Introduction to SCIP. Gregor Hendel, SCIP Introduction Day September 26, rd IMI-ISM-ZIB MODAL Workshop

Transcription

1 Introduction to SCIP Gregor Hendel, SCIP Introduction Day September 26, rd IMI-ISM-ZIB MODAL Workshop

2 What is SCIP? SCIP (Solving Constraint Integer Programs)... provides a full-scale MIP and MINLP solver, is constraint based, incorporates MIP features (cutting planes, LP relaxation), and MINLP features (spatial branch-and-bound, OBBT) CP features (domain propagation), SAT-solving features (conflict analysis, restarts), is a branch-cut-and-price framework, has a modular structure via plugins, is free for academic purposes, and is available in source-code under Gregor Hendel, hendel@zib.de SCIP Introduction 1/70

3 Meet the SCIP Team 31 active developers 7 running Bachelor and Master projects 16 running PhD projects 8 postdocs and professors 4 development centers in Germany ZIB: SCIP, SoPlex, UG, ZIMPL TU Darmstadt: SCIP and SCIP-SDP FAU Erlangen-Nu rnberg: SCIP RWTH Aachen: GCG Many international contributors and users more than downloads per year from 100+ countries Careers 10 awards for Masters and PhD theses: MOS, EURO, GOR, DMV 7 former developers are now building commercial optimization software at CPLEX, FICO Xpress, Gurobi, MOSEK, and GAMS Gregor Hendel, hendel@zib.de SCIP Introduction 2/70

4 Outline SCIP Solving Constraint Integer Programs Constraint Integer Programming The Solving Process of SCIP Extending SCIP by Plugins The SCIP Optimization Suite Gregor Hendel, SCIP Introduction 3/70

5 Outline SCIP Solving Constraint Integer Programs Constraint Integer Programming The Solving Process of SCIP Extending SCIP by Plugins The SCIP Optimization Suite Gregor Hendel, SCIP Introduction 4/70

6 An example: the Traveling Salesman Problem Definition (TSP) Given a complete graph G = (V, E) and distances d e for all e E: Find a Hamiltonian cycle (cycle containing all nodes, tour) of minimum length. K 8 Gregor Hendel, hendel@zib.de SCIP Introduction 5/70

7 An example: the Traveling Salesman Problem Definition (TSP) Given a complete graph G = (V, E) and distances d e for all e E: Find a Hamiltonian cycle (cycle containing all nodes, tour) of minimum length. K 8 Gregor Hendel, hendel@zib.de SCIP Introduction 5/70

8 An example: the Traveling Salesman Problem Definition (TSP) Given a complete graph G = (V, E) and distances d e for all e E: Find a Hamiltonian cycle (cycle containing all nodes, tour) of minimum length. Gregor Hendel, hendel@zib.de SCIP Introduction 5/70

9 What is a Constraint Integer Program? Mixed Integer Program Objective function: linear function Feasible set: described by linear constraints Variable domains: real or integer values Constraint Program Objective function: arbitrary function Feasible set: given by arbitrary constraints Variable domains: arbitrary (usually finite) min c T x min c(x) s.t. Ax b s.t. x F (x I, x C ) Z I R C (x I, x N ) Z I X Gregor Hendel, hendel@zib.de SCIP Introduction 6/70

10 TSP Integer Programming Formulation Given complete graph G = (V, E) distances d e > 0 for all e E x e Binary variables x e = 1 if edge e is used K 8 Gregor Hendel, hendel@zib.de SCIP Introduction 7/70

11 TSP Integer Programming Formulation Given complete graph G = (V, E) distances d e > 0 for all e E x e Binary variables x e = 1 if edge e is used K 8 min subject to d e x e e E e δ(v) e δ(s) x e = 2 x e 2 x e {0, 1} v V S V, S e E Gregor Hendel, hendel@zib.de SCIP Introduction 7/70

12 TSP Integer Programming Formulation Given complete graph G = (V, E) distances d e > 0 for all e E x e Binary variables x e = 1 if edge e is used K 8 min subject to d e x e e E e δ(v) e δ(s) x e = 2 x e 2 x e {0, 1} v V node degree S V, S e E Gregor Hendel, hendel@zib.de SCIP Introduction 7/70

13 TSP Integer Programming Formulation Given complete graph G = (V, E) distances d e > 0 for all e E x e Binary variables x e = 1 if edge e is used K 8 min subject to d e x e e E e δ(v) e δ(s) x e = 2 x e 2 x e {0, 1} v V S V, S subtour elimination e E Gregor Hendel, hendel@zib.de SCIP Introduction 7/70

14 TSP Integer Programming Formulation Given complete graph G = (V, E) distances d e > 0 for all e E x e Binary variables x e = 1 if edge e is used K 8 min subject to d e x e e E x e = 2 v V distance e δ(v) x e 2 S V, S e δ(s) x e {0, 1} e E Gregor Hendel, hendel@zib.de SCIP Introduction 7/70

15 TSP Constraint Programming Formulation Given complete graph G = (V, E) for each e E a distance d e > 0 Integer variables x v position of v V in tour x v K 8 Gregor Hendel, hendel@zib.de SCIP Introduction 8/70

16 TSP Constraint Programming Formulation Given complete graph G = (V, E) for each e E a distance d e > Integer variables x v position of v V in tour min length(x 1,..., x n) subject to alldifferent(x 1,..., x n) x v {1,..., n} v V Gregor Hendel, hendel@zib.de SCIP Introduction 8/70

