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## Robert Fourer Industrial Engineering & Management Sciences Northwestern Univers

Keith, Chris, Host has reference to this Academic Journal, PHwiki organized this Journal Robert Fourer Industrial Engineering & Management Sciences Northwestern University Evanston, Illinois 60208-3119, U.S.A. 4er@iems.northwestern.edu http://www.iems.northwestern.edu/~4er/SLIDES/ INFORMS Conference on OR/MS Practice Cambridge, Massachusetts Tuesday, April 27, 2004 Track 14: Selected Presentations: Features of Current Practice Languages in addition to Servers as long as Optimization Support Large-Scale Optimization Minimization or maximization of an objective that depends on many decision variables Subject to many interrelated restrictions (constraints) on the values of the variables Large-Scale Optimization Modeling Central Truth: Optimization Modeling is Hard Given access to the right technical tools in addition to expertise, building in addition to analyzing models is most of the work Subjects of this presentation Helping people build in addition to analyze models is the purpose of optimization modeling languages Giving access to the right technical tools in addition to expertise is the purpose of optimization servers

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Optimization Modeling Languages Examples Simple: Diet Complicated: Fleet sizing General observations Essential features Choices New developments The McDonalds Diet Problem Foods: QP Quarter Pounder FR Fries, small MD McLean Deluxe SM Sausage McMuffin BM Big Mac 1M 1% Lowfat Milk FF Filet-O-Fish OJ Orange Juice MC McGrilled Chicken Nutrients: Prot Protein Iron Iron VitA Vitamin A Cals Calories VitC Vitamin C Carb Carbohydrates Calc Calcium McDonalds Diet Problem Data

Formulation: Too General Minimize cx Subject to Ax = b x 0 Diet Problem Formulation: Too Specific Minimize 1.84 xQP + 2.19 xMD + 1.84 xBM + 1.44 xFF + 2.29 xMC + 0.77 xFR + 1.29 xSM + 0.60 x1M + 0.72 xOJ Subject to 28 xQP + 24 xMD + 25 xBM + 14 xFF + 31 xMC + 3 xFR + 15 xSM + 9 x1M + 1 xOJ 55 15 xQP + 15 xMD + 6 xBM + 2 xFF + 8 xMC + 0 xFR + 4 xSM + 10 x1M + 2 xOJ 100 6 xQP + 10 xMD + 2 xBM + 0 xFF + 15 xMC + 15 xFR + 0 xSM + 4 x1M + 120 xOJ 100 30 xQP + 20 xMD + 25 xBM + 15 xFF + 15 xMC + 0 xFR + 20 xSM + 30 x1M + 2 xOJ 100 20 xQP + 20 xMD + 20 xBM + 10 xFF + 8 xMC + 2 xFR + 15 xSM + 0 x1M + 2 xOJ 100 510 xQP + 370 xMD + 500 xBM + 370 xFF + 400 xMC + 220 xFR + 345 xSM + 110 x1M + 80 xOJ 2000 34 xQP + 35 xMD + 42 xBM + 38 xFF + 42 xMC + 26 xFR + 27 xSM + 12 x1M + 20 xOJ 350 Diet Problem Algebraic Model Given F, a set of foods N, a set of nutrients in addition to aij 0, as long as each i N in addition to j F : units of nutrient i in one serving of food j bi > 0, as long as each i N : units of nutrient i required, cj > 0, as long as each j F : cost per serving of food j, Define xj 0, as long as each j F : number of servings of food j to be purchased Minimize j F cj xj Subject to j F aij xj bi, as long as each i N Diet Problem

Algebraic Model in AMPL set NUTR; nutrients set FOOD; foods param amt {NUTR,FOOD} >= 0; nutrient in each food param n-min {NUTR} > 0; lower bounds on nutrients param cost {FOOD} > 0; costs of foods var Buy {FOOD} integer >= 0; foods to be purchased minimize TotalCost: sum {j in FOOD} cost[j] Buy[j]; subject to Need {i in NUTR}: sum {j in FOOD} amt[i,j] Buy[j] >= n-min[i]; Diet Problem Airline Fleet Assignment set FLEETS; param fleet-size {FLEETS} >= 0; set CITIES; set TIMES circular; set FLEET-LEGS within {f in FLEETS, c1 in CITIES, t1 in TIMES, c2 in CITIES, t2 in TIMES: c1 <> c2 in addition to t1 <> t2}; (f,c1,t1,c2,t2) represents availability of fleet f to cover the leg that leaves c1 at t1 in addition to whose arrival time plus turnaround time at c2 is t2 param leg-cost {FLEET-LEGS} >= 0; Computed Sets set LEGS := setof {(f,c1,t1,c2,t2) in FLEET-LEGS} (c1,t1,c2,t2); set of all legs that can be covered by some fleet set SERV-CITIES {f in FLEETS} := union {(f,c1,c2,t1,t2) in FLEET-LEGS} {c1,c2}; as long as each fleet, set of cities that it serves set OP-TIMES {f in FLEETS, c in SERV-CITIES[f]} circular by TIMES := setof {(f,c,c2,t1,t2) in FLEET-LEGS} t1 union setof {(f,c1,c,t1,t2) in FLEET-LEGS} t2; as long as each fleet in addition to city served by that fleet, set of active arrival & departure times, with arrival time padded as long as turn requirements Fleet Assignment

