MiniZinc Interface for R

Introduction

MiniZinc is a free and open-source constraint modeling language. Constraint satisfaction and discrete optimization problems can be formulated in a high-level modeling language. Models are compiled into an intermediate representation that is understood by a wide range of solvers. MiniZinc itself provides several solvers, for instance GeCode. The existing packages in R are not powerful enough to solve even mid-sized problems in combinatorial optimization.

There are implementations of an Interface to MiniZinc in Python like MiniZinc Python and pymzn and JMiniZinc for Java but such an interface does not exist for R.

This package provides an implementation of a very simple and easy to use interface for R that will help R users to solve optimization problems that can’t be solved with R currently.

It’s important to understand R6 classes before getting into the details. If you are not comfortable with R6, please go through this tutorial.

It would be nice to go through the tutorials on the MiniZinc website to understand more about MiniZinc. This is mainly for those who are interested in contributing to the package.

Installation

1. Build libminizinc

First, You need to download the latest libminizinc release and build libminizinc library for MiniZinc to work properly.

Please follow these steps for Linux:

• Download the latest libminizinc release from https://github.com/MiniZinc/libminizinc/releases.
• Extract the downloaded tar.gz or zip (for Windows) and name the extracted folder libminizinc.
• cd libminizinc/
  
• sudo sed -i '3 i set(CMAKE_POSITION_INDEPENDENT_CODE ON)' CMakeLists.txt
  
• sudo cmake CMakeLists.txt
  
• sudo make
  
• sudo make install

Similarly, build libminizinc on Windows (can use cygwin) and OSX.

If sed command doesn’t work for you, just add set(CMAKE_POSITION_INDEPENDENT_CODE ON) in the 3rd line (or any empty line in the starting) of CMakeLists.txt and follow the next steps.

2. Get Solver Binaries

Solvers are required to solve the MiniZinc models. The solvers currently supported by rminizinc are Chuffed, FindMUS and Gecode. Any solver can be selected based on the type of problem that is required to be solved.

Now download the solver binaries from the binary bundles at (https://www.minizinc.org/) to be able to solve the models and achieve full functionality of the package.

To get the solver binaries, the Users can download the MiniZinc binary bundles for Windows, MAC OS or Linux from https://www.minizinc.org/software.html and the provide the path to the bin folder of the MiniZinc bundle folder as the --with-bin argument. All the required solver binaries are present in that folder. The solver binary corresponding to Gecode will be fzn-gecode, FindMUS will be findMUS, Chuffed will be fzn-chuffed (.exe extentions will be there on Windows for eg. fzn-gecode.exe). ALternatively, if you don’t want to keep the MiniZinc bundle, you can copy the solver binaries to another folder and just provide the path to that folder with --with-bin.

Once these steps are over, you just need to re-install rminizinc by using

install.packages("rminizinc", configure.args="--with-mzn=/path/to/libminizinc --with-bin=/path/to/bin")

NOTE: Please don’t use \ at the end of the path given to --with-bin as it will cause some solver configuration issues.

Please note that if path arguments are not passed along with the installation (as --with-mzn), the default path /usr/local/lib for Linux and OSX, and C:/Program Files/ for Windows will be chosen but only if libminizinc in present in these default paths.

Getting Started

Load the library and the project root directory path

library(rminizinc)

## Loading required package: rjson

# load the project directory
data("proot")
# check if the library is present
data("config")
parse.next = FALSE
if(LIBMINIZINC_PATH == ""){
  warning("Please install libminizinc on your system!")
  parse.next = TRUE
}
# check if solver binaries are present
data("slvbin")
evaluate.next = FALSE
if(SOLVER_BIN == ""){
  warning("Please download solver binaries to solve the model")
  evaluate.next = TRUE
}

## Warning: Please download solver binaries to solve the model

# check if vignettes should be executed
if (!requireNamespace("rmarkdown") ||
!rmarkdown::pandoc_available("1.14")) {
     warning(call. = FALSE, "This vignette assumes that rmarkdown and pandoc
version 1.14 are available. These were not found. Older versions will not work.")
     knitr::knit_exit()
   }

# mzn file path
"
NOTE: This path is useful only when you build the package on your system, otherwise the project root directory path will be in tmp as the installation starts there. If the user builds the package on the system, then the project root path will be the build directory and vignette will run properly.
"

