  Xpress Mosel examples  Models by problem type / modeling tasks Folio - Modelling examples from 'Getting started'LP, MIP and QP models, data input/output, user graphs, heuristics  Folio - Advanced modelling and solving tasksMultiple MIP solutions, infeasibility handling, data transfer in memory, remote execution, XML and JSON data formats, solver tuning  Linearizations and approximations via SOS and piecewise linear (pwlin) expressionsPiecewise linear, approximation, SOS, SOS1, SOS2, SOS-1, SOS-2, Special Ordered Set, pwlin, pws, step function, piecewise linear function  General constraints and Boolean variablesgeneral constraints, boolvar, logctr, Boolean variables, logical expressions, minimum value, maximum value, absolute value  Indicator constraintsindicator constraints, logic constraints, logctr  Assignmentsimple LP problem, graphical representation of results  Bin packingsimple MIP problem, random generation of data,
                    use of model parameters, setting Optimizer controls  Blending oressimple LP problem, formulation of blending constraints  Capital budgetingsimple MIP problem  Contract allocationsimple MIP problem, semi-continuous variables,
                    graphical representation of results  Cutting stockMIP problem solved by column generation, 
                    working with multiple problems, using 'sethidden',
                   setting Optimizer and Mosel control parameters  Lot sizingMIP problem, implementation of Branch-and-Cut and
                   Cut-and-Branch algorithms, definition of Optimizer callbacks,
                   Optimizer and Mosel parameter settings, 'case', 'procedure',
                   'function', time measurement  Facility locationMIP problem, graphical solution representation,
                  re-solving with modified bounds, data input from file,
                  dynamic arrays for data and decision variables, use of
                  'exists', model cuts  Knapsacksimple IP problem, formulation of knapsack constraints,
                   model parameters, function 'random'  Multi-period, multi-site production planningLP or MIP problem, formulation of resource constraints and
                    material balance constraints, formatted solution printing, if-then-else, if-then-elif statements  Project planning with resource constraintsMIP problem, alternative formulation with SOS-1,
                    tricky formulation of resource use profiles and
                   calculation of benefits, graphical solution representation  Purchasing with price breaksMIP problem, modeling a piecewise linear function with SOS-2,
                     graphical representation of data  Transportsimple LP problem, using dynamic arrays for data and
                     decision variables, formatted output printing, inline 'if',
                     format of data files  TSPMIP problem, loop over problem solving, TSP subtour 
                     elimination algorithm; 
                     procedure for generating additional constraints, recursive 
                     subroutine calls, working with sets, 'forall-do', 
                     'repeat-until', 'getsize', 'not', graphical representation
                     of solutions  Set coveringMIP problem, modeling an equivalence; sparse data format,
                     graphical output representation, 'if-then-else'  Single period product mixSimple LP problem, single period production planning  Personnel requirement planningsimple MIP problem, formulation of balance constraints
                     using inline 'if'  Matching flight crews2 MIP problems with different objectives, data preprocessing,
                     incremental definition of data array, encoding of arcs, 
                     logical 'or' (cumulative version) and 'and', 'procedure' 
                     for printing solution, 'forall-do', 'max', 'finalize',
                     graphical representation of results, 'sin', 'cos'  Maximum flow in a telecom networkMIP problem, encoding of arcs, 'range', 'exists', 'create',
                     algorithm for printing paths, 'forall-do', 'while-do', 
                     'round', graphical representation of results  Multi-commodity network flowMIP problem, encoding of paths, 'finalize', 'getsize'  Vehicle routingMIP problem, formulation of constraints to eliminate
                     inadmissible subtours, definition of model cuts,
                     selection  with '|', algorithm for printing the tours, 
                     graphical solution representation  Minimum cost flowMIP problem, formulation with extra nodes for modes of
                     transport; encoding of arcs, 'finalize', union of sets, 
                     nodes labeled with strings, graphical solution representation  Line balancingMIP problem, encoding of arcs, 'range', formulation of 
                     sequencing constraints  Minimum weight spanning treeMIP problem, formulation of constraints to exclude subcycles,
                     graphical representation of results  Flow-shop schedulingMIP problem, alternative formulation using SOS1,
                     graphical solution representation  Job shop schedulingMIP problem, formulating disjunctions (BigM); 
                     'dynamic array', 'range', 'exists', 'forall-do',
                     graphical solution representation  Transshipment formulation of multi-period production planningMIP problem, representation of multi-period production 
                     as flow; encoding of arcs, 'exists', 'create', 'isodd', 
                     'getlast', inline 'if'  Set partitioningMIP problem, algorithm for data preprocessing; file 
                     inclusion, 3 nested/recursive procedures, working with 
                     sets, 'if-then', 'forall-do', 'exists', 'finalize'  Open shop schedulingMIP problem, data preprocessing, algorithm for preemptive 
                     scheduling that involves looping over optimization,
                     ''Gantt chart'' printing and drawing  Sequencing jobs on a single machineMIP problem with 3 different objectives; 'procedure' 
                     for solution printing, 'if-then'  Timetable for courses and teachersMIP problem, many specific constraints, tricky (pseudo-)
                     objective function, 'finalize'  Basic LP tasks: problem statement and solving; solution analysisLP solving, solution printout, array and set data structures  Basic MIP tasks: binary variables; logic constraintsMIP solving, binary variables, index set types, logic constraints  LCSP: Labour constrained scheduling problemDynamic creation of variables, formulation of resource constraints  Transportation problem with piecewise linear cost expressionsMIP problem  Approximating nonlinear univariate functions via   piecewise linear constraintsMIP problem  MAXSAT solving via MIPMAXSAT model  Conditional creation of decision variablesuse of 'exists', finalization of index sets  Delivery: Infeasibility analysis with IISRetrieving and displaying IIS  Overview of Mosel examples for 'Business Optimization' bookLP, MIP, NLP problem formulations, solution reporting, graphical display, multiple problems, iterative solution algorithms 