17 What is a Constraint Integer Program? Constraint Integer Program Objective function: linear function min s.t. c T x x F (x I, x C ) Z I R C Feasible set: Remark: described by arbitrary constraints Variable domains: arbitrary objective or variables modeled by constraints real or integer values Gregor Hendel, hendel@zib.de SCIP Introduction 9/70

18 What is a Constraint Integer Program? Constraint Integer Program Objective function: linear function Feasible set: min s.t. d e x e e E x e = 2 v V e δ(v) nosubtour(x) x e {0, 1} e E (CIP formulation of TSP) described by arbitrary constraints Variable domains: real or integer values Single nosubtour constraint rules out subtours (e.g. by domain propagation). It may also separate subtour elimination inequalities. Gregor Hendel, hendel@zib.de SCIP Introduction 9/70

19 Mixed-Integer Nonlinear Programs (MINLPs) min c T x s.t. g k (x) 0 x i Z x i [l i, u i ] The functions g k C 1 ([l, u], R) can be k [m] i I [n] i [n] convex or nonconvex Gregor Hendel, hendel@zib.de SCIP Introduction 10/70

20 Application: Data Classification Support Vector Machine, e.g., with ramp loss. min w T w 2 + C n n (ξ i + 2(1 z i )) i=1 s.t. z i (y i (w T x i + b) 1 + ξ i ) 0 i ξ i [0, 2], z i {0, 1} i w R d, b R Gregor Hendel, hendel@zib.de SCIP Introduction 11/70

21 Constraint Integer Programming Mixed Integer Programs MIP Gregor Hendel, SCIP Introduction 12/70

22 Constraint Integer Programming Mixed Integer Programs SATisfiability problems MIP SAT Gregor Hendel, SCIP Introduction 12/70

23 Constraint Integer Programming Mixed Integer Programs SATisfiability problems Pseudo-Boolean Optimization MIP SAT PBO Gregor Hendel, SCIP Introduction 12/70

24 Constraint Integer Programming Mixed Integer Programs SATisfiability problems Pseudo-Boolean Optimization MIP Mixed Integer Nonlinear Programs SAT PBO MINLP Gregor Hendel, SCIP Introduction 12/70

25 Constraint Integer Programming Mixed Integer Programs SATisfiability problems Pseudo-Boolean Optimization MIP Mixed Integer Nonlinear Programs SAT PBO MINLP CP Constraint Programming Gregor Hendel, SCIP Introduction 12/70

26 Constraint Integer Programming Mixed Integer Programs CIP SATisfiability problems Pseudo-Boolean Optimization MIP Mixed Integer Nonlinear Programs SAT PBO MINLP CP Constraint Programming Constraint Integer Programming Gregor Hendel, SCIP Introduction 12/70

27 Constraint Integer Programming Mixed Integer Programs CIP SATisfiability problems Pseudo-Boolean Optimization MIP Mixed Integer Nonlinear Programs SAT PBO MINLP CP Constraint Programming Constraint Integer Programming Relation to CP and MIP Every MIP is a CIP. MIP CIP Every CP over a finite domain space is a CIP. FD CIP Gregor Hendel, hendel@zib.de SCIP Introduction 12/70

28 Outline SCIP Solving Constraint Integer Programs Constraint Integer Programming The Solving Process of SCIP Extending SCIP by Plugins The SCIP Optimization Suite Gregor Hendel, SCIP Introduction 13/70

29 Branch-and-bound Gregor Hendel, SCIP Introduction 14/70

30 SCIP Interactive Shell Basics Basic Workflow r e a d.. / check / i n s t a n c e s /MIP/ b e l l 5. mps o p t i m i z e w r i t e s o l u t i o n m y s o l u t i o n. s o l q u i t Displaying information Use the display... command to enter the menu and obtain solution information print the current transproblem to the console display plugin information, e.g., list all available branching rules Changing Settings Use the set... command to list the settings menu. Gregor Hendel, hendel@zib.de SCIP Introduction 15/70

31 Important Parameters Numerical parameters These must be set before reading a problem. numerics/feastol, 10 6 numerics/epsilon, 10 9 numerics/infinity, Limits limits/time limits/nodes limits/gap Randomization randomization/randomseedshift randomization/lpseed randomization/permutationseed Gregor Hendel, hendel@zib.de SCIP Introduction 16/70

32 Different Tasks Different Plugins Different plugin classes are responsible of the following tasks. 1. Presolving and node propagation Constraint handlers Presolvers Propagators 2. Separation Constraint handlers Separators 3. Improving solutions Primal heuristics 4. Branching Constraint handlers Branching rules 5. Node selection Node selectors Gregor Hendel, SCIP Introduction 17/70

33 Operational Stages Init Init Solve Problem Transforming Presolving Solving Free Transform Free Solve Gregor Hendel, SCIP Introduction 18/70

34 Operational Stages Init Init Solve Problem Transforming Presolving Solving Free Transform Free Solve Basic data structures are allocated and initialized. User includes required plugins (or just takes plugins). Gregor Hendel, SCIP Introduction 18/70

35 Problem Specification Init Init Solve Problem Transforming Presolving Solving Free Transform Free Solve User creates and modifies the original problem instance. Problem creation is usually done in file readers. Gregor Hendel, SCIP Introduction 19/70

