Table Of ContentLINDO
API 13.0
User Manual
LINDO Systems, Inc.
1415 North Dayton Street, Chicago, Illinois 60642
Phone: (312)988-7422 Fax: (312)988-9065
E-mail: [email protected]
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iii
TABLE OF CONTENTS
TABLE OF CONTENTS ............................................................................................................ iii
Preface ...................................................................................................................................... ix
Chapter 1: .................................................................................................................................. 1
Introduction ................................................................................................................................ 1
What Is LINDO API? ............................................................................................................ 1
Linear Solvers ................................................................................................................... 2
Mixed-Integer Solver......................................................................................................... 2
Nonlinear Solver ............................................................................................................... 3
Global Solver .................................................................................................................... 3
Stochastic Solver .............................................................................................................. 3
Installation ............................................................................................................................ 3
Windows Platforms ........................................................................................................... 4
Unix-Like Platforms ........................................................................................................... 4
Updating License Keys ......................................................................................................... 6
Solving Models from a File using Runlindo .......................................................................... 7
Sample Applications ........................................................................................................... 11
Array Representation of Models ......................................................................................... 12
Sparse Matrix Representation ........................................................................................ 13
Simple Programming Example ....................................................................................... 16
Chapter 2: ................................................................................................................................ 21
Function Definitions ................................................................................................................. 21
Common Parameter Macro Definitions .............................................................................. 22
Structure Creation and Deletion Routines .......................................................................... 26
License and Version Information Routines ........................................................................ 28
Input-Output Routines ........................................................................................................ 30
Parameter Setting and Retrieving Routines ....................................................................... 49
Available Parameters...................................................................................................... 64
Available Information .................................................................................................... 139
Model Loading Routines ................................................................................................... 160
Solver Initialization Routines ............................................................................................ 192
Optimization Routines ...................................................................................................... 198
Solution Query Routines .................................................................................................. 207
Model Query Routines ...................................................................................................... 227
Model Modification Routines ............................................................................................ 270
Model and Solution Analysis Routines ............................................................................. 293
Error Handling Routines ................................................................................................... 305
Advanced Routines .......................................................................................................... 307
Matrix Operations ......................................................................................................... 316
Callback Management Routines ...................................................................................... 329
Memory Management Routines ....................................................................................... 343
Random Number Generation Routines ............................................................................ 346
Sampling Routines ........................................................................................................... 352
Date and Time Routines ................................................................................................... 367
Tuner Routines ................................................................................................................. 370
Chapter 3: .............................................................................................................................. 383
iv TABLE OF CONTENTS
Solving Linear Programs ....................................................................................................... 383
A Programming Example in C .......................................................................................... 383
A Programming Example in Visual Basic ......................................................................... 393
VB and Delphi Specific Issues ......................................................................................... 401
Solving Large Linear Programs using Sprint .................................................................... 402
Solving Linear Programs using the –fileLP option in Runlindo .................................... 403
A Programming Example in C ...................................................................................... 404
Multiobjective Linear Programs and Alternate Optima ..................................................... 410
Chapter 4: Solving Mixed-Integer Programs ......................................................................... 415
Staffing Example Using Visual C++ ................................................................................. 416
Staffing Example Using Visual Basic ............................................................................... 423
Solving MIPs using BNP .................................................................................................. 430
Solving MIPs using the –bnp option in Runlindo .............................................................. 430
A Programming Example in C .......................................................................................... 432
Chapter 5: Solving Quadratic Programs ............................................................................... 435
Setting up Quadratic Programs ........................................................................................ 436
Loading Quadratic Data via Extended MPS Format Files ............................................ 436
Loading Quadratic Data via API Functions .................................................................. 437
Sample Portfolio Selection Problems ............................................................................... 440
Example 1. The Markowitz Model: ............................................................................... 440
Example 2. Portfolio Selection with Restrictions on the Number of Assets Invested: .. 444
Chapter 6: Solving Conic Programs ...................................................................................... 451
Second-Order Cone Programs......................................................................................... 451
Setting up Second-Order Cone Programs ....................................................................... 454
Loading Cones via Extended MPS Format Files .......................................................... 454
Loading Cones via API Functions ................................................................................ 456
Example 3: Minimization of Norms: .............................................................................. 456
Converting Models to SOCP Form ............................................................................... 461
Example 4: Ratios as SOCP Constraints: .................................................................... 463
Quadratic Programs as SOCP ..................................................................................... 467
Semi-Definite Programs ................................................................................................... 468
Loading SDP via SDPA Format Files ........................................................................... 469
Loading SDPs via API Functions .................................................................................. 473
Chapter 7: Solving Nonlinear Programs ................................................................................ 481
Instruction-List/MPI Style Interface .................................................................................. 482
Postfix Notation in Representing Expressions ............................................................. 482
Supported Operators and Functions ............................................................................ 484
Inputting SDP/POSD Constraints via MPI File/Instruction List ..................................... 502