   Models by application area Introductory examples Mining and process industries Scheduling problems Planning problems Loading and cutting problems Ground transport Air transport Telecommunication problems Economics and finance Timetabling and personnel planning Local authorities and public services
   Programming with Mosel Dynamic package loadingdynamic package loading, model compilation, BIM file  Recursive remote filesAccess to files on remote (parent or
                   child) nodes  Basic set operationsInitializing sets, set operations, set comparison  Using moseldocGenerating online documentation for Mosel models and packages  Largest common divisorRecursive function calls; using 'readln'  Smallest and largest value in a setThe 'if-then-elif-then' selection statement  Perfect numbersUsing the 'forall' loop  Prime numbers using the Sieve of EratosthenesNested loops: repeat-until, while, while-do  Read two tables and a set from a text data fileFile access, using 'readln', 'fskipline'  Parsing a CSV-format data fileText parsing functionality  Sort an array of numbers using Shell's methodNested loops: repeat-until, forall-do, while-do  Sort an array of numbers using QuicksortRecursive subroutine calls, overloading of subroutines  Defining a package to handle binary treesDefinition of subroutines, data structures list and record, type definition  Encapsulate binary file into a BIMSubmodel included in model source, datablock, deployment as executable  Generate an executable from a Mosel source filedeployment as executable, deployment via scripts  Using the automatic translation systemUsing xprnls, generating dictionary files  Debugging models via the Remote Invocation ProtocolRemote model execution in debugging mode, implementation of a debugger  Profiling and code coverage via the Remote Invocation ProtocolRemote model execution in profiling mode, decoding of profiling and coverage results  Creating and saving XML documentsSimple access routines - adding nodes, recursive display of subtrees  Using XML-format files as databasesRetrieving XML nodes using xpath search expressions; modifying and formatting XML files  Parsing XML and JSON documentsParsing documents with unknown structure  Converting WCNF to Mosel formatProcessing a text file into a different text format, generating Mosel code, deployment as executable  Defining a package to read JSON documents of unknown structureDefinition of subroutines, data structures of union types, type definition, JSON parsing  Error handlinghandling I/O errors during data input  Using countersUsing and combining 'count' and 'as counter'  Local declarations in with statementsLocal declaration of entities, array aliasing  Working with arraysarray initialization, indexation, sparse array, array dimensions, array size  Working with listsLists: initialization, enumeration, operators, access functions  Eulerian circuit - working with listslist operators, list handling routines  Working with recordsDefining and initializing records  Definition of a networkWorking with record data structures  User type definitionDefining a user type with a record  Working with unionsdefining unions, type any, specifying union type, initialization of unions from/to text format files, reference to operator  SubroutinesSubroutine definition, overloading, recursive function calls, function return values, variable number of arguments, subroutine references, mmreflect  Output formattingreal number format, text formatting  Using the debugger and profilerDebugging and profiling commands, parallel debugging  Checking memory usageUsing sparse arrays, dynamic array, ahsmap array  Writing packages: definition of constant symbols, subroutines, types, and parametersImplementing subroutines, overloading, using packages  Namespace definitionImplementing packages, defining namespaces, namespace search, namespace groups  Package version managementImplementing packages, version management, deprecation, annotations  Text handling and regular expressionsTypes 'text', 'textarea', 'parsectx'; text parsing  Defining and retrieving annotationsAccessing annotations from a model or host application  Using documentation annotationsUsing documentation annotations, moseldoc tool  Using 'exists' for loops over sparse arraysEnumeration of sparse data, exists  Parameters: tolerancesComparison tolerance  Using the model return value for error handlingModel exit code  Preprocessing Mosel codePreprocessing source code, preprocessor symbol, positioning markers 
   Solving techniques Using the AEC2 package with mmjobsFind or start AEC2 instance, start Mosel, model execution  Column generation for a cutting stock problemVariable creation, using 'sethidden', working with multiple problems  Cut generation for an economic lot-sizing (ELS) problemAdding constraints and cuts, using the cut manager, run-time parameters  Binary fixing heuristic for the Coco problemWorking with bases, saving and loading MIP solutions  Branch-and-Price for the Generalized Assignment ProblemWorking with submodels, record data structures  Pre-emptive and Archimedian goal programmingChanging constraint type, redefining the objective  Using multi-objective solvingMultiple objectives, configuration of objectives  Successive linear programming (SLP) model for a financial planning problemRedefinition of constraints  Output formatting for a transportation modelDynamic arrays for data and decision variables, formatting output  Solving an optimization problem via nlsolvUsing module nlsolv  Cut-and-branch and branch-and-cutUsing the optnode callback, addcuts, storecuts and loadcuts, subroutine reference  Hybrid MIP-CP problem solving: sequential solvingSolving a sequence of CP subproblems, in-memory data exchange  Hybrid MIP-CP problem solving: concurrent solvingParallel and sequential solving of subproblems  MIP start solutions and subtour elimination algorithm for the traveling salesman problem (TSP)CP target values, MIP start solution, MIP callbacks, cutting plane algorithm  Working with multiple models: submodels, coordination, communication, and parallelizationParallel computing, distributed computing, distributed architecture, in-memory data exchange, shmem, job queue, events, detach submodel, clone submodel  Dantzig-Wolfe decomposition: combining sequential and parallel solvingConcurrent subproblem solving, coordination via events, in-memory data exchange, mempipe, mempipe notifications, remote mempipe  Benders decomposition: sequential solving of submodelsMultiple concurrent submodels, events, in-memory data exchange  Jobshop scheduling - Generating start solutions via parallel computationSequential and parallel submodel execution, loading partial MIP start solutions, model cloning, shared data  Outer approximation