36 Define Variables (LOP Example) SCIP_VAR * var ; SCIP_CALL ( // return value macro SCIPcreateVar ( scip, // SCIP pointer &var, // save in variable " varname ", // pass variable name 0.0, // lower bound 1.0, // upper bound length, // obj. value SCIP_VARTYPE_BINARY, // type TRUE, // initial FALSE, // removable NULL, NULL, NULL, // no callback functions NULL // no variable data ) ); SCIP_CALL ( SCIPaddVar ( scip, var ) ); // add var. Gregor Hendel, hendel@zib.de SCIP Introduction 20/70

37 TSP: Define Degree Constraints SCIP_CALL ( SCIPcreateConsLinear ( scip, // SCIP pointer &cons, // save in cons " consname ", // name nvar, // number of variables vars, // array of variables vals, // array of values 2.0, // left hand side 2.0, // right hand side ( equation ) TRUE, // initial? FALSE, // separate? TRUE, // enforce? TRUE, // check? TRUE, // propagate? FALSE, // local? FALSE, // modifable? FALSE, // dynamic? FALSE, // removable? FALSE // stick at node? )); SCIP_CALL ( SCIPaddCons (scip, cons ) ); // add constraint SCIP_CALL ( SCIPreleaseCons (scip, & cons ) ); // free cons. space MIPs are specified using linear constraints only (may be upgraded ). Gregor Hendel, hendel@zib.de SCIP Introduction 21/70

38 Transformation Init Init Solve Problem Transforming Presolving Solving Free Transform Free Solve Creates a working copy of the original problem. Gregor Hendel, hendel@zib.de SCIP Introduction 22/70

39 Original and Transformed Problem Original CIP Transformed CIP Original variables Transformed variables Original constraints Transformed constraints data is copied into separate memory area presolving and solving operate on transformed problem original data can only be modified in problem modification stage Gregor Hendel, SCIP Introduction 23/70

40 Presolving Init Init Solve Problem Transforming Presolving Solving Free Transform Free Solve Gregor Hendel, SCIP Introduction 24/70

41 Presolving Task reduce size of model by removing irrelevant information strengthen LP relaxation by exploiting integrality information make the LP relaxation numerically more stable extract useful information Primal Reductions: based on feasibility reasoning no feasible solution is cut off Dual Reductions: consider objective function at least one optimal solution remains Gregor Hendel, SCIP Introduction 25/70

42 Presolving Tips and Parameters Use display presolvers to list all presolvers of SCIP. Disable Presolving Disable all presolving for a model s e t p r e s o l v i n g emphasis o f f Deactivate single techniques s e t p r e s o l v i n g tworowbnd maxrounds 0 s e t p r o p a g a t i n g p r o b i n g maxprerounds 0 s e t c o n s t r a i n t s components advanced maxprerounds 0 Aggressive Presolving s e t p r e s o l v i n g emphasis a g g r e s s i v e General Rule of Thumb Only deactivate single presolving techniques if you encounter performance problems. Gregor Hendel, hendel@zib.de SCIP Introduction 26/70

43 Solving Init Init Solve Problem Transforming Presolving Solving Free Transform Free Solve Gregor Hendel, SCIP Introduction 27/70

44 Flow Chart SCIP Presolving Stop Domain propagation Node selection Solve LP Conflict analysis Pricing Primal heuristics Processing Enforce constraints Cuts Branching Gregor Hendel, SCIP Introduction 28/70

45 Flow Chart SCIP Presolving Stop Domain propagation Node selection Solve LP Conflict analysis Pricing Primal heuristics Processing Enforce constraints Cuts Branching Gregor Hendel, SCIP Introduction 28/70

46 Node Selection Techniques basic rules depth first search (DFS) early feasible solutions best bound search (BBS) improve dual bound best estimate search (BES) improve primal bound Task improve primal bound keep comp. effort small improve global dual bound combinations BBS or BES with plunging hybrid BES/BBS interleaved BES/BBS Gregor Hendel, SCIP Introduction 29/70

47 Node Selection Tips and Parameters Available Node Selectors d i s p l a y n o d e s e l e c t o r s node selector std p r i o r i t y memsave prio description e s t i m a t e b e s t e s t i m a t e s e a r c h b f s b e s t f i r s t s e a r c h... d f s depth f i r s t s e a r c h Switching Node Selectors Only the node selector with highest standard priority is active. Use s e t n o d e s e l e c t i o n d f s s t d p r i o r i t y to activate depth first search also in non-memsave mode. Gregor Hendel, hendel@zib.de SCIP Introduction 30/70

48 Flow Chart SCIP Presolving Stop Domain propagation Node selection Solve LP Conflict analysis Pricing Primal heuristics Processing Enforce constraints Cuts Branching Gregor Hendel, SCIP Introduction 31/70

49 Flow Chart SCIP Presolving Stop Domain propagation Node selection Solve LP Conflict analysis Pricing Primal heuristics Processing Enforce constraints Cuts Branching Gregor Hendel, SCIP Introduction 31/70

50 Domain Propagation x 1 x 1 x 2 x 3 x 2 x 3 Techniques constraint specific each cons handler may provide a propagation routine reduced presolving (usually) x 4 Task x 4 dual propagation root reduced cost strengthening objective function simplify model locally improve local dual bound detect infeasibility special structures variable bounds Gregor Hendel, hendel@zib.de SCIP Introduction 32/70

51 Flow Chart SCIP Presolving Stop Domain propagation Node selection Solve LP Conflict analysis Pricing Primal heuristics Processing Enforce constraints Cuts Branching Gregor Hendel, SCIP Introduction 33/70

