# CUTEst: a Constrained and Unconstrained Testing Environment with safe threads for mathematical optimization

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## Abstract

We describe the most recent evolution of our constrained and unconstrained testing environment and its accompanying SIF decoder. Code-named SIFDecode and CUTEst, these updated versions feature dynamic memory allocation, a modern thread-safe Fortran modular design, a new Matlab interface and a revised installation procedure integrated with GALAHAD.

## Keywords

CUTE CUTEr CUTEst Optimization Modeling Benchmarking## 1 Introduction

The Constrained and Unconstrained Testing Environment (CUTE) [3] and its associated set of optimization examples have been widely adopted and used since their introduction in 1993. The test set has grown over time and now numbers approximately 1,150 examples, many of them of variable dimension. In addition, since both the MPS linear programming format [14] and its quadratic programming extensions [13, 16, 17] are compatible with CUTE’s Standard Input Format (SIF) [5, Chap. 7], CUTE and its successor CUTEr [11] provide access to other test sets such as those from Netlib [9] and Maros and Meszaros [16].

To set the scene, recall that a SIF file provides a portable description of group-partially separable optimization problem [4]. Such a file is translated by the package SifDec to a number of Fortran subroutines that compute values and derivatives of constituent element and group functions, together with data that explains how the functions are glued together. Armed with these components, CUTE(r) reassembles them to allow users to compute values and derivatives of both the objective function and/or its constraints as required, and provides static information such as bounds on variables and constraints.

The core (Fortran 77) routines behind CUTE(r) have not changed significantly since their original release. A main limitation of standard Fortran 77 is that it offers no mechanism for dynamic memory management, something programmers of other languages (particularly C) take for granted. This defect had a significant implication for CUTE and CUTEr, namely that a one-size-fits-all set of array dimensions are set at compile time, and CUTEr and its relatives return to the user if this choice is insufficient, with a recommendation for recompilation with values that might be appropriate. Many CUTEr users have learned to detest this inflexibility, and it is certainly the main source of complaint we receive.

Of course, modern Fortran (90 and later) provide dynamic memory allocation, and it has mostly been the scale of the task of rewriting CUTEr to do this that has stopped us; CUTEr (and its dependent SifDec) number roughly 50,000 lines of code. Now, we have done so. The new, Fortran 2003 packages CUTEst and SIFDecode both request array storage as needed. The data for any array that is not currently large enough is written to temporary storage (or, if there is insufficient room in memory, to disk), the array de-allocated and re-allocated with some “elbow-room” and the existing data copied back. A more general concern about the lack of freely-available reliable modern Fortran compilers has also vanished with the arrival of both g95 and gfortran; there are of course many excellent commercial Fortran compilers available.

An additional limitation of CUTE(r) is that it relies on Fortran common blocks to share data between tools. Some of this data, such as that required to describe the structure of a problem, is fixed after calling “setup” routines, while the remainder is constantly rewritten as problem function (and derivative) evaluations take place. This use of common means that the packages are not thread safe, and cannot be used in a multi-threaded (parallel) environment (for example to test branch-and-bound methods for integer programming or global optimization). This deficiency has also been addressed in CUTEst, and indeed the data is now split so that a single copy of the fixed data is available to all threads, while dynamic data is stored on a per-thread basis.

We have also taken the opportunity to revise the way the packages are organised and installed. We have adopted the scheme we currently use within GALAHAD [12], leading to some isolation of common components that are distributed separately. Since GALAHAD is itself a major user of CUTEr, we have also updated components of GALAHAD to use CUTEst packages. In addition, we have upgraded all of CUTEr’s interfaces to external optimization packages—written in a variety of languages—that are still distributed (there have been a few casualties since 2003), and have also provided interfaces to a number of new ones. We have also considerably simplified the interface to Matlab.

This short paper is arranged as follows. We first describe how CUTEst is now organised, and how it may be used to test external packages. We then give a few details of the new features provided. A few words about the SIF decoder are followed by a description of the installation procedure.

