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DM841 D ISCRETE O PTIMIZATION Introduction to Gecode Marco Chiarandini Department of Mathematics & Computer Science University of Southern Denmark [ Based on slides by Christian Schulte, KTH Royal Institute of Technology ] Constraint

  1. DM841 D ISCRETE O PTIMIZATION Introduction to Gecode Marco Chiarandini Department of Mathematics & Computer Science University of Southern Denmark [ Based on slides by Christian Schulte, KTH Royal Institute of Technology ]

  2. Constraint Languages Outline Gecode 1. Constraint Languages 2. Gecode 2

  3. Constraint Languages Resume Gecode ◮ Modelling in CP ◮ Examples: graph labelling with consecutive numbers, cryptoarithmetic ◮ Overview on Constraint Programming ◮ modelling ◮ search = backtracking + branching ◮ propagate (inference) + filtering Constraint Programming: representation (modeling language) + reasoning (search + propagation) 3

  4. Constraint Languages Outline Gecode 1. Constraint Languages 2. Gecode 4

  5. Constraint Languages Constraint Programming Systems Gecode (modeling) Expressive language stream + (efficient solvers) Algorithm stream CP systems typically include ◮ general purpose algorithms for constraint propagation (arc consistency on finite domains) ◮ built-in constraint propagation for various constraints (eg, linear, Boolean, global constraints) ◮ built-in for constructing various forms of search 5

  6. Constraint Languages Logic Programming Gecode Logic programming is the use of mathematical logic for computer programming. First-order logic is used as a purely declarative representation language, and a theorem-prover or model-generator is used as the problem-solver. Logic programming supports the notion of logical variables ◮ Syntax – Language ◮ Alphabet ◮ Well-formed Expressions E.g., 4X + 3Y = 10; 2X - Y = 0 ◮ Semantics – Meaning ◮ Interpretation ◮ Logical Consequence ◮ Calculi – Derivation ◮ Inference Rule ◮ Transition System 6

  7. Constraint Languages Logic Programming Gecode Example: Prolog A logic program is a set of axioms, or rules, defining relationships between objects. A computation of a logic program is a deduction of consequences of the program. A program defines a set of consequences, which is its meaning. Sterling and Shapiro: The Art of Prolog, Page 1. To deal with the other constraints one has to add other constraint solvers to the language. This led to Constraint Logic Programming 7

  8. Constraint Languages Prolog Approach Gecode ◮ Prolog II till Prolog IV [Colmerauer, 1990] ◮ CHIP V5 [Dincbas, 1988] http://www.cosytec.com (commercial) ◮ CLP [Van Hentenryck, 1989] ◮ Ciao Prolog (Free, GPL) ◮ GNU Prolog (Free, GPL) ◮ SICStus Prolog ◮ ECLiPSe [Wallace, Novello, Schimpf, 1997] http://eclipse-clp.org/ (Open Source) ◮ Mozart programming system based on Oz language (incorporates concurrent constraint programming) http://www.mozart-oz.org/ [Smolka, 1995] 8

  9. Constraint Languages Other Approaches Gecode Libraries: Constraints are modeled as objects and are manipulated by means of special methods provided by the given class. ◮ CHOCO (free) http://choco.sourceforge.net/ ◮ Kaolog (commercial) http://www.koalog.com/php/index.php ◮ ILOG CP Optimizer www.cpoptimizer.ilog.com (ILOG, commercial) ◮ Gecode (free) www.gecode.org C++, Programming interfaces Java and MiniZinc ◮ G12 Project http://www.nicta.com.au/research/projects/constraint_ programming_platform 9

  10. Constraint Languages Other Approaches Gecode Modelling languages: ◮ OPL [Van Hentenryck, 1999] ILOG CP Optimizer www.cpoptimizer.ilog.com (ILOG, commercial) ◮ MiniZinc [] (open source, works for various systems, ECLiPSe, Geocode) ◮ Comet ◮ AMPL 10

  11. Constraint Languages Gecode ◮ Catalogue of Constraint Programming Tools: http://openjvm.jvmhost.net/CPSolvers/ ◮ Workshop "CPSOLVERS-2013" http://cp2013.a4cp.org/node/99 11

  12. Constraint Languages CP Languages Gecode Greater expressive power than mathematical programming ◮ constraints involving disjunction can be represented directly ◮ constraints can be encapsulated (as predicates) and used in the definition of further constrains However, CP models can often be translated into MIP model by ◮ eliminating disjunctions in favor of auxiliary Boolean variables ◮ unfolding predicates into their definitions 12

  13. Constraint Languages CP Languages Gecode ◮ Fundamental difference to LP ◮ language has structure (global constraints) ◮ different solvers support different constraints ◮ In its infancy ◮ Key questions: ◮ what level of abstraction? ◮ solving approach independent: LP, CP, ...? ◮ how to map to different systems? ◮ Modeling is very difficult for CP ◮ requires lots of knowledge and tinkering 13