## [1] "\nNOTE: This path is useful only when you build the package on your system, otherwise the project root directory path will be in tmp as the installation starts there. If the user builds the package on the system, then the project root path will be the build directory and vignette will run properly.\n"

mzn_path = paste0(PROJECT_DIRECTORY, "/inst/extdata/mzn_examples/jobshop/jobshop_0.mzn")

# parse the model
parseObj = rminizinc:::mzn_parse(mzn_path = mzn_path)

missingPars = get_missing_pars(model = parseObj)
print(missingPars)

## [1] "n"  "m"  "d"  "mc"

pVals = list(Int$new(3), Int$new(4),
             Array$new(exprVec = intExpressions(c(3, 3, 4, 4, 4, 3, 2, 2, 3, 3, 3, 4)),
               dimranges = list(IntSetVal$new(1,3), IntSetVal$new(1,4))), 
             Array$new(exprVec = intExpressions(c(1, 2, 3, 4, 1, 3, 2, 4, 4, 2, 1, 3)),
               dimranges = list(IntSetVal$new(1,3), IntSetVal$new(1,4))))
names(pVals) = missingPars
model = set_params(model = parseObj, modData = pVals)
cat(model$mzn_string())

## int: n = 3;
## 
## set of int: JOB = (1 .. n);
## 
## int: m = 4;
## 
## set of int: MACH = (1 .. m);
## 
## set of int: TASK = (1 .. m);
## 
## array[JOB, TASK] of int: d = [|3, 3, 4, 4
## |4, 3, 2, 2
## |3, 3, 3, 4
## |];
## 
## array[JOB, TASK] of MACH: mc = [|1, 2, 3, 4
## |1, 3, 2, 4
## |4, 2, 1, 3
## |];
## 
## int: maxt = sum([d[j, t] | j in JOB , t in TASK ]);
## 
## array[JOB, TASK] of var (0 .. maxt): s;
## 
## var (0 .. maxt): makespan = max([(s[j, m] + d[j, m]) | j in JOB ]);
## 
## constraint forall([((s[j, t] + d[j, t]) <= s[j, (t + 1)]) | j in JOB , t in (1 .. (m - 1)) ]);
## 
## constraint forall([nonoverlap(s[j1, t1], d[j1, t1], s[j2, t2], d[j2, t2]) | j1,j2 in JOB , t1,t2 in TASK where ((j1 < j2) /\ (mc[j1, t1] = mc[j2, t2]))]);
## 
## solve  :: int_search([s[j, t] | j in JOB , t in TASK ], input_order, indomain_min, complete) minimize makespan;
## 
## predicate nonoverlap(var int: s1, var int: d1, var int: s2, var int: d2) = (((s1 + d1) <= s2) \/ ((s2 + d2) <= s1));
## include "solver_redefinitions.mzn";
## 
## include "stdlib.mzn";

# R List object containing the solutions
solObj = rminizinc:::mzn_eval(model, solver = "org.gecode.gecode",
                   lib_path = paste0(PROJECT_DIRECTORY, "/inst/minizinc/"))

## Error in rminizinc:::mzn_eval(model, solver = "org.gecode.gecode", lib_path = paste0(PROJECT_DIRECTORY, : Please install libminizinc (2.5.2) on your system and provide solver binaries!

# get all the solutions
print(solObj$SOLUTIONS)

## Error in print(solObj$SOLUTIONS): object 'solObj' not found

# file path
mzn_path = paste0(PROJECT_DIRECTORY, "/inst/extdata/mzn_examples/knapsack/knapsack_0.mzn")

# get missing parameter values
missingVals=rminizinc:::get_missing_pars( model = mzn_parse(mzn_path = mzn_path))
print(missingVals)

## [1] "n"        "capacity" "profit"   "size"

# list of the data
pVals = list(Int$new(3), Int$new(9), Array$new(intExpressions(c(15,10,7)))
             , Array$new(intExpressions(c(4,3,2))))

## dimensions not provided: initializing as 1d Array with
##                                min index 1 and max index 3
## dimensions not provided: initializing as 1d Array with
##                                min index 1 and max index 3

names(pVals) = missingVals

# set the missing parameters
model = rminizinc:::set_params(modData = pVals, 
                                   mzn_parse(mzn_path = mzn_path))

# R List object containing the solutions
solObj = rminizinc:::mzn_eval(r_model = model)

## Error in rminizinc:::mzn_eval(r_model = model): Please install libminizinc (2.5.2) on your system and provide solver binaries!