52 LP Solving LP solver is a black box interface to different LP solvers: SoPlex, CPLEX, XPress, Gurobi, CLP,... primal/dual simplex barrier with/without crossover feasibility double-checked by SCIP condition number check resolution by changing parameters: scaling, tolerances, solving from scratch, other simplex Gregor Hendel, hendel@zib.de SCIP Introduction 34/70

53 LP Solving Tips and Parameters Most Important LP Parameters lp/initalgorithm, lp/resolvealgorithm Primal/Dual Simplex Algorithm Barrier w and w/o crossover lp/pricing normally LP solver specific Devex Steepest edge Quick start steepest edge lp/threads Slow LP performance is a blocker for the solving process and can sometimes be manually tuned significantly. Gregor Hendel, hendel@zib.de SCIP Introduction 35/70

54 Flow Chart SCIP Presolving Stop Domain propagation Node selection Solve LP Conflict analysis Pricing Primal heuristics Processing Enforce constraints Cuts Branching Gregor Hendel, SCIP Introduction 36/70

55 Pricing Pricing find variable with negative reduced costs or prove that there exists none typically problem specific Branch-and-Price huge number of variables start with subset add others, when needed dynamic aging of variables problem variable pricer to add them again early branching possible lazy variable bounds Gregor Hendel, SCIP Introduction 37/70

56 Flow Chart SCIP Presolving Stop Domain propagation Node selection Solve LP Conflict analysis Pricing Primal heuristics Processing Enforce constraints Cuts Branching Gregor Hendel, SCIP Introduction 38/70

57 Cutting Plane Separation Techniques general cuts complemented MIR cuts Gomory mixed integer cuts strong Chvátal-Gomory cuts implied bound cuts reduced cost strengthening Task strengthen relaxation add valid constraints generate on demand problem specific cuts 0-1 knapsack problem stable set problem 0-1 single node flow problem Gregor Hendel, SCIP Introduction 39/70

58 Cuts for the 0-1 Knapsack Problem Feasible region: (b Z +, a j Z + j N) X BK := { x {0, 1} n : j N a j x j b } Minimal Cover: C N j C a j > b j C\{i} a j b i C Minimal Cover Inequality x j C 1 j C 5x 1 + 6x 2 + 2x 3 + 2x 4 8 Minimal cover: C = {2, 3, 4} Minimal cover inequality: x 2 + x 3 + x 4 2 Gregor Hendel, hendel@zib.de SCIP Introduction 40/70

59 Separation Tips and Parameters Disable/Speed up/emphasize All Separation s e t s e p a r a t i n g emphasis o f f / f a s t / a g g r e s s i v e Disable Single Separation Techniques s e t s e p a r a t i n g c l i q u e f r e q 1 s e t c o n s t r a i n t s c a r d i n a l i t y s e p a f r e q 1 Some Important Parameters separating/maxcuts, separating/maxcutsroot separating/maxrounds, separating/maxroundsroot separating/maxstallrounds, separating/maxstallroundsroot Gregor Hendel, hendel@zib.de SCIP Introduction 41/70

60 Flow Chart SCIP Presolving Stop Domain propagation Node selection Solve LP Conflict analysis Pricing Primal heuristics Processing Enforce constraints Cuts Branching Gregor Hendel, SCIP Introduction 42/70

61 Constraint Enforcement LP solution may violate a constraint not contained in the relaxation. Enforcing is necessary for a correct implementation! Constraint handler resolves the infeasibility by... Reducing a variable s domain, Separating a cutting plane (may use integrality), Adding a (local) constraint, Creating a branching, Concluding that the subproblem is infeasible and can be cut off, or Just saying solution infeasible. Gregor Hendel, hendel@zib.de SCIP Introduction 43/70

62 Constraint Enforcement Presolving Stop Domain propagation Node selection Solve LP Pricing Conflict analysis Processing Enforce constraints Cuts Primal heuristics Branching Reduced domain Added cut Cutoff Infeasible Added constraint Branched Feasible Gregor Hendel, SCIP Introduction 44/70

63 Constraint Enforcement Presolving Stop Domain propagation Node selection Solve LP Pricing Conflict analysis Processing Enforce constraints Cuts Primal heuristics Branching Reduced domain Added cut Cutoff Infeasible Added constraint Branched Feasible Gregor Hendel, SCIP Introduction 44/70

64 Constraint Enforcement Presolving Stop Domain propagation Node selection Solve LP Pricing Conflict analysis Processing Enforce constraints Cuts Primal heuristics Branching Reduced domain Added cut Cutoff Infeasible Added constraint Branched Feasible Gregor Hendel, SCIP Introduction 44/70

65 Constraint Enforcement Presolving Stop Domain propagation Node selection Solve LP Pricing Conflict analysis Processing Enforce constraints Cuts Primal heuristics Branching Reduced domain Added cut Cutoff Infeasible Added constraint Branched Feasible Gregor Hendel, SCIP Introduction 44/70

66 Constraint Enforcement Presolving Stop Domain propagation Node selection Solve LP Pricing Conflict analysis Processing Enforce constraints Cuts Primal heuristics Branching Reduced domain Added cut Cutoff Infeasible Added constraint Branched Feasible Gregor Hendel, SCIP Introduction 44/70

67 Constraint Enforcement Presolving Stop Domain propagation Node selection Solve LP Pricing Conflict analysis Processing Enforce constraints Cuts Primal heuristics Branching Reduced domain Added cut Cutoff Infeasible Added constraint Branched Feasible Gregor Hendel, SCIP Introduction 44/70