for quadratic facility location: solving different problem types in sequenceIterative sequential submodel solving, nonlinear subproblem,  MIQP formulation  Solving the TSP problem by a series of optimization subproblemsSolution heuristic, parallel submodel execution  Looping over optimization runs (within a model, batch executions, and multiple models/submodel)Multiple problem runs, submodel  Names handling for decision variables and constraintsNames generation, variable name, constraint name, location information, compilation options, loading names, public declaration  Using Optimizer Console for running matrices within Moselmmxprs command, Xpress Solver command line, running matrix file  Evolutionary algorithm for supply managementEvolutionary algorithm, iterative LP solving  Lagrangian Relaxation for a Generalized Assignment ProblemWorking with subproblems, iterative LP solving  News Vendor Problem2-stage stochastic program, scenario-based robust optimization  Multi-stage stochastic portfolio investmentIterative submodel runs, in-memory data exchange  Sludge production planning solved by recursionIterative solving, recursion, SLP 
   Nonlinear optimization with Mosel Locate airport while minimizing average distancequadratic constraints and objective  Maximise discount at a bookstoreDiscrete variables  Nonlinear objective with integer decision variablesDiscrete variables  Determine chain shapeQuadratic constraints  Facility locationNonlinear objective  Approximation of a functionApproximation of a function  Maximal inscribing squareTrigonometric functions  Static load balancing in a computer networkNonlinear objective  Minimum surface between boundariesNonlinear constraints and objective  Moon landingNonlinear objective and constraints  Polygon construction under constraintsTrigonometric constraints and objective  Portfolio optimizationQuadratic constraints and quadratic objective  Locating electrons on a conducting sphereNonlinear constraint and objective, alternative objective functions  Find the shape of a chain of springsQuadratic constraints  Steiner tree problemQuadratic constraints  Trafic equilibriumNonlinear objective  Modeling hang glider trajectoryNonlinear constraints, trapezoidal discretization  Force required to lift an objectSOCP formulation  Maximize the sum of radii of N non-overlapping circles in a squareNonlinear constraints, Nonconvex-QCP, circle packing  Minimize the pairwise distance ratio for N pointsNonlinear constraints, Nonconvex-QCP, squared distance, ratio  Convex hull of two trianglesTrigonometric constraints, graphical representation  Optimal number and distribution of grid points for a nonlinear functionDiscretization, GNUPlot graphic, subroutine references  Nonlinear trimloss problemNLP, alternative solvers 
   Robust optimization with Mosel Introductory examplesDefining robust constraints, uncertainty sets, nominal values  Robust formulations of the single knapsack problemTypes of uncertainty sets  Robust portfolio optimization'ellipsoid' uncertainty set, retrieving the worst value of an uncertain  Security constrained robust unit commitment'scenario' and 'cardinality' uncertainty sets  Production planning under demand uncertainty'scenario' and polyhedral uncertainty sets  Production planning under energy supply uncertaintypolyhedral uncertainty set  Robust shortest path'cardinality' uncertainty set  Robust network optimization for VPN designpolyhedral uncertainty set 
   Data handling ( ODBC/SQL, sparse data, I/O drivers, Spreadsheets ) Energyforecast - regression analysis with RRegression analysis, data exchange with R, evaluating R functions from Mosel  Logistic regression on flight delay data using RLogistic regression, data exchange with R, evaluating R functions from Mosel, graph drawing with R  Blend - data input from external sourcesAccessing data sources (text, spreadsheets, databases)  Output of expressionsUsing 'initializations to' with 'evaluation of'  Transport - data formats for online useXML and JSON data formats, generation of HTML  Reading sparse data from text files, spreadsheets and databases, and from memoryData input, initializations from, SQL, ODBC, spreadsheet, CSV  Data output to text files, spreadsheets and databases, and to memoryData output, initializations to, SQL, ODBC, spreadsheets, CSV  Dataframe formatsdataframe, union types, CSV format  Dense vs. sparse data formatarray types, noindex  Auto-indexation for single-dimensional arraysauto-indexation  Writing out solution values to text files, spreadsheets or databasessolution data output, 'evaluation of'  Spreadsheets and databases: working with multiple data tables and arraysdata input/output, multiple tables, multiple data arrays  Formulation of SQL (selection) statementsAdvanced SQL functionality, retrieve database and table structure  Reading and writing records and listsrecord data structure, list data structure  Reading and writing union typesTypes any, date, time; data input/output  Reading and writing dates and timesdata types date, time, datetime  Reading 3-dimensional arraysMultidimensional array input, option partndx  Burglar - Data source access from Mosel models'mmodbc.odbc', 'mmsheet.excel', 'mmetc.diskdata' I/O drivers, SQL, XML, JSON  Burglar - In-memory data exchange between Mosel models'bin', 'shmem', 'raw', 'text', 'tmp', 'rmt' I/O drivers 
   Graphing examples MandelbrotQueued execution of remote models with result
      graphic  Drawing results of multiple optimization runsIterating over MIP solves, graphical representation of solution values  Drawing line fractalsLines with simple styling, recursive subroutine calls  Drawing line plotsPoints and polylines with various styling options  Drawing a bar chartGraphical objects rectangle and text, simple styling  Drawing a pie chartGraphical objects pie and text, simple styling  Drawing a Gantt chartGraphical objects rectangle and text, simple styling, reading free-format input text data file, animation  Iterative display of toursPoints and polylines, pausing display, intercepting window closing, animation, image inclusion  Display matrix scaling informationRetrieving matrix coefficient ranging information, getscale, SVG graph drawing 
   Distributed calculation and remote invocation Reading and writing data using the 'bin:' formatBinary data format  Implementing a file managerRemote model execution, file manager, events  Approximating PI numberRemote execution of multiple Mosel models  Runprime - Remote model executionRemote model execution, data exchange between remote nodes  Basic tasks: remote connection, coordination, communication, and parallelizationDistributed computing, concurrent submodel execution, job queue, events  ELS - Solving several model instances in parallelParallel execution of submodels, parallel execution of submodels, stopping submodels  Mandelbrot - Java GUI for distributed computation with MoselParallel execution of submodels, Java solution graph  Folio - remote execution of optimization modelsSubmodel execution, events, bindrv binary format, in-memory data I/O 
