions
• Consider dynamic algorithm choice during
execution.
• CBR; intelligent candidate feature and similarity
measure identification