CPM!

Just do it!

JChoco We jumped in, and took it for a spin Some counting problems Meeting scheduling problem … you got your hands dirty

JChoco Meeting scheduling problem … you got your hands dirty Model and solve Reflect on alternative models Symmetries Heuristics Pre-processing Equitable graph colouring with side constraints A surprisingly rich problem!

Opening up the hood: part 1, search

So how does CP work? BT: Chronological BackTracking Thrashing! FC: forward checking Thrashing! CBJ: Conflict-directed BackJumping Thrashing!

Opening up the hood: part 2, arc-consistency

So how does CP work? Arc-consistency Definition (aka 2-consistency) Covered Consistency Algorithms AC3 AC4/6/2001 AC5 Is AC a decision procedure?

modelling

We modelled some problems number partitioning jobshop scheduling magic square n-queens bin packing knight’s tour Ramsey number Orthogonal Latin Squares Crystal Maze graph colouring m-queens Team allocation Crossword Puzzle Round-robin scheduling Meeting scheduling problem 75 integer sequence sudoku

What are the decision variables? Are there any symmetries? Is there a variable/value ordering heuristic? Is there another model? We modelled some problems How does search go? Redundant constraints? Dual or Hidden Variable encoding?

Variables & their domains Constraints Identifying the decision variables Size of the model number of variables, number of constraints Use big-O Size of the search space (worst case) Use big-O Symmetries And how to eliminate if possible Heuristics Alternative models Swap the perspective variable/values? Replace constraints with variables? Did this in crossword puzzle Zero/one possible? Did this in team allocation and others Channeling between models See above We modelled some problems

phase transition phenomena

Where are the hard problems? Constrainedness? Who cares? In optimisation, as a heuristic, in solving problems

heuristics

Variable and value ordering heuristics Static, topological properties Fail-first, and it’s realisation Constrainedness Dual viewpoint heuristics Promise Regret Domain Specific (example JSSP slack-based, Warnsdorff)

Specialised constraints

specialised constraints max sub-tour elimination Knight’s tour … the glass box

local search

Search againLocal search (aka neighbourhood search) HC, SA, TS, GLS, GA, ACO, … Why we need them escape local optima Problems in using them incompleteness, move operators, evaluation/fitness functions, tuning parameters, Problems in using them in CP aka meta-heuristics

Search againLimited Discrepancy Search lds motivation for LDS when might we use it? when should we not use it? what happens when problem is unsat?

Parallel search Amdahl’s law How much speed up can we get? Satisfiable v Unsatisfiable problems Optimisation Superlinear? BitSet parallelism How to split up work Static Embarrassingly Dynamic work stealing/donation

change of representation

dual and hidden variable encoding change of representation Crossword puzzle, turn constraints into variables Interchange values and variables Zero/one? SAT encoding of Graph Colouring

Levels of consistency

Node Consistency (NC) Arc-consistency (AC) Path Consistency (PC) Generalised arc-consistency (GAC) Bounds consistency Inverse Path Consistency (IPC aka PIC) Singleton Arc-consistency (SAC) … and others consistency

Mechanics of choco

homework Ramsey & max Local Search demo m-queens 75 integers

summary

theory csp and it’s complexity search (bt, fc, cbj, …) thrashing arc-consistency levels of consistency heuristics local search & lds & parallel search dual & hidden variables sat phase transition phenomena & constrainedness summary

practice number partitioning jobshop scheduling magic square n-queens bin packing knight’s tour Meeting SchedulingOrthogonal Latin Squares Crystal Maze graph colouring Modelling & Solving Problems

practice variables (enumerated/bound/setsVar) and their domains constraints (neq, allDiff, ifOnlyIf, …) decision variables what propagation might take place size of the encoding/model (how it scales with problem size) heuristics (dynamic/static, variable/value) size of the search/state space how search goes (example was knight’s tour) alternative models (dual? hidden? values as variables?) optimisation (with maximise/minimise, seqn of decision problems) dealing with conflicts (soft constraints & penalties) symmetry breaking (ramsey, bin packing, …) redundant constraints (magic square, MOLS …) what will make problems hard to solve and what will make them easy? Modelling & Solving Problems

Where to next?

smarter (explanation/interaction) local search (comet & beyond) exploiting multi-cores (Moore’s law ends July 2017) in propagation in search easier to use (Miguel & Frisch) don’t need a BSc, MSc, MRes, PhD a killer app constraint spread sheet? something on a phone? you