IBM ILOG CPLEX Optimizer 12.5 教程：ILGO AMPL 使用详解

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"IBM ILGO AMPL 使用手册" IBM ILOG CPLEX Optimizer 12.5 是一个强大的数学优化求解器，专门用于处理线性编程（LP）、混合整数编程（MIP）和二次规划（QP）问题。这款工具在IT行业中广泛应用于决策优化，帮助企业解决复杂的问题，如供应链管理、财务规划、生产调度等。 ILGO (ILOG) 是IBM旗下的一个产品系列，主要提供优化和建模解决方案。AMPL是其中的一个组件，它是一种高级的数学建模语言，用户可以使用AMPL来描述和构建各种复杂的优化模型。通过结合AMPL与CPLEX Optimizer，用户能够方便地将业务问题转化为数学模型，并利用CPLEX的高效算法找到最优解。在"IBMILOGCPLEXV12.1User'sManualforCPLEX"中，用户可以获得关于如何使用CPLEX Optimizer的详细指南。该手册涵盖了CPLEX的功能、用法、参数设置以及性能调优等方面的内容。它不仅指导用户如何编写和求解优化模型，还介绍了如何分析结果，以及如何利用CPLEX提供的接口和其他工具进行进一步的分析和报告。手册中的“Legal notices”部分强调了IBM的产品版权信息，指出美国政府用户在使用、复制或披露该软件时受到GSA ADP Schedule Contract with IBM Corp.的限制。同时，手册列出了IBM及其他公司的商标信息，包括IBM、WebSphere、ILOG、CPLEX等，这些都是国际知名的品牌。此外，手册可能还包括对第三方软件如Adobe PostScript和Linux的相关引用，这些技术可能被集成到CPLEX的文档或者操作环境中。例如，Adobe PostScript是一种页面描述语言，常用于打印和排版；而Linux是操作系统的基础，可能作为CPLEX运行的平台。 IBM ILOG CPLEX Optimizer 12.5与AMPL的组合提供了一个强大且全面的优化工具包，适合需要解决各种数学优化问题的专业人士。用户手册则是掌握这一工具的关键，它能帮助用户充分利用这些功能，实现业务效率的最大化。

Filtering the solution pool...........................................................................................................................617

What are filters of the solution pool?...............................................................................................618

Diversity filters.................................................................................................................................619

Range filters....................................................................................................................................620

Filter files.........................................................................................................................................621

Example: controlling properties of solutions with filters...................................................................622

Incumbent callback as a filter..........................................................................................................623

Using special ordered sets (SOS)..........................................................................................625

What is a special ordered set (SOS)?........................................................................................................626

Example: SOS Type 1 for sizing a warehouse............................................................................................627

Declaring SOS members............................................................................................................................628

Example: using SOS and priority................................................................................................................629

ilomipex3.cpp..................................................................................................................................630

mipex3.c..........................................................................................................................................631

Using semi-continuous variables: a rates example.............................................................633

What are semi-continuous variables?........................................................................................................634

Describing the problem..............................................................................................................................635

Representing the problem..........................................................................................................................636

Building a model.........................................................................................................................................637

Solving the problem....................................................................................................................................638

Ending the application................................................................................................................................639

Complete program......................................................................................................................................640

Using piecewise linear functions in optimization: a transport example............................641

What is a piecewise linear function?..........................................................................................................643

Syntax of piecewise linear functions...........................................................................................................644

Discontinuous piecewise linear functions...................................................................................................646

Isolated points in piecewise linear functions...............................................................................................649

Using IloPiecewiseLinear in expressions...................................................................................................650

Describing the problem..............................................................................................................................651

Problem statement..........................................................................................................................652

Variable shipping costs...................................................................................................................653

Model with varying costs.................................................................................................................655

Developing a model....................................................................................................................................657

Creating the environment and model..............................................................................................658

Representing the data.....................................................................................................................659

Adding constraints...........................................................................................................................660

Checking convexity and concavity...................................................................................................661

Adding an objective.........................................................................................................................662

Solving the problem....................................................................................................................................663

Displaying a solution...................................................................................................................................664

Ending the application................................................................................................................................665

Complete program: transport.cpp...............................................................................................................666

USER'S MANUAL FOR CPLEX

Logical constraints in optimization.......................................................................................667