# get all the solutions
print(solObj$SOLUTIONS)

## Error in print(solObj$SOLUTIONS): object 'solObj' not found

Variables

There are two types of variables in MiniZinc namely, decision variables and parameters.

The data types of variables can be single types i.e integers (int), floating point numbers (float), Booleans (bool) and strings (string) and collections i.e sets, enums and arrays (upto 6 dimensional arrays).

Parameter is used to specify a parameter in a given problem and they are assigned a fixed value or expression.

Decision variables are the unknowns that Minizinc model is finding solutions for. We do not need to give them a value, but instead we give them a domain of possible values. Sometimes expressions involving other variables and parameters are also assigned to decision variables. Decision variables need to satisfy a set of constraints which form the core of the problem.

To create a variable declaration one needs to understand the elements of R6 classes that will be used to create the variables.

Easy to use declaration functions have been created for the users to declare variables and parameters of different data types. Examples of how to declare variables is shown below.

# create the variable and parameter declarations
decl = IntDecl(name = "n", kind = "par")
item1 = VarDeclItem$new(decl = decl)

par2_val = BinOp$new(lhs = Int$new(1), binop = "..", rhs = item1$getId())
item2 = VarDeclItem$new(decl = IntSetDecl(name = "OBJ", kind = "par", value = par2_val))

item3 = VarDeclItem$new(decl = IntDecl(name = "capacity", kind = "par"))

item4 = VarDeclItem$new(decl = IntArrDecl(name = "profit", kind = "par", ndim = 1, 
                                          ind = list(item2$getId())))

item5 = VarDeclItem$new(decl = IntArrDecl(name = "size", kind = "par", ndim = 1, ind =                                                            list(item2$getId())))

item6 = VarDeclItem$new(decl = IntArrDecl(name = "x", kind = "var", ndim = 1, ind = list(item2$getId())))

Constraints

Constraints are defined on the decision variables to restrict the range of values that they can take. They can also be thought of as the rules of a problem.

Constraints can be created using different R6 sub classes of the super class Expression. In this example Generator, BinOp, Comprehension and Call classes have been used. These classes take in the elements required to create an expression that will be used as a constraint. More information can be found using ?<class Name>

Create constraints:

# declare parameter for iterator
parIter = IntDecl(name = "i", kind = "par")


gen_forall = Generator$new(IN = item2$getId(), decls = list(parIter))
bop1 = BinOp$new(lhs = ArrayAccess$new(v = item6$getId(),  args= list(gen_forall$getDecl(1)$getId())),
                                                             binop = ">=", rhs = Int$new(0))

Comp1 = Comprehension$new(generators = list(gen_forall), body = bop1, set = FALSE)
cl1 = Call$new(fnName = "forall", args = list(Comp1))
item7 = ConstraintItem$new(e = cl1)

gen_sum = Generator$new(IN = item2$getId(), decls = list(parIter))

bop2 = BinOp$new(lhs = ArrayAccess$new(v = item5$getId(), args = list(gen_sum$getDecl(1)$getId())),             
                 binop = "*",  rhs = ArrayAccess$new(v = item6$getId() , 
                 args = list(gen_sum$getDecl(1)$getId())))

Comp2 = Comprehension$new(generators = list(gen_sum), body = bop2, set = FALSE)
cl2 = Call$new(fnName = "sum", args = list(Comp2))
bop3 = BinOp$new(lhs = cl2, binop = "<=", rhs = item3$getId())
item8 = ConstraintItem$new(e = bop3)

Solve Type

The constraint programming problem can be of three types, namely: Satisfaction , Minimization and Maximization. Satisfaction problems produce all the solutions that satisfy the constraints whereas minimization and maximization problems produce the solution which minimizes and maximizes the given expression.

