1. Problem Reformulation and Search
Patrick Prosser & Evgeny Selensky

5. funded by EPSRC supported by ILOG A 3 year project Car Sequencing
define constrainedness
derive heuristics
investigate reformulations
Routing & Scheduling
investigate reformulations
use Scheduler and Dispatcher
… and other things

6. Current Status … 4 things
investigations of stable marriage problem
paper at CP01
initial study of reformulation in the large
VRP & OSSP & JSSP
using Scheduler and Dispatcher
paper at Formul’01
initial study of reformulation in the small
0/1 encodings
using Solver and Choco
Constrainedness of car sequencing
meetings with IPG and BMS
And now for vrp&ssp and 0/1 encoding

7. VRP and JSSP: Extremes on a Spectrum
CVRPTW
Dispatcher
JSSP
Scheduler
Extremes
will there be problems somewhere in between?
where you might use Dispatcher and/or Scheduler
a pragmatic study

8. Encoding VRP as an Open Shop Scheduling Problem
vehicles
with capacities
visits
with loads/demand
with time windows
distance between visits
minimise distance traveled
reduce vehicles used
machines
with consumable resource
operations/activities
with resource requirement
with time windows
transition times between operations
minimise make span
Translate CVRPTW into OSSP
solve OSSP with Scheduler
solve CVRPTW with Dispatcher
compare, using tools as intended
an extreme … expect to be bad

9. Encoding Job Shop Scheduling Problem as a VRP
vehicles
visits
specified vehicles
with time windows
with durations
sequence constraints between visits
zero travel times
respect time windows on vehicles
minimise make span
machines
operations/activities
specified resource
with time windows
with duration
jobs
sequence of operations
minimise make span
Translate JSSP to VRPTW with zero travel
solve VRPTW with Dispatcher
solve JSSP with Scheduler
again, compare, using tools as intended
an extreme … expect to be bad

10. The study continues: VRP and OSSP problem generation
use benchmark vrp’s
select R local (nearby) visits
R visits in same vehicle
produce an optimal tour for R
write out sequence constraints
iterate
the R sequences/tours maybe like a job
but on one resource

11. Problem Reformulation in the Small
Investigate problems with 0/1 variables
independent set of a hypergraph
maximal independent set of a hypergraph
construction of bibd <v,b,r,k,l>
Two common constraints
summation of variables
biconditional
Variety of encodings
for summation
for biconditional
Two toolkits
ILOG Solver
Choco

12. A hypergraph G = (V,E)
V is a set of vertices
E is a set of hyperedges
an edge with 2 or more vertices
An independent set S
assume vertices(e) is set of vertices in hyperedge e
Maximal independent set S
there is no independent set S’ that subsumes S
add anything to S and you lose independence!

13. A Hypergraph 1 2 3 4 5 7 9 8 6

14. An Independent Set 1 2 3 4 5 7 9 8 6

15. The Largest Independent Set1 2 3 4 5 7 9 8 6

16. A Maximal Independent Set1 2 3 4 5 7 9 8 6

17. More Generally

18. Independent Set
ind1
the sum of the variables is less than or equal to k
ind2
the number occurrences of 1’s is less than or equal to k
ind1S and ind2S in Solver
ind1C and ind2C in Choco
Hypergraphs are bibd’s where blocks are hyperedges
I.e. regular degree hypergraphs

19. Nodes are same for all (same level of consistency?)
summation 3 times faster than occurrence in Solver
occurrence 20 times faster than sum in Choco

20. Maximality and the biconditional
Three encodings of the biconditional

22. p and q or not p and not q is best for Solver
worst for Choco
can be 3 times

26. Conclusion?
On 0/1 encodings
big variations within a toolkit
variation across toolkits
experiment!
On VRP/Dispatcher and OSSP/Scheduler
extremes explored
experiments being designed
Car Sequencing
on the stack (one pop away)
Stable Marriage
need a long term project

27. Other Things
4th year Student Projects
student handbook, a design problem
anaesthetist’s rota
3d year Student Projects
vrp system (3d year)
Teaching Goal
4th year course in constraint programming
Research
SAC, a new algorithm (with Kostas)
stable marriage and consraint programming
bioinformatics?

29. Thanks for supporting us

30. Questions?