   C Library examples Folio - Embedding examples from 'Getting started'Model compilation, parameterized model execution, matrix output, accessing results  Compiling a model file into a BIM fileModel compilation  Retrieving data from a Mosel modelAccessing sets, arrays, lists, records; retrieving solution information  Working with models and accessing dynamic libraries in MoselDisplay information and contents of models and libraries  Interrupting a running model using Ctrl-CStopping a model run  Data input/output via I/O driversCompilation to/from memory; data input/output in memory; redirect output using the 'cb' driver  Implementing a source coverage testing toolUsing the debugger interface  Basic embedding tasksCompile/load/run models, retrieve information about model objects, redirect model output  In-memory data exchangeData exchange during model execution  Switching to solving with Xpress OptimizerUsing the Xpress Optimizer library with Mosel  Compilation to/from memoryUsing the 'mem' I/O driver  Burglar - Exchange of information with embedded models'cb', 'bin', 'mem', 'raw', 'sysfd' I/O drivers 
   Java Library examples Folio - Embedding examples from 'Getting started'Model compilation, parameterized model execution, matrix output, accessing results  Retrieving data from a Mosel modelAccessing sets, arrays, lists, records; retrieving solution information  Working with models and accessing dynamic libraries in MoselDisplay information and contents of models and libraries  Data input/output via I/O driversCompilation to/from memory; data input/output in memory; redirect output using the 'java' driver  Implementing a source coverage testing toolUsing the debugger interface  Basic embedding tasksCompile/load/run models, retrieve information about model objects, redirect model output  In-memory data exchangeData exchange during model execution  Compilation to/from memoryUsing the 'java' I/O driver 
   VBA Library examples Folio - Embedding examples from 'Getting started'Model compilation, parameterized model execution  Folio - Embedding examples from 'Getting started'Parameterized model execution, data exchange in memory  Launching Mosel from Excel using VBALP solving, start Mosel from a VBA script in Excel, data input from Excel  Start/stopping Mosel from Excel and capturing outputMIP solving, start and interrupt Mosel from a VBA script in Excel, Mosel output to Excel  Basic embedding tasksCompile/load/run models, redirect model output 
   C#.NET Library examples Folio - Embedding examples from 'Getting started'Model compilation, parameterized model execution, matrix output, accessing results  Retrieving data from a Mosel modelAccessing sets, arrays, lists, records; retrieving solution information  Working with models and accessing dynamic libraries in MoselDisplay information and contents of models and libraries  Data input/output via I/O driversCompilation to/from memory; data input/output in memory  Basic embedding tasksCompile/load/run models, retrieve information about model objects, redirect model output  In-memory data exchangeData exchange during model execution  Compilation to/from memoryUsing C# 
   VB.NET Library examples Working with models, data and dynamic libraries in MoselAccessing sets and arrays; retrieving solution information; displaying information and contents of models and libraries; Compilation to/from memory; data input/output in memory 
   Writing Mosel modules Definition of constants of different typesDefining integer, real, string, boolean constants  Definition of a procedure for getting solution values into an arrayImplementing a subroutine  Definition of complex numbers and operators to work with themDefining an external type with operators  Definition of type 'task' and subroutines for accessing itDefining an external type with operators and access routines; defining module parameters and services  Definition of type 'date' and subroutines for accessing itDefining an external type with operators and access routines; defining module parameters and services  Definition of three new types and operators to work with themDefining external types with operators  Basic LP/MIP solver interface for Xpress OptimizerUsing the NI matrix handling functionality, extending a type, defining parameters and subroutines, defining a callback function  Basic QCQP solver interface for Xpress OptimizerUsing the mmnl matrix handling functionality, extending a type, defining parameters and subroutines, defining a callback function  Declaring a static moduleModule embedded in a C program  Using the 'zlib' library to provide IO driver 'compress' functionalityDefining I/O drivers  Module implementing driver 'toC' to save the compilation result to a C fileDefining an I/O driver  How best to debug a moduleCreating a static module 
   Calling static Java methods from Mosel Passing single values from a Mosel model to a Java method Passing an array from a Mosel model to a Java method Returning an object from a Java method Handling exceptions thrown by a Java method called from a Mosel model
   Calling Python 3 from Mosel Portfolio optimization using pandas to calculate covariance Invert a Mosel matrix with NumPy Python I/O driver example
   Puzzles and Recreational Mathematics Sudoku (CP and MIP models)Using 'all_different', enumerating all feasible solutions, SVG graphs showing progress of solving  Futoshiki (CP and MIP models)Using 'all_different', formatted solution printout  Fantasy OR: Sangraal (CP and MIP models)Formulation of a scheduling problem with MIP and CP  Fiveleaper (MIP model and graphics)Subtour elimination algorithm  Puzzles and pastimes from the book `Programmation Lineaire'MIP and CP formulations for discrete feasibility problems 
   Mosel blog examples Mosel files for the Mosel-Python comparison blogMultiple problem runs, comparison, blog 
 
  
  Xpress Optimizer examples  Calling the Optimizer library from C Folio - Introductory examples from 'Getting Started'LP, MIP and QP models, explicit initialization, index sets, heuristic solution  The travelling salesman problemUsing Xpress callbacks  Cut Generation for an economic lot-sizing (ELS) problemUsing the cut round callback and adding cutting planes.  Branching rule branching on the most violated Integer/BinaryUsing the change branch callbacks  Apply a binary fixing heuristic to an unpresolved MIP problemChanging bounds, accessing solver controls  Perform objective function parametrics on a MIP problemSaving/loading bases, changing objective coefficients  Perform RHS parametrics on a MIP problemChanging RHS coefficients, working with bases  Apply a primal heuristic to a knapsack problemUsing the MIP log callback  Apply an integer fixing heuristic to a MIP problemChanging bounds  Load an LP and modify it by adding an extra constraintLoad LP problem, adding a constraint  Save/access a postsolved solution in memoryRetrieving solution values and tree search information  Adding MIP solutions to the OptimizerUsing the optnode callback, saving/loading bases, changing bounds  Solve LP, displaying the initial and optimal tableauRetrieve basic variables and their names, btran  Modify problem: add an extra variable within an additional constraintAdding rows and columns, branching directives  10 best solutions with the MIP solution enumeratorUsing the solution enumerator and MIP solution pool  Collecting all solutions with the MIP solution poolUsing the solution enumerator and MIP solution pool  Repairing infeasibilityUsing repairinfeas  Goal programmingLexicographic goal programming using the Xpress multi-objective API  Solution enumerationUsing callbacks, customizing the branch and bound search 