An example is shown below:

bop4 = BinOp$new(lhs = ArrayAccess$new(v = item4$getId(), args = list(gen_sum$getDecl(1)$getId())),
                      binop = "*", rhs = ArrayAccess$new(v = item6$getId(), 
                      args = list(gen_sum$getDecl(1)$getId())))

Comp3 = Comprehension$new(generators = list(gen_sum), body = bop4, set = FALSE)

cl3 = Call$new(fnName = "sum", args = list(Comp3))

item9 = SolveItem$new(solve_type = "maximize", e = cl3)

Create the Model

Combine all the items to create a MiniZinc model.

items  = c(item1, item2, item3, item4, item5, item6, item7, item8, item9)
mod = Model$new(items = items)
modString = mod$mzn_string()
cat(modString)

## int: n;
## 
## set of int: OBJ = (1 .. n);
## 
## int: capacity;
## 
## array[OBJ] of int: profit;
## 
## array[OBJ] of int: size;
## 
## array[OBJ] of var int: x;
## 
## constraint forall([(x[i] >= 0) | i in OBJ ]);
## 
## constraint (sum([(size[i] * x[i]) | i in OBJ ]) <= capacity);
## 
## solve  maximize sum([(profit[i] * x[i]) | i in OBJ ]);

Delete Items

All the Item and Expression classes have a delete() function which is used to delete the objects from everywhere in the model. Note that the objects will be deleted from all the models present in the environment from where the delete() function is called. An example to demonstrate the same is shown below:

# delete the item 1 i.e declaration of n 
item1$delete()
cat(mod$mzn_string())

## set of int: OBJ = (1 .. n);
## 
## int: capacity;
## 
## array[OBJ] of int: profit;
## 
## array[OBJ] of int: size;
## 
## array[OBJ] of var int: x;
## 
## constraint forall([(x[i] >= 0) | i in OBJ ]);
## 
## constraint (sum([(size[i] * x[i]) | i in OBJ ]) <= capacity);
## 
## solve  maximize sum([(profit[i] * x[i]) | i in OBJ ]);

Create Items Using Strings

The strings containing MiniZinc syntax of items can be directly supplied to the constructors to initialize the objects. If strings are supplied, no other argument should be supplied to any of the Item classes except for AssignItem where you need to provided the associated variable declaration for the assignment.

declItem = VarDeclItem$new(mzn_str = "set of int: WORKSHEET = 0..worksheets-1;")
sprintf("Is this a parameter? %s", declItem$getDecl()$isPar())
sprintf("Is this a set? %s", declItem$getDecl()$ti()$type()$isSet())
sprintf("Base type of set: %s", declItem$getDecl()$ti()$type()$bt())
sprintf("Name: %s", declItem$getId()$getName())
sprintf("Value: %s", declItem$getDecl()$getValue()$c_str())

## [1] "Is this a parameter? TRUE"
## [1] "Is this a set? TRUE"
## [1] "Base type of set: int"
## [1] "Name: WORKSHEET"
## [1] "Value: (0 .. (worksheets - 1))"

CstrItem = ConstraintItem$new(mzn_str = "constraint forall (i in PREC)
                  (let { WORKSHEET: w1 = preceeds[i];
                             WORKSHEET: w2 = succeeds[i]; } in
                   g[w1] * e[w1] <= d[w2] + days * (1 - g[w2]));")
sprintf("Expression involved: %s", CstrItem$getExp()$c_str())
sprintf("Call function name: %s", CstrItem$getExp()$getName())
sprintf("Number of Arguments: %s", CstrItem$getExp()$nargs())
sprintf("Class of Argument: %s",  class(CstrItem$getExp()$getArg(1))[1])
sprintf("Number of Generators: %s", CstrItem$getExp()$nargs())
sprintf("Generator: %s", CstrItem$getExp()$getArg(1)$getGen(1)$c_str())
sprintf("Comprehension body: %s", CstrItem$getExp()$getArg(1)$getBody()$c_str())

## [1] "Expression involved: forall([let {WORKSHEET: w1 = preceeds[i], WORKSHEET: w2 = succeeds[i]} in ((g[w1] * e[w1]) <= (d[w2] + (days * (1 - g[w2])))) | i in PREC ])"
## [1] "Call function name: forall"
## [1] "Number of Arguments: 1"
## [1] "Class of Argument: Comprehension"
## [1] "Number of Generators: 1"
## [1] "Generator: i in PREC "
## [1] "Comprehension body: let {WORKSHEET: w1 = preceeds[i], WORKSHEET: w2 = succeeds[i]} in ((g[w1] * e[w1]) <= (d[w2] + (days * (1 - g[w2]))))"

SlvItem = SolveItem$new(mzn_str = "solve 
    :: int_search(
        [ if j = 1 then g[import_first[i]] else -d[import_first[i]] endif  | i in 1..worksheets, j in 1..2], 
        input_order, indomain_max, complete)
    maximize objective;")
sprintf("Objective: %s", SlvItem$getSt())
cat(sprintf("Annotation: %s", SlvItem$getAnn()$c_str()))