  14. Constraint Languages Summary Gecode ◮ Model your problem via Constraint Satisfaction Problem ◮ Declare Constraints + Program Search ◮ Constraint Propagation ◮ Languages 14

  15. Constraint Languages Outline Gecode 1. Constraint Languages 2. Gecode 15

  16. Gecode an open constraint solving library Christian Schulte KTH Royal Institute of Technology, Sweden

  17. Gecode People � Core team September 2013 � Christian Schulte , Guido Tack , Mikael Z. Lagerkvist. � Code � contributions: Christopher Mears, David Rijsman, Denys Duchier, Filip Konvicka, Gabor Gecode, Christian Schulte Szokoli, Gabriel Hjort Blindell, Gregory Crosswhite, Håkan Kjellerstrand, Joseph Scott, Lubomir Moric, Patrick Pekczynski, Raphael Reischuk, Stefano Gualandi, Tias Guns, Vincent Barichard. � fixes: Alexander Samoilov, David Rijsman, Geoffrey Chu, Grégoire Dooms, Gustavo Gutierrez, Olof Sivertsson, Zandra Norman. � Documentation � contributions: Christopher Mears. � fixes: Seyed Hosein Attarzadeh Niaki, Vincent Barichard, Pavel Bochman, Felix Brandt, Markus Böhm, Roberto Castañeda Lozano, Gregory Crosswhite, Pierre Flener, Gustavo Gutierrez, Gabriel Hjort Blindell, Sverker Janson, Andreas Karlsson, Håkan Kjellerstrand, Chris Mears, Benjamin Negrevergne, Flutra Osmani, Max Ostrowski, David Rijsman, Dan 2 Scott, Kish Shen.

  18. Gecode Generic Constraint Development Environment � open September 2013 � easy interfacing to other systems � supports programming of: constraints, branching strategies, search engines, variable domains Gecode, Christian Schulte � comprehensive � constraints over integers, Booleans, sets, and floats � different ¡propagation ¡strength, ¡half ¡and ¡full ¡reification, ¡… ¡ � advanced branching heuristics (accumulated failure count, activity) � many search engines (parallel, interactive graphical, restarts) � automatic symmetry breaking (LDSB) � no-goods from restarts � MiniZinc support 3

  19. Gecode Generic Constraint Development Environment � efficient September 2013 � all gold medals in all categories at all MiniZinc Challenges � documented � tutorial (> 500 pages) and reference documentation � free Gecode, Christian Schulte � MIT license, listed as free software by FSF � portable � implemented in C ++ that carefully follows the C ++ standard � parallel � exploits multiple cores of today's hardware for search � tested � some 50000 test cases, coverage close to 100% 4

  20. SOME BASIC FACTS Gecode, Christian Schulte September 2013 5

  21. Architecture modeling layer September 2013 Gist search integers sets floats interactive search engines tool Gecode, Christian Schulte Gecode kernel � Small domain-independent kernel � Modules � per variable type: variables, constraint, branchings , ¡… � search, FlatZinc support, ¡… � Modeling layer � arithmetic, ¡set, ¡Boolean ¡operators; ¡regular ¡expressions; ¡matrices, ¡… 6 � All APIs are user-level and documented (tutorial + reference)

  22. Openness � MIT license permits commercial, closed-source use September 2013 � motivation: public funding, focus on research � not a reason: attitude, politics, dogmatism � More than a license � license Gecode, Christian Schulte restricts what users may do � code and documentation restrict what users can do � Modular, structured, documented, readable � complete tutorial and reference documentation � new ideas from Gecode available as scientific publications � Equal rights: Gecode users are first-class citizens � you can do what we can do: APIs � you can know what we know: documentation 7 � on every level of abstraction

  23. Constraints in Gecode � Constraint families September 2013 � arithmetics, Boolean, ordering, ¡…. � alldifferent, count (global cardinality, …), ¡ element, scheduling, table and regular, sorted, sequence, circuit, channel, bin-packing, lex, geometrical packing, nvalue, lex , ¡value ¡precedence, ¡… � Families Gecode, Christian Schulte � many different variants and different propagation strength � All global constraints from MiniZinc have a native implementation � Gecode  Global Constraint Catalogue: > 70 constraints abs_value, all_equal, alldifferent, alldifferent_cst, among, among_seq, among_var, and, arith, atleast, atmost, bin_packing, bin_packing_capa, circuit, clause_and, clause_or, count, counts, cumulative, cumulatives, decreasing, diffn, disjunctive, domain, domain_constraint, elem, element, element_matrix, eq, eq_set, equivalent, exactly, geq, global_cardinality, gt, imply, in, in_interval, in_intervals, in_relation, in_set, increasing, int_value_precede, int_value_precede_chain, inverse, inverse_offset, leq, lex, lex_greater, lex_greatereq, lex_less, lex_lesseq, link_set_to_booleans, lt, maximum, minimum, nand, neq, nor, not_all_equal, not_in, nvalue, nvalues, or, roots, scalar_product, set_value_precede, sort, sort_permutation, strictly_decreasing, 8 strictly_increasing, sum_ctr, sum_set, xor

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