The Aimms Interface to Constraint Programming Willem-Jan van Hoeve1, Marcel Hunting2, and Chris Kuip2 1 Tepper School of Business, Carnegie Mellon University 2 Paragon Decision Technology Abstract. We present an extension of the modeling system Aimms to handle constraint programming problems. Our goal is to provide a more accessible interface to CP technology than current systems o"er. We #rst present basic CP modeling constructs that can be realized with minimum changes to the existing syntax. We then discuss the handling of global constraints &astly, %e present our extensions to modeling scheduling problems, based on the no%'classical representation as activities and re- sources (n important bene#t of the Aimms interface to CP is the ease with which hybrid CP)!* solution methods can be developed 1 Introduction From its inception, the academic field of Constraint Programming (CP) has een coupled with !ell-engineered solvers that !ere applied to challenging, of- ten large-scale, industrial problems (e.g., CHIP, Cosytec, #%&' Solver, (#CStus, )clipse, Choco, Kalis, 'ecode, Comet)" Most, if not all, of these solvers require a considerable amount of training efore they can e used $ an engineering stu- dent or &perations Research practitioner, let alone an MB- student" &ne reason for this is that each of these solvers has its o!n specific modeling language, for example in the st$le of Prolog or C+/" -nother reason is that CP requires a different modeling st$le than mathematical programming, to the extent that even a d$namic search strateg$ can e modeled in most systems" Finall$, even though most available solvers share the most important characteristics of CP, each comes with its o!n li rary of global constraints, associated filtering algo- rithms, modeling concepts (e.g., resource constrained scheduling, set variables, local search), and specialized search techniques. Consequently, a problem ma$ e modeled and solved in entirel$ different !a$s $ different solvers" -ll of this limits the accessi ilit$ of CP to t$pical &perations Research practitioners. &ne of the main goals of the pro2ect descri ed in this abstract is to ma3e CP more accessible to a !ider range of practitioners, from industrial &+ experts to M,- students. In order to achieve this, !e have developed a Constraint Programming e.tension of the modeling s$stem Aimms, 3eeping the following requirements and targets in mind. First, !e !ould li3e the difference et!een standard mathematical programming models and CP models to e minimal for a user, and in particular for an Aimms user" Second, !e must offer the most +, Willem-Jan van .oeve, Marcel .unting, and Chris Kuip po!erful CP technolog$ that is available (e.g", access to advanced algorithms for resource-constrained scheduling), as !ell as all common global constraints. Third, the system should e designed for solving hard industrial problems" Note that these targets can e conflicting, e"g., the support of global constraints for their filtering po!er does not align with standard mathematical programming terminology" 2 Background and Related Work (everal other industrial and academic modeling languages/systems have een de- veloped to make the use of CP and h$brid methods more accessi le. Academic systems focusing on the integration of solvers include Zinc 9:; and SIMP% 9<=;" In- dustrial systems include IBM #%&' CP%)> &ptimization Studio (with the &P% language 9<1]), Fico Xpress &ptimization (tudio (with the Mosel language 9?;), and Comet 9<@;" Even though these systems are po!erful and provide advanced interfaces, they mostl$ appeal to specialized developers, and suffer from the aforementioned shortcomings !ith respect to accessi ilit$ to non-specialists, in our opinion" &ur goal is to contri ute to these developments $ focusing specif- icall$ at a solver-independent, intuitive graphical modeling interface, as offered $ the Aimms system, in order to attract non-experts to use CP technology" The modeling language underl$ing Aimms 92,<A; !as originall$ developed in a similar spirit as 'AM( 9=; or AMPL 9B;" (imilar to those systems, it is ased on an algebraic s$ntax and offers access to (at least) #LP, CP, and