Inputting SDP/POSD Constraints via a C Program ...................................................... 505
Black-Box Style Interface ................................................................................................. 514
Loading Model Data...................................................................................................... 515
Evaluating Nonlinear Terms via Callback Functions .................................................... 517
Grey-Box Style Interface .................................................................................................. 521
Instruction Format ......................................................................................................... 523
Example 1 ..................................................................................................................... 523
Example 2 ..................................................................................................................... 523
Example 3 ..................................................................................................................... 524
Differentiation ................................................................................................................... 524
Solving Non-convex and Non-smooth models ................................................................. 525
Linearization ................................................................................................................. 525
TABLE OF CONTENTS v
Multistart Scatter Search for Difficult Nonlinear Models ............................................... 527
Global Optimization of Difficult Nonlinear Models ........................................................ 529
Sample Nonlinear Programming Problems ...................................................................... 530
Example 1: Black-Box Style Interface: ......................................................................... 530
Example 2: Instruction-List Style Interface ................................................................... 536
Example 3: Multistart Solver for Non-Convex Models ................................................. 546
Example 4: Global Solver with MPI Input Format ......................................................... 550
Example 5: Grey-Box Style Interface ........................................................................... 556
Example 6: Nonlinear Least-Square Fitting .................................................................. 563
Chapter 8: .............................................................................................................................. 568
Stochastic Programming ....................................................................................................... 568
Multistage Decision Making Under Uncertainty ............................................................ 568
Multistage Recourse Models ............................................................................................ 570
Scenario Tree ................................................................................................................... 571
Setting up SP Models: ...................................................................................................... 573
Loading Core Model: .................................................................................................... 573
Loading the Time Structure: ......................................................................................... 576
Loading the Stochastic Structure: ................................................................................. 578
Decision Making under Chance-Constraints .................................................................... 585
Individual and Joint Chance-Constraints: ..................................................................... 585
Monte Carlo Sampling ...................................................................................................... 588
Automatic Sampling of Scenario Trees ........................................................................ 592
Limiting Sampling to Continuous Parameters .............................................................. 592
Using Nested Benders Decomposition Method ............................................................ 593
Sample Multistage SP Problems ...................................................................................... 595
An Investment Model to Fund College Education: ....................................................... 595
An American Put-Options Model: ................................................................................. 597
Sample Chance-Constrainted Problems .......................................................................... 599
A Production Planning Problem: ................................................................................... 599
Models with User-defined Distribution: ......................................................................... 600
A Farming Problem: ...................................................................................................... 602
About alternative formulations: ..................................................................................... 605
Appendix 8a: Correlation Specification......................................................................... 605
Appendix 8b: Random Number Generation ................................................................ 609
Appendix 8c: Variance Reduction ............................................................................... 610
Appendix 8d: The Costs of Uncertainty: EVPI and EVMU .......................................... 610
Appendix 8e: Introducing Dependencies between Stages .......................................... 614
Chapter 9: .............................................................................................................................. 617
Using Callback Functions ...................................................................................................... 617
Specifying a Callback Function ........................................................................................ 617
A Callback Example Using C ........................................................................................... 620
A Callback Example Using Visual Basic .......................................................................... 625
Integer Solution Callbacks ................................................................................................ 627
Chapter 10: Analyzing Models and Solutions ....................................................................... 631
Sensitivity and Range Analysis of an LP .......................................................................... 631
Diagnosis of Infeasible or Unbounded Models................................................................. 633
Infeasible Models .......................................................................................................... 633
Workings of the IIS Finder: ........................................................................................... 635
Unbounded Linear Programs ....................................................................................... 636
Infeasible Integer Programs ......................................................................................... 636
vi TABLE OF CONTENTS
Infeasible Nonlinear Programs ..................................................................................... 637
An Example for Debugging an Infeasible Linear Program ............................................... 637
Debugging an infeasible model with runlindo................................................................... 643
Block Structured Models .................................................................................................. 644
Determining Total Decomposition Structures ............................................................... 647
Determining Angular Structures ................................................................................... 648
Techniques Used in Determining Block Structures ...................................................... 649
Generalized Assignment Problem ................................................................................ 649
Chapter 11: ............................................................................................................................ 651
Parallel Optimization ............................................................................................................. 651
Thread Parameters .......................................................................................................... 651
Concurrent vs. Parallel Parameters ................................................................................. 652
Solving MIPs Concurrently ............................................................................................... 653
Solvers with built-in Parallel Algorithms ........................................................................... 656
Reproducibility .................................................................................................................. 657
Chapter 12: Parameter Tuning Tool ...................................................................................... 658
Setting up the Tuning Tool ............................................................................................... 658
Tuning with a Configuration File ....................................................................................... 659
Tuning with API Calls Programmatically .......................................................................... 661
Running the Tuning Tool .................................................................................................. 662
Chapter 13: Multiobjective Models and Alternate Optima ..................................................... 664
Setting up Objective Pool ................................................................................................. 665
Accessing Solution Pool ................................................................................................... 666
Example: Bi-objective Linear Assignment Problem ......................................................... 669
Appendix A: Error Codes ...................................................................................................... 673