What are logical constraints?.....................................................................................................................668

What can be extracted from a model with logical constraints?...................................................................669

Overview.........................................................................................................................................670

Logical constraints in the C++ API..................................................................................................671

Logical constraints in the Java API.................................................................................................672

Logical constraints in the .NET API.................................................................................................673

Which nonlinear expressions can be extracted?........................................................................................674

Logical constraints for counting..................................................................................................................675

Logical constraints as binary variables.......................................................................................................676

How are logical constraints extracted?.......................................................................................................677

Indicator constraints in optimization....................................................................................679

What is an indicator constraint?.................................................................................................................680

Example: fixnet.c........................................................................................................................................681

Indicator constraints in the Interactive Optimizer........................................................................................682

What are indicator variables?.....................................................................................................................683

Restrictions on indicator constraints...........................................................................................................684

Best practices with indicator constraints.....................................................................................................685

Using logical constraints: Food Manufacture 2...................................................................687

Introducing the example.............................................................................................................................688

Describing the problem..............................................................................................................................689

Representing the data................................................................................................................................690

Developing the model.................................................................................................................................693

Formulating logical constraints...................................................................................................................694

Solving the problem....................................................................................................................................695

Early tardy scheduling............................................................................................................697

Describing the problem..............................................................................................................................699

Understanding the data file........................................................................................................................700

Reading the data........................................................................................................................................701

Creating variables.......................................................................................................................................702

Stating precedence constraints..................................................................................................................703

Stating resource constraints.......................................................................................................................704

Representing the piecewise linear cost function........................................................................................705

Transforming the problem...........................................................................................................................706

Solving the problem....................................................................................................................................707

Using column generation: a cutting stock example.............................................................709

What is column generation?.......................................................................................................................711

Column-wise models in Concert Technology..............................................................................................712

Describing the problem..............................................................................................................................713

Representing the data................................................................................................................................715

Developing the model: building and modifying...........................................................................................717

The master model and column generator in this application...........................................................718

USER'S MANUAL FOR CPLEX

Adding extractable objects: both ways............................................................................................719

Adding columns to a model.............................................................................................................720

Changing the type of a variable......................................................................................................721

Cut optimization model....................................................................................................................722

Pattern generator model.................................................................................................................723

Changing the objective function.................................................................................................................724

Solving the problem: using more than one algorithm.................................................................................725

Ending the program....................................................................................................................................727

Complete program......................................................................................................................................728

Infeasibility and unboundedness..........................................................................729

Preprocessing and feasibility.................................................................................................731

Issues of infeasibility and unboundedness.................................................................................................732

Early reports of infeasibility based on preprocessing reductions...............................................................733

Managing unboundedness.....................................................................................................735

What is unboundedness?...........................................................................................................................736

Avoiding unboundedness in a model..........................................................................................................737

Diagnosing unboundedness.......................................................................................................................738

Diagnosing infeasibility by refining conflicts.......................................................................739

What is a conflict?......................................................................................................................................741

What a conflict is not..................................................................................................................................742

How to invoke the conflict refiner................................................................................................................743

How a conflict differs from an IIS................................................................................................................744

Meet the conflict refiner in the Interactive Optimizer..................................................................................745

Limits of the conflict refiner in the Interactive Optimizer..................................................................746

A model for the conflict refiner........................................................................................................747

Optimizing the example...................................................................................................................748

Interpreting the results and detecting conflict.................................................................................749

Displaying a conflict in the Interactive Optimizer.............................................................................750

Interpreting conflict.....................................................................................................................................751

Understanding the conflict in the model..........................................................................................752

Deleting a constraint.......................................................................................................................753

Understanding a conflict report.......................................................................................................755

Summing equality constraints.........................................................................................................756

Changing a bound...........................................................................................................................757

Adding a constraint.........................................................................................................................758

Changing bounds on cost...............................................................................................................759

Relaxing a constraint.......................................................................................................................760

More about the conflict refiner....................................................................................................................761

Refining a conflict in a MIP start.................................................................................................................763

Using the conflict refiner in an application..................................................................................................765

Example: modifying ilomipex2.cpp..................................................................................................766

What belongs in an application to refine conflict.............................................................................768

USER'S MANUAL FOR CPLEX

Comparing a conflict application to Interactive Optimizer...........................................................................769