## [1] "Objective: maximize"
## Annotation:  :: int_search([if ((j = 1)) then (g[import_first[i]]) else (-(d[import_first[i]])) endif | i in (1 .. worksheets) , j in 1..2 ], input_order, indomain_max, complete)

fnItem = FunctionItem$new(mzn_str = "predicate nonoverlap(var int:s1, var int:d1,
                     var int:s2, var int:d2)=
          s1 + d1 <= s2 \\/ s2 + d2 <= s1;")
sprintf("Function name: %s", fnItem$name())
sprintf("No of function declarations: %s", length(fnItem$getDecls()))
sprintf("Function expression: %s", fnItem$getBody()$c_str())

## [1] "Function name: nonoverlap"
## [1] "No of function declarations: 4"
## [1] "Function expression: (((s1 + d1) <= s2) \\/ ((s2 + d2) <= s1))"

iItem = IncludeItem$new(mzn_str = "include \"cumulative.mzn\" ;")
sprintf("Included mzn name: %s", iItem$getmznName())

## [1] "Included mzn name: solver_redefinitions.mzn"

Modify Variable Domain

vd = VarDomainDecl(name = "n", dom = Set$new(IntSetVal$new(imin = 1, imax = 2)))
sprintf("The current declaration is: %s", vd$c_str())
vd$setDomain(Set$new(IntSetVal$new(imin = 3, imax = 5)))
sprintf("The modified declaration is: %s", vd$c_str())

## [1] "The current declaration is: var 1..2: n"
## [1] "The modified declaration is: var 3..5: n"

Modify Constraints

There are various getter and setter functions for the expression classes that can be used to modify existing constraints. For example:

vItem = VarDeclItem$new(mzn_str = "set of int: a = {1, 2, 3, 4};") 
cItem = ConstraintItem$new(mzn_str = "constraint sum(a) < 10;")
sprintf("The current constraint is: %s", cItem$c_str())
cItem$setExp(BinOp$new(lhs = Call$new(fnName = "max", args = list(vItem$getDecl()$getId())),
                       binop = "<", rhs = Int$new(10)))
sprintf("The modified constraint is: %s", cItem$c_str())

## [1] "The current constraint is: constraint (sum(a) < 10);\n"
## [1] "The modified constraint is: constraint (max(a) < 10);\n"

Some Common CP Problems

Functions have been provided to directly solve some of the common constraint programming problems.

1. Knapsack problem

The knapsack problem is a problem in combinatorial optimization: Given a set of items, each with a weight and a value, determine the number of each item to include in a collection so that the total weight is less than or equal to a given limit and the total value is as large as possible. It derives its name from the problem faced by someone who is constrained by a fixed-size knapsack and must fill it with the most valuable items. The problem often arises in resource allocation where the decision makers have to choose from a set of non-divisible projects or tasks under a fixed budget or time constraint, respectively.

Here, n is the number of items, capacity is the total capacity of carrying weight, profit is the profit corresponding to each item and weight is the weight/size of each item. The goal is to maximize the total profit.

# knapsack problem
print(knapsack(n = 3, capacity = 9, profit = c(15,10,7), size = c(4,3,2)))

## dimensions not provided: initializing as 1d Array with
##                                min index 1 and max index 3
## dimensions not provided: initializing as 1d Array with
##                                min index 1 and max index 3

## Error in mzn_eval(r_model = model): Please install libminizinc (2.5.2) on your system and provide solver binaries!

2. Assignment problem

The assignment problem is a fundamental combinatorial optimization problem. In its most general form, the problem is as follows:

The problem instance has a number of agents and a number of tasks. Any agent can be assigned to perform any task, incurring some cost that may vary depending on the agent-task assignment. It is required to perform as many tasks as possible by assigning at most one agent to each task and at most one task to each agent, in such a way that the total cost of the assignment is minimized.

Here, n is the number of agents, m is the number of tasks and the profit(cost) is an m x n 2D array where each row corresponds to the cost of each task for that agent. Please provide the profit array as a 1D vector only as shown below:

# assignment problem
print(assignment(n = 4, m = 5, cost = c(7,1,3,4,6,8,2,5,1,4,4,3,7,2,5,3,1,6,3,6)))

## Error in mzn_eval(r_model = model): Please install libminizinc (2.5.2) on your system and provide solver binaries!

More problems will be added with version updates.