68 Constraint Enforcement Presolving Stop Domain propagation Node selection Solve LP Pricing Conflict analysis Processing Enforce constraints Cuts Primal heuristics Branching Reduced domain Added cut Cutoff Infeasible Added constraint Branched Feasible Gregor Hendel, SCIP Introduction 44/70

69 Constraint Enforcement Presolving Stop Domain propagation Node selection Solve LP Pricing Conflict analysis Processing Enforce constraints Cuts Primal heuristics Branching Reduced domain Added cut Cutoff Infeasible Added constraint Branched Feasible Gregor Hendel, SCIP Introduction 44/70

70 Flow Chart SCIP Presolving Stop Domain propagation Node selection Solve LP Conflict analysis Pricing Primal heuristics Processing Branching Enforce constraints Cuts Gregor Hendel, SCIP Introduction 45/70

71 Branching Rules Task divide into (disjoint) subproblems improve local bounds Techniques branching on variables most infeasible least infeasible random branching strong branching pseudocost reliability VSIDS hybrid reliability/inference branching on constraints SOS1 SOS2 Gregor Hendel, SCIP Introduction 46/70

72 Branching Rule Tips and Parameters Branching Rule Selection Branching rules are applied in decreasing order of priority. SCIP> d i s p l a y b r a n c h i n g b r a n c h i n g r u l e p r i o r i t y maxdepth maxbddist r e l p s c o s t % p s c o s t % i n f e r e n c e % m o s t i n f % Reliability Branching Parameters All parameters prefixed with branching/relpscost/ sbiterquot, sbiterofs to increase the budget for strong branching minreliable (= 1), maxreliable (= 5) to increase threshold to consider pseudo costs as reliable Gregor Hendel, hendel@zib.de SCIP Introduction 47/70

73 Flow Chart SCIP Presolving Stop Domain propagation Node selection Solve LP Conflict analysis Pricing Primal heuristics Processing Enforce constraints Cuts Branching Gregor Hendel, SCIP Introduction 48/70

74 Primal Heuristics Task improve primal bound effective on average guide remaining search Techniques structure-based clique variable bounds rounding possibly solve final LP least infeasible guided objective objective feasibility pump Large Neighborhood Search RINS, local branching RENS Adaptive LNS Completion of partial solutions Gregor Hendel, SCIP Introduction 49/70

75 Primal Heuristics Tips and Parameters Disable/Speed Up/Emphasize Heuristics s e t h e u r i s t i c s emphasis o f f / f a s t / a g g r e s s i v e Disable an individual heuristic via s e t h e u r i s t i c s feaspump f r e q 1 Important Parameters heuristics/alns/nodesofs, heuristics/alns/nodesquot to increase the computational budget of this LNS technique heuristics/guided/... lpsolvefreq, maxlpiterofs maxlpiterquot to control the LP solving during this technique Advice Use emphasis settings. Do not attempt to individually tune heuristics by hand. Gregor Hendel, hendel@zib.de SCIP Introduction 50/70

76 Flow Chart SCIP Presolving Stop Domain propagation Node selection Solve LP Conflict analysis Pricing Primal heuristics Processing Enforce constraints Cuts Branching Gregor Hendel, SCIP Introduction 51/70

77 Conflict Analysis Task Analyze infeasibility Derive valid constraints Help to prune other nodes Techniques Analyze: Propagation conflicts Infeasible LPs Bound-exceeding LPs Strong branching conflicts Detection: Cut in conflict graph LP: Dual ray heuristic Use conflicts: Only for propagation As cutting planes Gregor Hendel, SCIP Introduction 52/70

78 Operational Stages Init Init Solve Problem Transforming Presolving Solving Free Transform Free Solve Gregor Hendel, SCIP Introduction 53/70

79 Outline SCIP Solving Constraint Integer Programs Constraint Integer Programming The Solving Process of SCIP Extending SCIP by Plugins The SCIP Optimization Suite Gregor Hendel, SCIP Introduction 54/70

80 The SCIP C API C code and documentation more than lines of C code, 20% documentation over assertions and debug messages HowTos: plugins types, debugging, automatic testing 10 examples illustrating the use of SCIP 5 problem specific SCIP applications to solve Coloring, Steiner Tree, or Multiobjective problems. Interface and usability Cross-platform availability due to CMake user-friendly interactive shell C++ wrapper classes LP solvers: SoPlex, CPLEX, Gurobi, Xpress, CLP, MOSEK, QSopt NLP solvers: IPOPT, FilterSQP, WORHP over parameters and 15 emphasis settings Gregor Hendel, hendel@zib.de SCIP Introduction 55/70

81 Interfaces to SCIP interactive shell supports 10 different input formats cip, cnf, flatzinc, rlp, lp, mps, opb, pip, wbo, zimpl C API/callable library C++ wrapper classes Python interface Java JNI interface AMPL GAMS Matlab (see also OPTI toolbox, Gregor Hendel, hendel@zib.de SCIP Introduction 56/70

82 Getting help If you should ever get stuck, you can type help in the interactive shell 2. read the documentation FAQ, HowTos for each plugin type, debugging, automatic testing, active mailing list (350+ members) search the mailing list archive (append site:listserv/pipermail/scip) register and post 4. search or post on Stack Overflow using the tag scip (more than 100 questions already answered) Gregor Hendel, SCIP Introduction 57/70