Underlying Network Model minimize Total-Cost; node Balance {f in FLEETS, c in SERV-CITIES[f], OP-TIMES[f,c]}; as long as each fleet in addition to city served by that fleet, a node as long as each possible time arc Fly {(f,c1,t1,c2,t2) in FLEET-LEGS} >= 0, <= 1, from Balance[f,c1,t1], to Balance[f,c2,t2], obj Total-Cost leg-cost[f,c1,t1,c2,t2]; arcs as long as fleet/flight assignments arc Sit {f in FLEETS, c in SERV-CITIES[f], t in OP-TIMES[f,c]} >= 0, from Balance[f,c,t], to Balance[f,c,next(t)]; arcs as long as planes on the ground Fleet Assignment Service in addition to Fleet-Size Constraints subj to Service {(c1,t1,c2,t2) in LEGS}: sum {(f,c1,t1,c2,t2) in FLEET-LEGS} Fly[f,c1,t1,c2,t2] = 1; each leg must be served by some fleet subj to FleetSize {f in FLEETS}: sum {(f,c1,t1,c2,t2) in FLEET-LEGS: ord(t2,TIMES) < ord(t1,TIMES)} Fly[f,c1,t1,c2,t2] + sum {c in SERV-CITIES[f]} Sit[f,c,last(OP-TIMES[f,c])] <= fleet-size[f]; planes used = the number in the air at the last time (arriving "earlier" than they leave) plus number on the ground at the last time Fleet Assignment Essential Modeling Language Features Sets in addition to indexing Simple sets Compound sets Computed sets Variables, objectives in addition to constraints Linear, piecewise-linear Nonlinear Integer in addition to much more Express problems in the many ways that people do Support a broad variety of modeling situations Drive varied solvers Modeling Language Features (contd) Recognizing other types of models Network problems Complementarity problems Exchanging in as long as mation with solvers Solver-specific directives Rays of unboundedness, infeasibility diagnostics, in addition to other results Programming iterative schemes Loops over sets; if-then-else tests Switching between subproblems Commercial Modeling Languages AIMMS www.aimms.com AMPL www.ampl.com GAMS www.gams.com LINGO www.lindo.com MPL www.maximalsoftware.com OPL www.ilog.com/products/oplstudio/ what about spreadsheet optimizers Choosing a Modeling Language The language itself Naturalness Power The modeling system Scalability of language translator Convenience of user interface Connections to other systems Support as long as varied solvers Database & spreadsheet links Callable interfaces Application development features New Directions in Modeling Languages Model types Semi-definite in addition to second-order cone programs Combinatorial optimization problems Complementarity in addition to equilibrium constrained problems Solver support MPEC solvers Constraint programming Global optimization Optimization Servers Challenges in optimization modeling Software challenges Solver challenges Server challenges Examples NEOS (www-neos.mcs.anl.gov) WEBOPT (www.webopt.org) Software Challenges No one way to solve Hundreds of solvers Competing free codes in addition to commercial products Competing methods Models built to order Competing modeling systems Each system supports multiple solvers Many solvers work with multiple systems Result: A tangle of software Unlike comprehensive statistics/simulation packages an opportunity as long as the Internet to offer guidance in addition to access Optimization Solver Challenges Power Faster computers More powerful algorithms Better implementations of algorithms Ease of use Modeling languages in addition to systems (AIMMS, AMPL, GAMS, LINGO, MPL, OPL, ) Add-ins to general-purpose systems (Excel, MATLAB) Object-oriented programming interfaces Accessibility Unpleasant to download in addition to install Trial versions have various limitations few solvers installed at any one site Optimization Server Challenges Offer optimization as an Internet resource One remote server offering many solvers Any local client can submit optimization jobs Support varied clients General-purpose software: web browsers, e-mailers General optimization software: modeling languages & systems Specialized tools History Servers as long as individual solvers Servers as long as individual modeling languages General-purpose servers Optimization NEOS www-neos.mcs.anl.gov A general-purpose optimization server About 50 solvers in all Commercial as well as experimental solvers Central scheduler with distributed solver sites A research project Currently free of charge Supported through the Optimization Technology Center of Northwestern Univ & Argonne National Laboratory

Using NEOS Varied submission options E-mail Web as long as ms TCP/IP socket-based submission tool: Java or tcl/tk Direct from optimization modeling environments Numerous as long as mats Low-level as long as mats: MPS, SIF, SDPA Programming languages: C/ADOL-C, Fortran/ADIFOR High-level modeling languages: AMPL, GAMS Using NEOS (contd) Examples Used through a web browser Used within a modeling environment Frequently asked questions Who uses NEOS What solvers does it offer How is it supported Learn About Your Problem NEOS Guide Optimization tree & software guide Frequently asked questions Using NEOS

Investigate Solvers NEOS Server home page Using NEOS Investigate Solvers NEOS Server solver listing Using NEOS Try a Solver: Web Interface Submission as long as m as long as your problem Using NEOS

Services Access to solvers in addition to modeling systems FortMP, FortSP, CPLEX MPL, AMPL Optimization-based decision support systems Supply chain management Portfolio optimization Remote workspace Model in addition to data files Solver Control in addition to solution files Data in addition to log files WEBOPT Graphical Interface WEBOPT New Directions in Optimization Servers Automated user help Problem analysis Solver choice Automated benchmarking Extension of services Clones Web service paradigms Charges as long as service Determining prices Scaling up

## Keith, Chris Host

Keith, Chris is from United States and they belong to Classic Gardens and Landscape Show – WERC-AM, The and they are from Birmingham, United States got related to this Particular Journal. and Keith, Chris deal with the subjects like Gardening

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