5funded by EPSRC supported by ILOG A 3 year project Car Sequencing define constrainednessderive heuristicsinvestigate reformulationsRouting & Schedulinginvestigate reformulationsuse Scheduler and Dispatcher… and other things
6Current Status … 4 things investigations of stable marriage problempaper at CP01initial study of reformulation in the largeVRP & OSSP & JSSPusing Scheduler and Dispatcherpaper at Formul’01initial study of reformulation in the small0/1 encodingsusing Solver and ChocoConstrainedness of car sequencingmeetings with IPG and BMSAnd now for vrp&ssp and 0/1 encoding
7VRP and JSSP: Extremes on a Spectrum CVRPTWDispatcherJSSPSchedulerExtremeswill there be problems somewhere in between?where you might use Dispatcher and/or Schedulera pragmatic study
8Encoding VRP as an Open Shop Scheduling Problem vehicleswith capacitiesvisitswith loads/demandwith time windowsdistance between visitsminimise distance traveledreduce vehicles usedmachineswith consumable resourceoperations/activitieswith resource requirementwith time windowstransition times between operationsminimise make spanTranslate CVRPTW into OSSPsolve OSSP with Schedulersolve CVRPTW with Dispatchercompare, using tools as intendedan extreme … expect to be bad
9Encoding Job Shop Scheduling Problem as a VRP vehiclesvisitsspecified vehicleswith time windowswith durationssequence constraints between visitszero travel timesrespect time windows on vehiclesminimise make spanmachinesoperations/activitiesspecified resourcewith time windowswith durationjobssequence of operationsminimise make spanTranslate JSSP to VRPTW with zero travelsolve VRPTW with Dispatchersolve JSSP with Scheduleragain, compare, using tools as intendedan extreme … expect to be bad
10The study continues: VRP and OSSP problem generation use benchmark vrp’sselect R local (nearby) visitsR visits in same vehicleproduce an optimal tour for Rwrite out sequence constraintsiteratethe R sequences/tours maybe like a jobbut on one resource
11Problem Reformulation in the Small Investigate problems with 0/1 variablesindependent set of a hypergraphmaximal independent set of a hypergraphconstruction of bibd <v,b,r,k,l>Two common constraintssummation of variablesbiconditionalVariety of encodingsfor summationfor biconditionalTwo toolkitsILOG SolverChoco
12A hypergraph G = (V,E)V is a set of verticesE is a set of hyperedgesan edge with 2 or more verticesAn independent set Sassume vertices(e) is set of vertices in hyperedge eMaximal independent set Sthere is no independent set S’ that subsumes Sadd anything to S and you lose independence!
18Independent Setind1the sum of the variables is less than or equal to kind2the number occurrences of 1’s is less than or equal to kind1S and ind2S in Solverind1C and ind2C in ChocoHypergraphs are bibd’s where blocks are hyperedgesI.e. regular degree hypergraphs
19Nodes are same for all (same level of consistency?) summation 3 times faster than occurrence in Solveroccurrence 20 times faster than sum in Choco
20Maximality and the biconditional Three encodings of the biconditional
26Conclusion?On 0/1 encodingsbig variations within a toolkitvariation across toolkitsexperiment!On VRP/Dispatcher and OSSP/Schedulerextremes exploredexperiments being designedCar Sequencingon the stack (one pop away)Stable Marriageneed a long term project
27Other Things4th year Student Projectsstudent handbook, a design problemanaesthetist’s rota3d year Student Projectsvrp system (3d year)Teaching Goal4th year course in constraint programmingResearchSAC, a new algorithm (with Kostas)stable marriage and consraint programmingbioinformatics?