83 Structure of SCIP SCIP Primal Heuristic actcons coef cross over dins feaspump fixand infer frac guided int int shifting linesearch local branching mutation subnlp objpscost octane oneopt pscost rens rins rootsol rounding shifting shift& prop simple rounding trivial trysol twoopt under cover veclen zi round Variable Event Branch allfull strong full strong infer ence leastinf mostinf pscost random relps cost Conflict Constraint Handler and bound disjunc. count sols cumu lative indi cator integral knap sack linear linking logicor or orbi tope quadr atic setppc soc sos1 sos2 var bound xor Cutpool LP clp cpx msk none qso spx xprs Dialog Display Node selector bfs dfs estimate hybrid estim restart dfs Presolver bound shift dualfix implics intto binary probing trivial Impli cations Tree Reader ccg cip cnf fix lp mps opb ppm rlp sol sos zpl Pricer Separator clique cmir flow cover gomory implied bounds intobj mcf odd cycle rapid learn redcost strong cg zero half Propa gator pseudo obj root redcost vbound Relax Gregor Hendel, SCIP Introduction 58/70

84 Structure of SCIP SCIP Primal Heuristic actcons coef cross over dins feaspump fixand infer frac guided int int shifting linesearch local branching mutation subnlp objpscost octane oneopt pscost rens rins rootsol rounding shifting shift& prop simple rounding trivial trysol twoopt under cover veclen zi round Variable Event Branch allfull strong full strong infer ence leastinf mostinf pscost random relps cost Conflict Constraint Handler and bound disjunc. count sols cumu lative indi cator integral knap sack linear linking logicor or orbi tope quadr atic setppc soc sos1 sos2 var bound xor Cutpool LP clp cpx msk none qso spx xprs Dialog Display Node selector bfs dfs estimate hybrid estim restart dfs Presolver bound shift dualfix implics intto binary probing trivial Impli cations Tree Reader ccg cip cnf fix lp mps opb ppm rlp sol sos zpl Pricer Separator clique cmir flow cover gomory implied bounds intobj mcf odd cycle rapid learn redcost strong cg zero half Propa gator pseudo obj root redcost vbound Relax Gregor Hendel, SCIP Introduction 58/70

85 Structure of SCIP SCIP Primal Heuristic actcons coef cross over dins feaspump fixand infer frac guided int int shifting linesearch local branching mutation subnlp objpscost octane oneopt pscost rens rins rootsol rounding shifting shift& prop simple rounding trivial trysol twoopt under cover veclen zi round Variable Event Branch allfull strong full strong infer ence leastinf mostinf pscost random relps cost Conflict Constraint Handler and bound disjunc. count sols cumu lative indi cator integral knap sack linear linking logicor or orbi tope quadr atic setppc soc sos1 sos2 var bound xor Cutpool LP clp cpx msk none qso spx xprs Dialog Display Node selector bfs dfs estimate hybrid estim restart dfs Presolver bound shift dualfix implics intto binary probing trivial Impli cations Tree Reader ccg cip cnf fix lp mps opb ppm rlp sol sos zpl Pricer Separator clique cmir flow cover gomory implied bounds intobj mcf odd cycle rapid learn redcost strong cg zero half Propa gator pseudo obj root redcost vbound Relax Gregor Hendel, SCIP Introduction 58/70

86 Plugin based design SCIP core branching tree variables conflict analysis solution pool cut pool statistics clique table implication graph... Gregor Hendel, SCIP Introduction 59/70

87 Plugin based design SCIP core branching tree variables conflict analysis solution pool cut pool statistics clique table implication graph... Plugins external callback objects interact with the framework through a very detailed interface Gregor Hendel, hendel@zib.de SCIP Introduction 59/70

88 Plugin based design SCIP core branching tree variables conflict analysis solution pool cut pool statistics clique table implication graph... Plugins external callback objects interact with the framework through a very detailed interface SCIP knows for each plugin type: the number of available plugins priority defining the calling order (usually) SCIP does not know any structure behind a plugin plugins are black boxes for the SCIP core Gregor Hendel, hendel@zib.de SCIP Introduction 59/70

89 Plugin based design SCIP core branching tree variables conflict analysis solution pool cut pool statistics clique table implication graph... Plugins external callback objects interact with the framework through a very detailed interface SCIP knows for each plugin type: the number of available plugins priority defining the calling order (usually) SCIP does not know any structure behind a plugin plugins are black boxes for the SCIP core Very flexible branch-and-bound based search algorithm Gregor Hendel, hendel@zib.de SCIP Introduction 59/70

90 Types of Plugins Constraint handler: assures feasibility, strengthens formulation Separator: adds cuts, improves dual bound Pricer: allows dynamic generation of variables Heuristic: searches solutions, improves primal bound Branching rule: how to divide the problem? Node selection: which subproblem should be regarded next? Presolver: simplifies the problem in advance, strengthens structure Propagator: simplifies problem, improves dual bound locally Reader: reads problems from different formats Event handler: catches events (e.g., bound changes, new solutions) Display: allows modification of output... Gregor Hendel, SCIP Introduction 60/70