Appendix B: ........................................................................................................................... 686
MPS File Format ................................................................................................................... 686
Integer Variables .............................................................................................................. 689
Semi-continuous Variables ............................................................................................... 689
SOS Sets .......................................................................................................................... 690
SOS2 Example ................................................................................................................. 691
Quadratic Objective .......................................................................................................... 693
Quadratic Constraints ....................................................................................................... 694
Second-Order Cone Constraints ...................................................................................... 695
Ambiguities in MPS Files .................................................................................................. 698
Appendix C: ........................................................................................................................... 699
LINDO File Format ................................................................................................................ 699
Flow of Control ................................................................................................................. 699
Formatting ........................................................................................................................ 699
Optional Modeling Statements ......................................................................................... 701
FREE Statement ........................................................................................................... 702
GIN Statement .............................................................................................................. 702
INT Statement ............................................................................................................... 702
SUB and SLB Statements ............................................................................................ 703
TITLE Statement ........................................................................................................... 704
Appendix D: ........................................................................................................................... 705
MPI File Format ..................................................................................................................... 705
Appendix E: ........................................................................................................................... 708
SMPS File Format ................................................................................................................. 708
CORE File ..................................................................................................................... 708
TABLE OF CONTENTS vii
TIME File ...................................................................................................................... 708
STOCH File .................................................................................................................. 710
Appendix F: ........................................................................................................................... 717
SMPI File Format .................................................................................................................. 717
Appendix G: mxLINDO .......................................................................................................... 721
A MATLAB Interface.............................................................................................................. 721
Introduction ....................................................................................................................... 721
Setting up MATLAB to Interface with LINDO ................................................................... 721
Using the mxLINDO Interface .......................................................................................... 722
Calling Conventions ......................................................................................................... 724
mxLINDO Routines .......................................................................................................... 724
Structure Creation and Deletion Routines .................................................................... 724
License Information Routines ....................................................................................... 727
Input-Output Routines................................................................................................... 728
Error Handling Routines ............................................................................................... 736
Parameter Setting and Retrieving Routines ................................................................. 738
Model Loading Routines ............................................................................................... 745
Solver Initialization Routines ........................................................................................ 758
Optimization Routines................................................................................................... 762
Solution Query Routines ............................................................................................... 763
Model Query Routines .................................................................................................. 770
Model Modification Routines ........................................................................................ 789
Model and Solution Analysis Routines ......................................................................... 806
Advanced Routines....................................................................................................... 813
Callback Management Routines ................................................................................... 818
Auxiliary Routines ......................................................................................................... 824
Sample MATLAB Functions ............................................................................................. 826
M-functions using mxLINDO ......................................................................................... 826
Appendix H: ........................................................................................................................... 829
An Interface to Ox ................................................................................................................. 829
Introduction ....................................................................................................................... 829
Setting up Ox Interface ..................................................................................................... 829
Calling Conventions ......................................................................................................... 830
Example. Portfolio Selection with Restrictions on the Number of Assets Invested ...... 832
Appendix I: ............................................................................................................................ 837
List of Abbreviations in Progress Logs .................................................................................. 837
Appendix J: ............................................................................................................................ 839
An R Interface ....................................................................................................................... 839
Introduction ....................................................................................................................... 839
Installation ........................................................................................................................ 839
Calling Conventions ......................................................................................................... 839
Example. Least Absolution Deviation Estimation ......................................................... 839
Appendix K: ........................................................................................................................... 843
A Python Interface ................................................................................................................. 843
Introduction ....................................................................................................................... 843
Installation ........................................................................................................................ 843
Calling Conventions ......................................................................................................... 843
Example. Solving an LP model with pyLindo ............................................................... 844
References ............................................................................................................................ 847
Acknowledgements ............................................................................................................... 849
viii TABLE OF CONTENTS
INDEX ................................................................................................................................... 851
ix
Preface
LINDO Systems is proud to introduce LINDO API 13.0. The general features include a) stochastic
optimization b) global and multistart solvers for global optimization, c) nonlinear solvers for general
nonlinear optimization, d) simplex solvers for linear optimization e) barrier solvers for linear,
quadratic and second-order-cone optimization f) mixed-integer solvers for linear-integer and
nonlinear-integer optimization, g) tools for analysis of infeasible linear, integer and nonlinear models,
h) features to exploit parallel processing on multi-core computers, i) interfaces to other systems such as
MATLAB, Ox, Java and .NET and j) support of more platforms
(see below).