## 2 New package organisation

Before installation begins, the subdirectories objects, modules, makefiles, versions and bin/sys will all be empty. The script install_cutest prompts the user for the answers to a series of questions aimed at determining what machine type, operating system and compiler should be used to build CUTEst—we call this combination of a machine, operating system and compiler an *architecture*. The architecture is selected from a large list of predefined possibilities encoded in a separate package, archdefs , that is shared between SIFDecode, CUTEst and GALAHAD. Each architecture is assigned a simple (mnemonic) architecture *code* name, say architecture—for example a version for the NAG Fortran 95 compiler on a PC runing Linux is coded pc.lnx.n95, while another for the IBM Fortran 95 compiler on a PowerPC system running AIX is ppc.aix.x95. Having determined the architecture, the installation script builds subdirectories of objects, modules and packages named architecture. Each of these subdirectories contains further subdirectories double and single to hold architecture-dependent compiled libraries, module file information and external package linking information if required. In addition, architecture-dependent makefile information and environment variables for execution scripts are placed in files named architecture in the makefiles and bin/sys subdirectories, and a file recording how the code is related to the architecture is put in versions.

The source code for each CUTEst package interface is located in a separate subdirectory of the src directory. The main CUTEst evaluation tools all lie in the subdirectory tools, while a set of comprehensive test programs are available in test. The remaining subdirectories contain interface programs between the tools and each of the external packages supported. Each subdirectory contains the interface, a default options specification file, an example program that tests the interface without requiring the external package, a README that explains what a user needs to do to make the external package work with CUTEst, and a makefile. Since the order of compilation of Fortran modules is important, and as we have seen there is a strong interdependency between the CUTEst packages, the makefiles have to be carefully crafted. For this reason, we have chosen not to use variants of tools such as imake to build and maintain the makefiles. A set of configuration files that provides default link details between CUTEst and each external package is provided in the directory packages/defaults. Users may copy and modify these to architecture and dimension specific subdirectories of packages to override the default choices. Man pages for CUTEst as a whole and for each individual tool are provided in subdirectories of the man directory, and versions in PDF format are also available in the pdf subdirectory of the documentation directory doc.

Once the correct directory structure is in place, the installation script builds a random-access library of the required precision by visiting each of the subdirectories of src and calling the Unix utility make. CUTEst package interfaces are all written in double precision, but if a user prefers to use single precision, the makefiles call suitable Unix sed scripts (stored in seds) to transform the source prior to compilation. A user may choose to install all of CUTEst with or without Matlab support. The tools for unconstrained and constrained optimization may also be installed separately. Recompilation following updates is easily performed by issuing the command make from the src directory, while make test from the same directory runs comprehensive tests of all compiled components.

## 3 Interfaces to the CUTEst test set

A few SIF examples are given in the sif directory, while the runcutest and cutest2matlab commands are in the bin subdirectory, and have man-page descriptions in the man/man1 subdirectory.

## 4 Improvements

### 4.1 New features

As we mentioned in the introduction, CUTEst and SIFDecode both use the Fortran 2003 allocate/deallocate features to create and modify array storage. Each CUTEst tool uses a module CUTEST that provides access to two derived types CUTEST_data_type and CUTEST_work_type used to store workspace arrays. The former collects data that describes problem structure and is set prior to any problem function evaluation, and unchanged thereafter, while the latter is used to hold data that may change at every evaluation. Data in these arrays is made available to the tools through a scalar CUTEST_data_global of type CUTEST_data_type and an allocatable array CUTEST_work_global of type CUTEST_work_type.

All evaluation tools are available as both simple (unthreaded) and threaded versions. For the latter, which may be distinguished by the suffix _threaded, CUTEST_work_global is allocated to be large enough to hold all the threads that will be used by the setup subroutines. Each evaluation call specifies access to CUTEST_work_global(i) for the particular thread i required.

We give a list of all CUTEst tools and their functionality in Appendix 1. Most are rewritten versions of their CUTEr counterparts, with argument-list changes to remove redundant size parameters and occasional order changes to handle inconsistencies. An additional status argument has been added to each to report any fatal memory errors (such as array allocation/deallocation failures) and inabilities to evaluate functions at specified values; CUTEr deals with such eventualities by terminating execution. We have added termination tools to allow users to deallocate all storage created by the setup procedure when they have no longer need for it. In addition, constraints may now be ordered so that equalities precede or follow inequalities, or so that linear constraints precede or follow nonlinear ones, and variables so that those that only appear linearly in the problem precede or follow those that appear nonlinearly. New tools have also been introduced to describe the sparsity patterns of the Hessian of the objective and Lagrangian functions. Finally, a new tool has been added to compute the sparse gradient of the objective function for constrained problems; this corrects an oversight since we already provide similar functionality for the gradients of individual constraints.