   Calling the Optimizer library from C++ Linearizations and approximations via SOS and piecewise linear (pwl) expressionsPiecewise linear, approximation, SOS, SOS1, SOS2, SOS-1, SOS-2, Special Ordered Set, piecewise linear function  General constraintsgeneral constraints, minimum value, maximum value, absolute value  Indicator constraintsindicator constraints, logic constraints  Burglar - Formulating logical constraintsMIP, indicator constraints  Constraint types - Logical, general, SOS, quadraticDefining different types of constraints  Boxes - Nonlinear constraintsNonlinear constraints  Capital budgeting - Using multi-objective optimizationMulti-objective solving  Catenary - Solving a QCQPStating quadratic constraints  Contract - Semi-continuous variablesDefining semi-continuous variables  Cutstk - Column generation for a cutting stock problemWorking with subproblems, modifying constraints  Els - An economic lot-sizing problem solved by  cut-and-branch and branch-and-cut heuristicsLooping of optimization, using the cut manager  Facility location problem - Data as arrays or collectionsData structures arrays and collections  Folio - Examples from 'Getting Started'MIP modeling, binary fixing heuristic, quadratic constraints, infeasibility handling  Hang glider trajectoryNonlinear constraints, trapezoidal discretization  Multi-knapsack - Constraint formulation alternativesConstraint formulation options  Polygon - Defining nonlinear constraintsNonlinear constraints  Project planning - Defining SOSBinary variables, SOS definition  Multi-period, multi-site production planningFormulation of resource constraints and
                    material balance constraints  Purchase - Definition of SOS-2Defining SOS-2, pwl, piecewise linear  Solving a non-linear problem by recursionIterative solving, modify constraint definitions  Sangraal - Scheduling problem with indicator constraintsFormulation of a scheduling problem with indicator constraints  The travelling salesman problemUsing Xpress callbacks 
   Calling the Optimizer library from Java Burglar - Formulating logical constraintsMIP, indicator constraints  Constraint types - Logical, general, SOS, quadraticDefining different types of constraints  Boxes - Nonlinear constraintsNonlinear constraints  Capital budgeting - Using multi-objective optimizationMulti-objective solving  Catenary - Solving a QCQPStating quadratic constraints  Contract - Semi-continuous variablesDefining semi-continuous variables  Cutstk - Column generation for a cutting stock problemWorking with subproblems, modifying constraints  Els - An economic lot-sizing problem solved by  cut-and-branch and branch-and-cut heuristicsLooping of optimization, using the cut manager  Facility location problem - Data as arrays or collectionsData structures arrays and collections  Folio - Examples from 'Getting Started'MIP modeling, binary fixing heuristic, quadratic constraints, infeasibility handling  General constraints - Minimium value and absolute valueMinimum value constraints and absolute value constraints  Hang glider trajectoryNonlinear constraints, trapezoidal discretization  Multi-knapsack - Constraint formulation alternativesConstraint formulation options  Multi problems - Modifying constraint and variable definitionsConstraint redefinition, multiple problems  Polygon - Defining nonlinear constraintsNonlinear constraints  Project planning - Defining SOSBinary variables, SOS definition  Multi-period, multi-site production planningFormulation of resource constraints and
                    material balance constraints  Purchase - Definition of SOS-2Defining SOS-2, pwl, piecewise linear  Solving a non-linear problem by recursionIterative solving, modify constraint definitions  Sangraal - Scheduling problem with indicator constraintsFormulation of a scheduling problem with indicator constraints  Wagon - MIP start solution heuristicLoading a MIP start solution  Adding the message callback in JavaUsing the message callback  Irreducible Infeasible Set SearchUsing IIS  10 best solutions with the MIP solution enumeratorUsing the solution enumerator and MIP solution pool  Collecting all solutions with the MIP solution poolUsing the solution enumerator and MIP solution pool  Collecting all solutions with the MIP solution poolModify a problem by adding extra rows and columns  Goal programmingLexicographic goal programming using the Xpress multi-objective API  The travelling salesman problemUsing Xpress callbacks  Apply a binary fixing heuristic to an unpresolved MIP problemChanging bounds, accessing solver controls  Apply a primal heuristic to a knapsack problemUsing the MIP log callback  Load an LP and modify it by adding an extra constraintLoad LP problem, adding a constraint  Save/access a postsolved solution in memoryRetrieving solution values and tree search information  Adding MIP solutions to the OptimizerUsing the optnode callback, saving/loading bases, changing bounds  Solve LP, displaying the initial and optimal tableauRetrieve basic variables and their names, btran  Branching rule branching on the most violated Integer/BinaryUsing the change branch callbacks  Repairing infeasibilityUsing repairinfeas  Apply an integer fixing heuristic to a MIP problemChanging bounds  Perform objective function parametrics on a MIP problemSaving/loading bases, changing the objective  Perform RHS parametrics on a MIP problemSaving/loading bases, changing right-hand side values 
   Calling the Optimizer library from C#.NET Burglar - Formulating logical constraintsMIP, indicator constraints  Constraint types - Logical, general, SOS, quadraticDefining different types of constraints  Boxes - Nonlinear constraintsNonlinear constraints  Capital budgeting - Using multi-objective optimizationMulti-objective solving  Catenary - Solving a QCQPStating quadratic constraints  Contract - Semi-continuous variablesDefining semi-continuous variables  Cutstk - Column generation for a cutting stock problemWorking with subproblems, modifying constraints  Els - An economic lot-sizing problem solved by  cut-and-branch and branch-and-cut heuristicsLooping of optimization, using the cut manager  Facility location problem - Data as collectionsCollections data structure  Folio - Examples from 'Getting Started'MIP modeling, binary fixing heuristic, quadratic constraints, infeasibility handling  Multi-knapsack - Constraint formulation alternativesConstraint formulation options  Polygon - Defining nonlinear constraintsNonlinear constraints  Project planning - Defining SOSBinary variables, SOS definition  Multi-period, multi-site production planningFormulation of resource constraints and