NLP technology" The main difference with these other languages, ho!ever, is that model development in Aimms revolves around a graphical modeling interface depicting the hierarchical structure in a model formulation" This enables the user to formulate a pro lem in an intuitive and naturall$ decomposed manner" - second important feature of Aimms is that it offers user-developed Dpages’, that can e used to graphicall$ depict solutions and even to build entire end-user applications that can e deplo$ed in practice" 3 Contributions The Aimms e.tension to CP supports all common global constraints, ranging from AllDifferent to Sequence and BinPacking" In addition, it supports ad- vanced scheduling concepts ased on the classical representation using Dactivi- tiesE and DresourcesE 9<;, as !ell as specialized global scheduling constraints as introduced recently in 9F;" Interestingl$, man$ modeling concepts from CP !ere alread$ present in the existing Aimms syntax, albeit restricted to non-variable identifiers" Namel$, Aimms already offers all standard arithmetic, logical, and set related operators" 4his allo!ed us to provide CP functionalit$ with minimal changes to the existing syntax in man$ cases" Finall$, !e have uilt an interface to the CP solvers IBM #%&' CP Optimizer and 'ecode" We refer to 9G; for more details. The Aimms 0nterface to Constraint Programming +1 In summary, the most important contribution of our e.tension to the practice of CP is that less-experienced users can access CP technology in a more intuitive !a$, and furthermore make use of all standard features of Aimms including its advanced graphical interface. In addition, !e remar3 that the related modeling systems 'AMS and AMP% do not support CP technology,1 while &PL, Mosel, and Comet do not provide access to NLP solvers such as C&NOPT, K5#4+O, IP&PT and %'&" With the addition of our CP interface, Aimms is currentl$ the only industrial-strength optimization modeling system that provides access to LP, MIP, CP, NLP, and CP solvers, !hich makes it possible to uild integrated models combining all these technologies. References 2 P Baptiste, C. &e Pape, and W. Nuijten Constraint-Based Scheduling: Applying Constraint Programming to Scheduling Problems Klu%er (cademic Publishers, ,552 , - Bisschop and * Entri7en AIMMS: The modeling system Paragon Decision Technology, 2881 1 - Bisschop and ( Meeraus. !n the development of a general algebraic modeling system in a strategic planning environment Mathematical Programming Study, pages 29,8, 28:, + ; Colombani and S Heipc7e Mosel: (n 6xtensible 6nvironment for Modeling and Programming Solutions. 0n Proceedings of the Fourth International Wor shop on Integration of AI and !" techniques in Constraint Programming for Combinatorial Optimisation Problems $CPAI!"%, ,55, = * >ourer and D.M Gay Extending an algebraic modeling language to support constraint programming. I&F!"MS 'ournal on Computing, 2+<1,,91++, ,55, @ * >ourer, D.M ?ay, and B.W Kernighan (MP&< ( Modeling Language for Mathematical Programming Management Science, 1@<=289==+, 2885 A W - van .oeve, M Hunting, and C. Kuip Constraint programming. 0n AIMMS ()*+: The ,anguage "eference, chapter ,2 Paragon Decision Technology, ,522 : P &aborie. 0BM 0&!? CP !ptimizer for Detailed Scheduling 0llustrated on Three Problems. 0n Proceedings of CPAI!", volume ==+A of ,&CS, pages 2+:92@, Springer, ,558 8 / Marriott, 3 3ethercote, * Rafeh, P - Stuc7ey, M Garcia De La Banda, and M Wallace. The design of the Zinc modelling language. Constraints, 21C1D<,,89 ,@A, ,55: 25 M *oelofs and - - Bisschop AIMMS ()**: The ,anguage "eference Paragon De' cision Technology, ,525 http<))%%% aimms com)downloads/manuals)language- reference. 22 P Ean .entenryc7 The OPL Optimi-ation Programming ,anguage The M0T Press, 2888 With contributions by 0 &ustig, & Michel, and - '> Puget 2, P Ean .entenryc7 and & Michel. Constraint-Based ,ocal Search The M0T Press, ,55= 21 T ;unes, 0 D. (ron, and - 3 .oo7er. (n integrated solver for optimization problems Operations "esearch, =:C,D<1+,91=@, ,525 1 We note that the (MP& language extensions to CP, as described in F=G, have not yet been implemented .