### 4.2 New Matlab calls

The Matlab interface has been substantially revised and simplified. It is now entirely written in C instead of Fortran to facilitate interaction with Matlab’s own API and usage of its index types. The interface merges the constrained and unconstrained tools together so users may use familiar and consistent function calls such as cutest_obj() to obtain the objective function value and possibly its gradient regardless of the presence of constraints. In this regard, the interface exploits Matlab’s ability to determine how many output arguments are required by the user. This allows both f = cutest_obj(x) and [f,g] = cutest_obj(x). Another example is the cuter_cons() function, which evaluates all or individual constraints and/or constraint gradients.

Help is included with all CUTEst tools, available to Matlab users by way of the familiar help call. In particular, help cutest gives an overview of the tools available.

See Appendix 2 for a complete description of the Matlab CUTEst tools and their functionality.

### 4.3 New interfaces

In addition to the still-current packages supported by CUTEr, CUTEst provides new interfaces to ALGENCAN [2], BOBYQA [18], Direct Search [7], filterSD [8], LINUOA [19], NEWUOA [20], NLPQLP [22], NOMAD [6], PENNLP [15], QL [23], SPG [1] and SQIC [10], as well as various new packages within GALAHAD [12]. An interface is also provided to translate SIF examples into a format used by the QPLIB2014 [21] quadratic programming collection.

Interfaces to the obsolete packages hsl_ve12, osl, va15, ve09 and ve14 supported in CUTEr have been withdrawn.

### 4.4 New test examples

Almost 200 new examples have been added to the test-problem collection since the release of CUTEr. These include large collections of problems arising from linear complementarity, and of real-life quadratic programming problems.

All test problems are now under version control in the same way as the source code and users may update their local repository easily when new problems are added or changes are made to existing problems.

## 5 A revised SIF decoder

As we mentioned in the introduction, the lack of dynamic memory allocation affects the SIF decoding package SifDec just as severely as it does CUTEr. A new stand-alone Fortran package SIFDecode has been written to address this issue. All of the functionality of the subroutines previously in SifDec have been combined into a single Fortran 2003 module SIFDECODE. Since required array sizes are not known beforehand, default initial values are increased as required as the package makes a single pass through the SIF file under consideration; default initial values may be changed to make the processing more efficient, but this is not crucial.

The distributed package is organised in the same way as CUTEst (see §2), although now the src directory simply contains two source subdirectories: decode that holds the decoder and its main program, and select containing the test-problem database interrogation tools from CUTE [3, §2.3].

## 6 New installation procedures

The installation procedure has been updated to recognise that most users will need to install both SIFDecode and CUTEst, and may also wish to integrate these with GALAHAD. A single script, install_optsuite, prompts the user to describe what features are needed and which architecture is desired. An opportunity to modify default compilation flags is provided, after which the script will automatically download and install the software.

## 7 Obtaining the packages

## 8 Conclusions and perspectives

We believe CUTEst is a considerable improvement over past versions because of its improved modular and thread-safe design exploiting recent additions to the Fortran standard, dynamic allocation, simplified and unified tool calling sequences, improved Matlab interface and, last but not least, the more user-friendly installation process. Despite the age of the standard input format and the advent of more modern modeling languages, CUTE and CUTEr remain widely-used tools in the optimization community and beyond, as illustrated by the large number of user comments and request that we receive, and the associated problem collection remains a staple of optimization software testing and benchmarking.

Since all packages and test problems are maintained and distributed via a source code revision system, bug fixes, improvements and additions are easily available.

## Notes

### Acknowledgments

We are extremely grateful to Roger Fletcher, Philip Gill, Bill Hager, Michal Kočvara, Michael Powell, Klaus Schittkowski and Elizabeth Wong for making their latest codes available to us so that we could build and test interfaces, and to two anonymous referees whose enthusiastic comments lead to a better paper. The work of the first author was supported by the EPSRC Grant EP/I013067/1. The work of the second author was supported by an NSERC Discovery Grant.

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