                    material balance constraints  Purchase - Definition of SOS-2Defining SOS-2, pwl, piecewise linear constarints  Solving a non-linear problem by recursionIterative solving, modify constraint definitions  Sangraal - Scheduling problem with indicator constraintsFormulation of a scheduling problem with indicator constraints  Wagon - MIP start solution heuristicLoading a MIP start solution  The travelling salesman problemUsing Xpress callbacks  Apply a binary fixing heuristic to an unpresolved MIP problemChanging bounds, accessing solver controls  Irreducible Infeasible Set SearchUsing IIS  Apply a primal heuristic to a knapsack problemUsing the MIP log callback  Load an LP and modify it by adding an extra constraintLoad LP problem, adding a constraint  10 best solutions with the MIP solution enumeratorUsing the solution enumerator and MIP solution pool  Collecting all solutions with the MIP solution poolUsing the solution enumerator and MIP solution pool  Save/access a postsolved solution in memoryRetrieving solution values and tree search information  Goal programmingLexicographic goal programming using the Xpress multi-objective API  Wagon - MIP start solution heuristicLoading a MIP start solution 
   Calling the Optimizer library from VB.NET Apply a binary fixing heuristic to an unpresolved MIP problemChanging bounds, accessing solver controls  Irreducible Infeasible Set SearchUsing IIS  Apply a primal heuristic to a knapsack problemUsing the MIP log callback  Load an LP and modify it by adding an extra constraintLoad LP problem, adding a constraint  10 best solutions with the MIP solution enumeratorUsing the solution enumerator and MIP solution pool  Collecting all solutions with the MIP solution poolUsing the solution enumerator and MIP solution pool  Save/access a postsolved solution in memoryRetrieving solution values and tree search information 
 
  
  Xpress NonLinear examples  Nonlinear C library examples Maximizing the area of a polygon using tokens based inputUsing token lists to express nonlinear formulas  Maximizing the area of a polygon using string based inputUsing string based formulas to express nonlinear formulas  Providing initial valuesProviding initial values to nonlinear variables  Implementing user functions returning their own derivativesImplementing complex user functions returning their own derivatives  Implementing the polygon examples as a black box functionImplementing user functions  Maximizing the area of a polygon using tokens based input - using a 'map' userfunctionUsing strings to express nonlinear formulas, including a 'map' userfunction  Maximizing the area of a polygon using tokens based input - using a 'vecmap' userfunctionUsing strings to express nonlinear formulas, including a 'vecmap' userfunction  Maximizing the area of a polygon using tokens based input - using a 'multimap' userfunctionUsing strings to express nonlinear formulas, including a 'multimap' userfunction  Maximizing the area of a polygon using tokens based input - using a 'mapdelta' userfunctionUsing strings to express nonlinear formulas, including a 'mapdelta' userfunction  Maximizing the area of a polygon using tokens based input - using a 'vecmapdelta' userfunctionUsing strings to express nonlinear formulas, including a 'vecmapdelta' userfunction  Maximizing the area of a polygon using tokens based input - using a 'multimapdelta' userfunctionUsing strings to express nonlinear formulas, including a 'multimapdelta' userfunction 
   Calling the Nonlinear library from C#.NET Maximizing the area of a polygonUsing strings to express nonlinear formulas  Maximizing the area of a polygon using a 'map' userfunctionUsing strings to express nonlinear formulas, including a 'map' userfunction  Maximizing the area of a polygon using a 'vecmap' userfunctionUsing strings to express nonlinear formulas, including a 'vecmap' userfunction  Maximizing the area of a polygon using a 'vecmapdelta' userfunctionUsing strings to express nonlinear formulas, including a 'vecmapdelta' userfunction  Maximizing the area of a polygon using a 'mapdelta' userfunctionUsing strings to express nonlinear formulas, including a 'mapdelta' userfunction  Maximizing the area of a polygon using a 'multimap' userfunctionUsing strings to express nonlinear formulas, including a 'multimap' userfunction  Maximizing the area of a polygon using a 'multimapdelta' userfunctionUsing strings to express nonlinear formulas, including a 'multimapdelta' userfunction 
   Calling the Nonlinear library from Java Maximizing the area of a polygonUsing strings to express nonlinear formulas  Maximizing the area of a polygon using a 'map' userfunctionUsing strings to express nonlinear formulas, including a 'map' userfunction  Maximizing the area of a polygon using a 'vecmap' userfunctionUsing strings to express nonlinear formulas, including a 'vecmap' userfunction  Maximizing the area of a polygon using a 'vecmapdelta' userfunctionUsing strings to express nonlinear formulas, including a 'vecmapdelta' userfunction  Maximizing the area of a polygon using a 'mapdelta' userfunctionUsing strings to express nonlinear formulas, including a 'mapdelta' userfunction  Maximizing the area of a polygon using a 'multimap' userfunctionUsing strings to express nonlinear formulas, including a 'multimap' userfunction  Maximizing the area of a polygon using a 'multimapdelta' userfunctionUsing strings to express nonlinear formulas, including a 'multimapdelta' userfunction 
   Mosel examples of the Xpress NonLinear manual Effects of convexityConvexity  Partial derivativesNumerical differentiaton  Local solutionsLocal optimality  Dual multipliersDual multipliers  Non-connected feasible regionNon-connected feasible regions  Feasiblity breakers \ penalty error vectorsFeasiblity breakers  Error costs and penalty multipliersPenalty multipliers  Solution support setsSupport sets  Step boundingStep bounding  Zero placeholdersZero placeholders 
 
  