91 A closer look: branching rules SCIP Primal Heuristic actcons coef cross over dins feaspump fixand infer frac guided int int shifting linesearch local branching mutation subnlp objpscost octane oneopt pscost rens rins rootsol rounding shifting shift& prop simple rounding trivial trysol twoopt under cover veclen zi round Variable Event Branch allfull strong full strong infer ence leastinf mostinf pscost random relps cost Conflict Constraint Handler and bound disjunc. count sols cumu lative indi cator integral knap sack linear linking logicor or orbi tope quadr atic setppc soc sos1 sos2 var bound xor Cutpool LP clp cpx msk none qso spx xprs Dialog Display Node selector bfs dfs estimate hybrid estim restart dfs Presolver bound shift dualfix implics intto binary probing trivial Impli cations Tree Reader ccg cip cnf fix lp mps opb ppm rlp sol sos zpl Pricer Separator clique cmir flow cover gomory implied bounds intobj mcf odd cycle rapid learn redcost strong cg zero half Propa gator pseudo obj root redcost vbound Relax Gregor Hendel, SCIP Introduction 61/70

92 A closer look: branching rules onflict simple rounding shifting bound disjunc. allfull strong full strong count sols cumu lative Branch infer ence indi cator leastinf knap sack integral relps cost random pscost mostinf linear Gregor Hendel, SCIP Introduction 61/70

93 What does SCIP know about branching rules? SCIP knows the number of available branching rules each branching rule has a priority SCIP calls the branching rule in decreasing order of priority the interface defines the possible results of a call: branched reduced domains added constraints detected cutoff did not run Gregor Hendel, hendel@zib.de SCIP Introduction 62/70

94 How does SCIP call a branching rule? /* start timing */ SCIPclockStart ( branchrule ->branchclock, set ); /* call external method */ SCIP_CALL ( branchrule ->branchexeclp (set ->scip, branchrule, allowaddcons, result ) ); /* stop timing */ SCIPclockStop ( branchrule ->branchclock, set ); /* evaluate result */ if( * result!= SCIP_CUTOFF && * result!= SCIP_CONSADDED && * result!= SCIP_REDUCEDDOM && * result!= SCIP_SEPARATED && * result!= SCIP_BRANCHED && * result!= SCIP_DIDNOTRUN ) { SCIPerrorMessage ( " branching rule <%s> returned invalid result code <%d> from LP \ solution branching \n", branchrule ->name, * result ); return SCIP_INVALIDRESULT ; } Gregor Hendel, hendel@zib.de SCIP Introduction 63/70

95 What can a plugin access? Plugins are allowed to access all global (core) information branching tree variables conflict analysis solution pool cut pool statistics clique table implication graph... Gregor Hendel, hendel@zib.de SCIP Introduction 64/70

96 What can a plugin access? Plugins are allowed to access all global (core) information branching tree variables conflict analysis solution pool cut pool statistics clique table implication graph... Ideally, plugins should not access data of other plugins!!! Gregor Hendel, hendel@zib.de SCIP Introduction 64/70

97 What can a plugin access? Plugins are allowed to access all global (core) information branching tree variables conflict analysis solution pool cut pool statistics clique table implication graph... Ideally, plugins should not access data of other plugins!!! Branching Rules LP solution variables statistics Gregor Hendel, hendel@zib.de SCIP Introduction 64/70

98 Constraint Handlers Constraint handlers most powerful plugins in SCIP define the feasible region a single constraint may represent a whole set of inequalities Functions check and enforce feasibility of solutions can add linear representation to LP relaxation constraint-specific presolving, domain propagation, separation Result SCIP is constraint based Advantage: flexibility Disadvantage: limited global view Gregor Hendel, hendel@zib.de SCIP Introduction 65/70

99 Default Plugins SCIP Primal Heuristic actcons coef cross over dins feaspump fixand infer frac guided int int shifting linesearch local branching mutation subnlp objpscost octane oneopt pscost rens rins rootsol rounding shifting shift& prop simple rounding trivial trysol twoopt under cover veclen zi round Variable Event Branch allfull strong full strong infer ence leastinf mostinf pscost random relps cost Conflict Constraint Handler and bound disjunc. count sols cumu lative indi cator integral knap sack linear linking logicor or orbi tope quadr atic setppc soc sos1 sos2 var bound xor Cutpool LP clp cpx msk none qso spx xprs Dialog Display Node selector bfs dfs estimate hybrid estim restart dfs Presolver bound shift dualfix implics intto binary probing trivial Impli cations Tree Reader ccg cip cnf fix lp mps opb ppm rlp sol sos zpl Pricer Separator clique cmir flow cover gomory implied bounds intobj mcf odd cycle rapid learn redcost strong cg zero half Propa gator pseudo obj root redcost vbound Relax Gregor Hendel, SCIP Introduction 66/70

100 Extending SCIP SCIP Primal Heuristic actcons coef cross over dins feaspump fixand infer frac guided int int shifting linesearch local branching mutation subnlp objpscost octane oneopt pscost rens rins rootsol rounding shifting shift& prop simple rounding trivial trysol twoopt under cover veclen zi round Variable Event Branch allfull strong full strong infer ence leastinf mostinf pscost random relps cost Conflict Constraint Handler and bound disjunc. count sols cumu lative indi cator integral knap sack linear linking logicor or orbi tope quadr atic setppc soc sos1 sos2 var bound xor Cutpool LP clp cpx msk none qso spx xprs Dialog Display Node selector bfs dfs estimate hybrid estim restart dfs Presolver bound shift dualfix implics intto binary probing trivial Impli cations Tree Reader ccg cip cnf fix lp mps opb ppm rlp sol sos zpl Pricer Separator clique cmir flow cover gomory implied bounds intobj mcf odd cycle rapid learn redcost strong cg zero half Propa gator pseudo obj root redcost vbound Relax Gregor Hendel, SCIP Introduction 67/70