Preferences in the conflict refiner....................................................................................................770

Groups in the conflict refiner...........................................................................................................771

Repairing infeasibilities with FeasOpt...................................................................................773

What is FeasOpt?.......................................................................................................................................774

Invoking FeasOpt........................................................................................................................................775

Specifying preferences...............................................................................................................................776

Example: FeasOpt in Concert Technology.................................................................................................777

Advanced programming techniques....................................................................783

User-cut and lazy-constraint pools........................................................................................785

What are user cuts and lazy constraints?...................................................................................................786

What are pools of user cuts or lazy constraints?........................................................................................787

Differences between user cuts and lazy constraints..................................................................................788

Limitations on pools in the C API...............................................................................................................789

Adding user cuts and lazy constraints........................................................................................................791

Using the Component Libraries.......................................................................................................792

Using the Interactive Optimizer.......................................................................................................793

Reading and writing LP files...........................................................................................................794

Reading and writing SAV files.........................................................................................................796

Reading and writing MPS files........................................................................................................797

Deleting user cuts and lazy constraints......................................................................................................799

Using goals..............................................................................................................................801

Branch & cut with goals..............................................................................................................................803

What is a goal?...............................................................................................................................804

Overview of goals in the search......................................................................................................805

How goals are implemented in branch & cut...................................................................................806

About the method execute in a goal................................................................................................807

Special goals in branch & cut.....................................................................................................................809

Or goal............................................................................................................................................810

And goal..........................................................................................................................................811

Fail goal...........................................................................................................................................812

Local cut goal..................................................................................................................................813

Null goal..........................................................................................................................................814

Branch as CPLEX goal...................................................................................................................815

Solution goal...................................................................................................................................816

Aggregating goals......................................................................................................................................817

Example: goals in branch & cut..................................................................................................................818

The goal stack............................................................................................................................................820

Memory management and goals................................................................................................................822

Cuts and goals...........................................................................................................................................823

Injecting heuristic solutions........................................................................................................................825

Controlling goal-defined search..................................................................................................................826

USER'S MANUAL FOR CPLEX

Example: using node evaluators in a node selection strategy....................................................................829

Search limits...............................................................................................................................................831

Using optimization callbacks.................................................................................................833

What are callbacks?...................................................................................................................................835

Informational callbacks...............................................................................................................................837

What is an informational callback?..................................................................................................838

Reference documents about informational callbacks......................................................................839

Where to find examples of informational callbacks.........................................................................840

What informational callbacks can return.........................................................................................841

Query or diagnostic callbacks....................................................................................................................843

What are query or diagnostic callbacks?........................................................................................844

Where query callbacks are called...................................................................................................845

Query callbacks and dynamic search.............................................................................................847

Query callbacks and deterministic parallel search..........................................................................848

Control callbacks........................................................................................................................................849

What are control callbacks?............................................................................................................850

What control callbacks do...............................................................................................................851

Control callbacks and dynamic search............................................................................................853

Control callbacks and deterministic parallel search........................................................................854

Implementing callbacks with Concert Technology......................................................................................855

How callback classes are organized...............................................................................................856

Writing callback classes by hand....................................................................................................857

Writing callbacks with macros in C++.............................................................................................858

Callback interface............................................................................................................................861

The continuous callback..................................................................................................................862

Example: deriving the simplex callback ilolpex4.cpp..................................................................................863

Implementing callbacks in the Callable Library..........................................................................................865

Callable Library callback facilities....................................................................................................866

Setting callbacks.............................................................................................................................867

Callbacks for continuous and discrete problems.............................................................................868

Example: using callbacks lpex4.c...............................................................................................................869

Example: controlling cuts iloadmipex5.cpp.................................................................................................870

Interaction between callbacks and parallel optimizers................................................................................875

Return values for callbacks........................................................................................................................876

Terminating without callbacks.....................................................................................................................877

Goals and callbacks: a comparison......................................................................................879

Overview.....................................................................................................................................................880

Advanced presolve routines..................................................................................................883

Introduction to presolve..............................................................................................................................884

A proposed example...................................................................................................................................886

Restricting presolve reductions..................................................................................................................887

When to alert presolve to modifications..........................................................................................888

Adding constraints to the first solution............................................................................................889

USER'S MANUAL FOR CPLEX

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