  Xpress Python examples  Python examples solving problems using the Xpress Solver Folio - Introductory examples from 'Getting Started'LP, MIP and QP models, explicit initialization, index sets, heuristic solution  Linearizations and approximations via SOS and piecewise linear (pwl) expressionsPiecewise linear, approximation, SOS, SOS1, SOS2, SOS-1, SOS-2, Special Ordered Set, piecewise linear function  General constraintsgeneral constraints, minimum value, maximum value, absolute value  Indicator constraintsindicator constraints, logic constraints  Using NumPy arrays to create variablesUsing NumPy arrays  Visualize the BB treeUsing the newnode callback  Irreducible Infeasible SetsUsing Irreducible Infeasible Sets  Loading a problemLoading a problem directly  Using Python model objects to build a problemModeling using Python objects  Changing the optimization problemModifying a problem  Extending a problemExtending a problem  Using NumPy and XpressUsing NumPy and Xpress  Finding an LP subsystem with as many constraints as possibleInfeasibility detection, infeasibility reporting  Basis and StabilityBasis handling and sensitivity methods  Solving a quadratic problemBuilding quadratic expressions  Repeatedly solving a problemSolving a problem multiple times  Using indicatorsModel with indicators  Using special ordered setsModel with special ordered sets  Writing and reading problem matrix filesWriting and reading a problem  Comparing MatricesCompare two optimization problems  Create a problem with piecewise linear functionsPiecewise linear, low-level API  Create a problem with general constraints that use operator absGeneral constraints, operators, low-level functions  Solving a quadratically constrained problemSolve a nonlinear problem  Solve a polynomial optimization problemModeling a polynomial optimization problem  Modeling with user functionsModeling with user functions  Implementing a branching rule using branch objectsDemonstrate the Xpress change branch object callback  Re-solving problem using the Barrier method's warm start Using the tuner functions in the Python interface Solution enumerationUsing callbacks, customizing the branch and bound search  The travelling salesman problemUsing Xpress callbacks  The feasiblity pump The n-queens problemPuzzle modeling  Min-cost-flow problemModeling a graph problem  Solving SudokuPuzzle modeling  Multicommodity flow problemSolve a multicommodity flow minimum cost optimization problem on a randomly created graph  Find largest-area inscribed polygonNonlinear programming, trigonometric functions  Solve a simple MIP using Benders decompositionBenders decomposition, callbacks  Create an iterative algorithm cutting stock problem Maximize the sum of logistic curves subject to linear and piecewise linear constraints Transportation problem with piecewise-linear costs Modeling Satisfiability and PseudoBoolean problems with MIP Multi-objective knapsack problemMulti-objective MIP problem with binary variables  Goal programmingLexicographic goal programming using the Xpress multi-objective API  Markowitz portfolio optimizationMulti-objective quadratic optimization  Basic LP tasks: problem statement and solving; solution analysisLP solving, modeling variables and constraints, printing the solution  Network problem: transport from depots to customersLP solving, modeling variables and constraints  Blend: A model for mineral blendingsimple LP problem, formulation of blending constraints  Basic MIP tasks: binary variables; logic constraintsMIP solving, binary variables, index set types, logic constraints  Coco: The Coco productional planning problemLP problem, formulation of resource constraints and
                    material balance constraints, formatted solution printing  Catenary: Determine chain shapeQCQP problem  Pplan: A project planning problemFormulation of resource use profiles  Firestns: A set-covering model for emergency service provisionSolve a MIP problem  Solve a nonconvex nonlinear problem from MINLPlib with a local or global solverSolving with local or global solvers  Pooling example for nonlinear solvingNonlinear solving  Firestation location problem using SciPy sparse arraysSparse arrays, Dot product  Facility location problem using Pandas data framesPandas data frames 
   Python blog examples Python files for the Mosel-Python comparison blogMultiple problem runs, comparison, blog  Python files for the Docker blogsDocker, container, blog 
   Python notebook examples Python notebooksMIP, NLP, problem formulations, notebook examples, Xpress Python interface, interactive solving, visualization 
 
  
  Xpress R Interface examples  R examples solving problems using the Xpress Optimizer Load and solve a simple 2x2 linear programxprs_loadproblemdata, displaying a solution as a data frame, a simple pipe workflow  Formulate and solve a Facility Location Problemxprs_loadproblemdata, writeprob, setoutput, xprs_optimize, getsolution  Solve an LP and a MIP using Xpress-Rxprs_loadproblemdata, getintattrib, getdblattrib, readprob, getmipsol, getsolution  Read and write problems to and from standard formats MPS and LPreadprob, setintcontrol, writeprob  Set controls of Xpressreadprob, setintcontrol, setdefaultcontrol, getintattrib, getdblattrib, setdefaults, dumpcontrols  Query Attributes of Xpresscreateprob, readprob, printing, getintattrib  Add indicator constraintscreateprob, readprob, mipoptimize, getsolution, addrows, setindicator  Register an R function as callback into Xpressreadprob, getintattrib, addcboptnode, addcbintnode, getdblattrib  Formulate a quadratic optimization problem in Xpressxprs_loadproblemdata, writeprob, xprs_optimize  Solving different types of Sudokus with the FICO Xpress Optimizerxprs_loadproblemdata, addrows, getmipsol, mipoptimize  Modeling Sudokus creating columns and rows incrementally using xprs_newcol and xprs_addrowcreateprob, setprobname, chgbounds, xprs_newcol, xprs_addrow, xprs_newrow, setoutput, getmipsol, mipoptimize  Solve Traveling Salesperson Problems using callbacks or delayed rowsxprs_loadproblemdata, addrows, addcuts, addcboptnode, addcbpreintsol, getcallbacksolution, loaddelayedrows  Solve a maximum flow problem and visualize the resultcreateprob, chgobjsense, setprobname, xprs_newcol, chgobj, xprs_addrow, getsolution  Solve a modified bin packing problem with the addition of a simple greedy heuristicaddmipsol, createprob, xprs_newcol, xprs_newrow, getsolution  Solve a routing problem using an arc-paths formulation for a telecommunication networkcreateprob, chgobjsense, xprs_newcol, xprs_addrow, getsolution  Solve a production planning problemcreateprob, chgbounds, xprs_newcol, xprs_newrow, getsolution  Model a piecewise linear function using binary variablescreateprob, chgbounds, xprs_newcol, xprs_addrow, getsolution  Optimize a composition of investment portfolios using semi-continuous variablescreateprob, chgcoltype, chgglblimit, chgrhs, chgobjsense, xprs_newcol, xprs_newrow, getsolution  Find an optimal schedule of jobs on different machines and visualize the result in ggplot2createprob, setprobname, xprs_newcol, xprs_newrow, xprs_addrow, setoutput, getdblattrib, getsolution  Solve two related problems assigning pilots to crews under different constraintscreateprob, chgobjsense, chgobj, setprobname, xprs_newcol, xprs_addrow, setoutput, getsolution  Solve a timetabling problem for college courses under various constraintscreateprob, chgbounds, chgobj, setprobname, xprs_newcol, xprs_newrow, setoutput, getsolution  Solve a small production problem with 2 products and 2 resource constraintscreateprob, chgobjsense, setprobname, xprs_newcol, xprs_addrow, setoutput, getsolution  Solve a minimum cost flow problem in a bipartite graphcreateprob, setprobname, xprs_newcol, xprs_addrow, setoutput, getsolution  Modeling a piecewise linear objective function using SOS2 constraintscreateprob, setprobname, addsets, getdblattrib, xprs_newcol, xprs_addrow, setoutput, getsolution  Infeasibility and IIS Detectioncreateprob, getiisdata, getintattrib, iisall, iisstatus, iisisolations, xprs_newcol, xprs_newrow, xprs_optimize  Basis and Stabilitybndsa, createprob, getbasis, getnamelist, loadbasis, objsa, rhssa, writebasis, writeslxsol, getsolution, xprs_newcol, xprs_newrow, xprs_optimize  Using the Tunercreateprob, setoutput, readprob, setintcontrol, tune, tunerreadmethod, tunerwritemethod, xprs_optimize  Goal programmingcreateprob, setoutput, xprs_newcol, xprs_addrow, chgobj, chgobjn, setobjintcontrol, setobjdblcontrol, xprs_optimize, getintattrib, getmipsol 
 
  