101 Extending SCIP SCIP Primal Heuristic actcons coef cross over dins feaspump fixand infer frac guided int int shifting linesearch local branching mutation subnlp objpscost octane oneopt pscost rens rins rootsol rounding shifting shift& prop simple rounding trivial trysol twoopt under cover veclen Variable Event Branch allfull strong full strong infer ence leastinf mostinf pscost random relps cost Conflict Constraint Handler and bound disjunc. count sols cumu lative indi cator integral knap sack linear linking logicor or orbi tope quadr atic setppc soc sos1 sos2 var bound Cutpool LP clp cpx msk none qso spx Dialog Display Node selector bfs dfs estimate hybrid estim Presolver bound shift dualfix implics intto binary probing Impli cations Tree Reader ccg cip cnf fix lp mps opb ppm rlp sol sos Pricer Separator clique cmir flow cover gomory implied bounds intobj mcf odd cycle rapid learn redcost strong cg Propa gator pseudo obj root redcost Relax Gregor Hendel, SCIP Introduction 67/70

102 Extending SCIP: TSP SCIP Primal Heuristic farthest insert coef 2-Opt dins feaspump fixand infer frac guided int int shifting linesearch local branching mutation subnlp objpscost octane oneopt pscost rens rins rootsol rounding shifting shift& prop simple rounding trivial trysol twoopt under cover veclen Variable Event sol found Branch allfull strong full strong infer ence leastinf mostinf pscost random relps cost Conflict Constraint Handler subtour bound disjunc. count sols cumu lative indi cator integral knap sack linear linking logicor or orbi tope quadr atic setppc soc sos1 sos2 var bound Cutpool LP clp cpx msk none qso spx Dialog Display Node selector bfs dfs estimate hybrid estim Presolver bound shift dualfix implics intto binary probing Impli cations Tree Reader tsp cip cnf fix lp mps opb ppm rlp sol sos Pricer Separator clique cmir flow cover gomory implied bounds intobj mcf odd cycle rapid learn redcost strong cg Propa gator pseudo obj root redcost Relax Gregor Hendel, SCIP Introduction 67/70

103 Extending SCIP: Coloring SCIP Primal Heuristic init coef 2-Opt dins feaspump fixand infer frac guided int int shifting linesearch local branching mutation subnlp objpscost octane oneopt pscost rens rins rootsol rounding shifting shift& prop simple rounding trivial trysol twoopt under cover veclen Variable Event Branch Ryan& Foster strong Ryan& Foster infer ence leastinf mostinf pscost random relps cost Conflict Constraint Handler store Graph bound disjunc. count sols cumu lative indi cator integral knap sack linear linking logicor or orbi tope quadr atic setppc soc sos1 sos2 var bound Cutpool LP clp cpx msk none qso spx Dialog Display Node selector bfs dfs estimate hybrid estim Presolver bound shift dualfix implics intto binary probing Impli cations Tree Reader col csol cnf fix lp mps opb ppm rlp sol sos Pricer coloring Separator clique cmir flow cover gomory implied bounds intobj mcf odd cycle rapid learn redcost strong cg Propa gator pseudo obj root redcost Relax Gregor Hendel, SCIP Introduction 67/70

104 Extending SCIP: STP SCIP Primal Heuristic TM coef local dins feaspump fixand infer frac guided int int shifting linesearch local branching mutation subnlp objpscost octane oneopt pscost rens rins rootsol rounding shifting shift& prop simple rounding trivial trysol twoopt under cover veclen Variable Event sol found Branch allfull strong full strong infer ence leastinf mostinf pscost random relps cost Conflict Constraint Handler stp bound disjunc. count sols cumu lative indi cator integral knap sack linear linking logicor or orbi tope quadr atic setppc soc sos1 sos2 var bound Cutpool LP clp cpx msk none qso spx Dialog Display Node selector bfs dfs estimate hybrid estim Presolver stp dualfix implics intto binary probing Impli cations Tree Reader stp cip cnf fix lp mps opb ppm rlp sol sos Pricer Separator clique cmir flow cover gomory implied bounds intobj mcf odd cycle rapid learn redcost strong cg Propa gator pseudo obj root redcost Relax Gregor Hendel, SCIP Introduction 67/70

105 Outline SCIP Solving Constraint Integer Programs Constraint Integer Programming The Solving Process of SCIP Extending SCIP by Plugins The SCIP Optimization Suite Gregor Hendel, SCIP Introduction 68/70

106 SCIP Optimization Suite Toolbox for generating and solving constraint integer programs free for academic use, available in source code Gregor Hendel, SCIP Introduction 69/70

107 SCIP Optimization Suite Toolbox for generating and solving constraint integer programs free for academic use, available in source code ZIMPL model and generate LPs, MIPs, and MINLPs SCIP MIP, MINLP and CIP solver, branch-cut-and-price framework SoPlex revised primal and dual simplex algorithm GCG generic branch-cut-and-price solver UG framework for parallelization of MIP and MINLP solvers Gregor Hendel, SCIP Introduction 69/70

108 Wrap-up How to solve your MINLP optimization problem: write down the mathematical description modeling language, e.g., ZIMPL, generates input for MINLP solver SCIP can even read ZIMPL files directly MIP and MINLP solving... is a bag of tricks new tricks are introduced almost every day advantages of SCIP open source, you can see everything that happens hundreds of parameters to play with broad scope easily extendable Gregor Hendel, hendel@zib.de SCIP Introduction 70/70