The new features are: a) Improved speed and robustness in all solvers; b) Several new functions and
constraint types are recognized, e.g., the AllDiff constraint for general integer variables, c) New
symmetry detection capabilities have been added to the integer (MIP) solver. This may dramatically
reduce the time needed to prove optimality on some models with integer variables.
The primary solvers in LINDO API 13.0 are:
❑ Global Solver:
The global solver combines a series of range bounding (e.g., interval analysis and convex
analysis) and range reduction techniques (e.g., linear programming and constraint
propagation) within a branch-and-bound framework to find proven global solutions to non-
convex NLPs. Traditional nonlinear solvers can get stuck at suboptimal, local solutions. API
13.0 incorporates substantial improvements in a) finding good feasible solutions quickly and
b) constructing bounds on both convex and nonconvex functions so optimality can be proven
more quickly.
❑ Mixed Integer Solver:
The mixed integer solver of LINDO API 13.0 solves linear, quadratic, and general nonlinear
integer models. It contains advanced techniques such as a) cut generation b) tree reordering
to reduce tree growth dynamically, c) improved heuristics for finding good solutions quickly,
and d) identifying certain model structures and exploiting for much faster solution, d)
recognition of the AllDiff (All Different constraint type).
❑ General Nonlinear Solver:
LINDO API is the first full-featured solver callable library to offer general nonlinear and
nonlinear/integer capabilities. This unique feature allows developers to use a single general
purpose solver into custom applications. As with its linear and integer capabilities, LINDO
API provides the user with a comprehensive set of routines for formulating, solving, and
modifying nonlinear models. API 13.0 supports several dozen additional nonlinear functions,
mainly in the area of probability distributions, pdf’s, cdf’s, and their inverses.
❑ Multistart Nonlinear Solver:
The multistart solver intelligently generates a sequence of candidate starting points in the
solution space of NLP and mixed integer NLPs. A traditional NLP solver is called with each
starting point to find a local optimum. For non-convex NLP models, the quality of the best
solution found by the multistart solver tends to be superior to that of a single solution from a
x PREFACE
traditional nonlinear solver. A user adjustable parameter controls the maximum number of
multistarts to be performed. See Chapter 7, Solving Nonlinear Models, for more information.
❑ Simplex Solvers:
LINDO API 13.0 offers two advanced implementations of the primal and dual simplex
methods as the primary means for solving linear programming problems. Its flexible design
allows the users to fine tune each method by altering several of the algorithmic parameters.
The Sprint method uses the standard simplex solvers efficiently to handle “skinny” LP’s,
those having millions of variables, but a modest number of constraints.
❑ Barrier (Interior-Point) Solver:
Barrier solver is an alternative way for solving linear and quadratic programming problems.
LINDO API’s state-of-the-art barrier solver offers great speed advantages for large scale
sparse models. LINDO API 13.0 also includes a special variant of the barrier solver
specifically designed to solve Second-Order-Cone (SOC) problems, including Semi-Definite
Programs (SDP). See Chapter 6, Solving Second-Order-Cone Models, for more information.
API 13.0 includes improved techniques for automatically identifying models than can be
solved as SOC.
❑ Stochastic Solver, Multistage and Chance Constrained:
LINDO API 13.0 supports decision making under uncertainty. Its powerful stochastic solver
offers the ability to solve:
a) chance-constrained models,
b) multistage stochastic models with recourse.
For both types, the user expresses the uncertainty by providing distribution functions, either
built-in or user-defined. In multistage models, the stochastic solver optimizes the model to
minimize the cost of the initial stage plus the expected value of recourse over all future
stages. In chance-constrained models, the solver finds the best solution that satisfies
constraints with a specified probability.
❑ Parallel Extensions:
LINDO API 13.0 includes multi-cpu optimization extensions to its solvers to take advantage
of computers with multicore processors. The multicore extensions are of two types:
concurrent optimizers and parallel optimizers (using built-in parallel algorithms). Parallel
versions of random number generators and sampling features are also provided.
❑ Statistical Sampling Tools:
LINDO API 13.0 offers extensive set of API functions for sampling from various statistical
distributions. Sampling error can be reduced by using variance reduction methods such as
Latin-Hyper-Square sampling and Antithetic variates. Generation of correlated (dependent)
samples based on Pearson, Spearman or Kendall’s correlation measures is provided. A
pseudo-random number generation API offers advanced generators with long cycles.
Description:LINDO Systems, Inc. warrants that on the date of receipt of your payment, the disk enclosed in the disk envelope contains an accurate reproduction of LINDO API and that the copy of the related documentation is accurately reproduced. Due to the inherent complexity of computer programs and computer