  Xpress Kalis examples  Xpress Kalis Mosel features Generic binary and n-ary constraintsMosel subroutine implementing a constraint relation  Table constraint: solving a binpacking problemConstraint definition via value tuples, optimization  All-different constraint: solving an assignment problemConstraint definition, check for feasible solution  'abs' and 'distance' constraintsConstraint definition  'distribute' and 'occurrence' constraintsConstraint definition, check for feasible solution, cardinality constraint  One- and two-dimensional 'element' constraintsConstraint definition  Implication and equivalence constraintsConstraint definition  Conjunctions and disjunctions (logical 'and' and 'or')Constraint definition  'cycle' constraint: formulating a TSP problemConstraint definition, solution callback, branching strategy  'cumulative' and 'disjunctive' constraints for scheduling and planning problemsScheduling with resource constraints  'producer_consumer' constraints: solving a resource-constrained project scheduling problemConfiguring resource and task objects, scheduling solver  Resource profilesAlternative resources, non-constant resource usage profiles  Minimum and maximum constraintsConstraint definition, constraint posting, cpvarlist  Defining, posting and propagating linear constraintsAutomated propagation, automated post, explicit post, scalar product, dot product  Non-linear constraints over real-valued decision variablesBranching strategy for cpfloatvar  Branching strategiesBranching schemes, enumeration for discrete or continuous variables, tasks, disjunctive constraints  Use of callbacks to output the search treeDefinition of branching callbacks  Working with 'reversible' objectsSetting and retrieving reversible values, behaviour on backtracking  Defining a linear relaxationLP or MIP solving within a CP problem 
   Xpress Kalis Mosel User Guide examples Introductory example: constraint handlingAutomated and explicit constraint posting  Basic modeling tasks: data input, optimization, enumerationData input from file, solving, branching strategy  Production of cane sugarLinear, 'ocurrence', and 'element' constraints  Sequencing jobs on a bottleneck machineLinear, 'element', 'disjunctive' constraints  Planning of paint productionLinear, 'element', 'implies', and 'all-different', 'element' ,'cycle' constraints  Euler knight tour problem'all-different', generic binary, 'cycle' constraints  Frequency assignment problem'abs', 'distance', and 'all-different' constraints; branching strategy, solution callback  Choice of locations for income tax officesLinear, 'element', 'occurrence', 'equiv' constraints; search strategy  Non-linear constraintsDefault bounds, cpfloatvar  Personnel planning problem'all_different', 'implies', 'occurrence', and 'distribute' constraints  Sudoku puzzle: retrieving status information through parameters'all-different' constraints, propagation algorithm, infeasibility conflict analysis  Assigning workers to machines: heuristics and user-defined searchLinear, 'all-different', and 'element' constraints, solution heuristic  Working with reversible numbersBranching strategy, reversible numbers, branching callbacks  Scenes allocation problem: symmetry breaking'implies', 'distribute', 'maximum' constraints, symmetry breaking  Construction of a stadium: project planningScheduling with precedence constraints, task objects  Backing up files: scheduling with cumulative resource constraintsCumulative scheduling, task and resource objects  Job-shop schedulingTask and resource objects, user search strategy  Renewable and non-renewable resourcesProvision/requirement of resource, production/consumption of resource  Resource usage profilesResource idle times, 'resusage', alternative resources  Linear relaxationsalldifferent' constraint reformulated by linear relaxations, user-defined linear relaxations 
   Xpress Kalis Mosel application examples Project scheduling problem with disjunctive resource constraintsScheduling objects, branching strategy  Solving the job-shop scheduling problemScheduling objects, solution callback  Frequency assignment with polaritySubmodel execution, solution heuristic  Resource-constrained project scheduling problemScheduling objects, resource consumption, task modes, RCPSP, MRCPSP, renewable resource, element constraint 
 
  
  Xpress MATLAB interface examples  Mosel MATLAB interface examples Running Mosel models from MATLABCalling Mosel from MATLAB, data exchange in memory  Folio - example from 'Getting started' executed in MATLABExchange model parameters and solution between MATLAB and Mosel  Evaluating MATLAB functions from MoselUsing MATLAB functions in Mosel  MATLAB using the Mosel Java interfaceCompile/load/run models from MATLAB 
 
  
  Xpress Cloud examples  S3 Uploading a file to an S3 bucket Downloading a file from an S3 bucket List objects available in an S3 bucket Setting tags on an object in an S3 bucket Querying tags on an object in an S3 bucket
   Xpress Executor Solving a Mosel model using a REST webservice, from Mosel Solving a Mosel model using a REST webservice, from NodeJS Solving an MPS problem using a REST webservice, from NodeJS Solving a non-fixed Mosel model using a REST webservice, from Mosel Solving a Mosel model using the 'executor' package, from Mosel Making a request to a DMP component Making a request to DMP Manager
 
  
  Xpress Insight examples  Mosel app examples Folio - Insight example from 'Getting started'Mosel Insight app  Transport - Insight example from Mosel User Guide Lightweight execution modes with Mosellightweight execution, partial entity population, custom execution modes, insightpopulate, insightcapture 
   Python app examples Folio - Insight example from 'Getting started'Python Insight app  Testing an Insight Python modeltest mode, unit testing, pytest  Lightweight execution modes with Pythonlightweight execution, partial entity population, custom execution modes 
 
  
 
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