1. Relational Operators
2. Logical Operators
3. Logical Expressions
4. Conditional Expressions
5. Conditional Structures
6. Binary Parameters

Lower[r] <= sum {i in INGREDIENTS} Contributes[r, i] * Amount[i] 

sum {s in SURFBOARDS} Recipe[m, s] * Production[s] <= Supply[m]; 

1. in is true if is a member of ;
2. not in is false if is a member of ;
3. exists { in } is true if some in has being true;
4. forall { in } is true if all in have being true;
5. within is true if all the elements in are in ;
6. not within is true if some element in is not in .

param ifvalue := if  then                                     [else                    ]; 

if  then   ; [else   ;] 

Note here that even if the else keyword is present you need to end with ;. If you want to include more than one statement within the conditional structures you can use { and } to enclose your statements:

if  then {    } [else {    }] 

param stillSearching binary; 

param isGreater binary;  let isGreater := if 4 > 5 then 1 else 0; # isGreater = 0 (false) let isGreater := if 6 > 5 then 1; # else 0 is the default, isGreater = 1 (true) 

let  := if  then 1; 

binary ;  if  then   let  := 1; else   let  := 0; 

Some example from depth first searching or column generation 

Some example from depth first searching or column generation 

1. <e> not in <SET> is false if <e> is a member of <SET>;

<-- Ready to Review -->

Logical Operators

Logical operators are used to combine logical expressions. They are most commonly used in conditional statements, conditional structures and conditional loops. The logical operators are not, and and or. They are used as shown in the table below:

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Conditional Expressions

A conditional expression is very much like the IF function in Microsoft Excel:

param ifvalue := if <some logical expression> then
                   <a value>
                [else
                   <another value>];

If the logical expression is true then ifvalue will be set to <a value>, otherwise it is set to 0 (by default) or, if the else part of the expression is present, <another value>. Note that if the else keyword is present, then no ; needs to be included after <a value>.

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Conditional Structures

A conditional structure is the same as the classical if_-_then_-_else statement in programming languages like MATLAB, Fortran, Visual Basic and C++:

if <logical expression> then
  <a statement>;
[else
  <another statement>;]

Note here that even if the else keyword is present you need to end <a statement> with ;. If you want to include more than one statement within the conditional structures you can use { and } to enclose your statements:

if <logical expression> then
{
  <some statements>
}
[else
{
  <some other statements>
}]

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Binary parameters are used in a similar way to boolean variables (in Matlab, C, etc) and logical variables (Fortran). If a binary parameter has the value 0 this is equivalent to false, and 1 is equivalent to true. Binary parameters can be used with conditional expressions to hold a true/false result from a logical expression:

let <binary parameter> := if <expression> then 1;

binary <binary parameter>;

Some example from depth first searching or column generation

Some example from depth first searching or column generation

Logical Expressions

Lower[r] <= sum {i in INGREDIENTS} Contributes[r, i] * Amount[i]

sum {s in SURFBOARDS} Recipe[m, s] * Production[s] <= Supply[m];

However, there are some special logical expressions in AMPL for use with sets:

1. <e> in <SET> is true if <e> is a member of <SET>;
2. {\tt <e> not in <SET>} is false if <e> is a member of <SET>;
3. exists {<e> in <SET>} <expression> is true if some <e> in <SET> has <expression> being true;
4. forall {<e> in <SET>} <expression> is true if all <e> in <SET> have <expression> being true;
5. <SUBSET> within <SET> is true if all the elements in <SUBSET> are in <SET>;
6. <SUBSET> not within <SET> is true if some element in <SUBSET> is not in <SET>.

Logical expressions can be built up from other logical expressions, binary parameters and logical operators.

Binary Parameters

Logic in AMPL

1. Relational Operators
2. Logical Expressions
3. Binary Parameters
4. Logical Operators
5. Conditional Expressions
6. Conditional Structures

Relational Operators

Relational operators are used to compare two expressions. They are most commonly used in constraints, but not exclusively. The relational operators are:

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Logical Expressions

\begin{verbatim} sum {i in INGREDIENTS} FatPercent[i] * Percentage[i] >= MinFat \end{verbatim}

\begin{verbatim} sum {i in INGREDIENTS} FibrePercent[i] * Percentage[i] <= MaxFibre; \end{verbatim}

However, there are some special logical expressions in AMPL for use with sets:

1. {\tt <e> in <SET>} is true if {\tt <e>} is a member of {\tt <SET>};
2. {\tt <e> not in <SET>} is false if {\tt <e>} is a member of {\tt <SET>};
3. exists { in } is true if some in has being true;
4. forall { in } is true if all in have being true;
5. within is true if all the elements in are in ;
6. not within is true if some element in is not in .

Logical expressions can be built up from other logical expressions, binary parameters and logical operators.

Under Construction

Binary Parameters

\begin{verbatim} param stillSearching binary; \end{verbatim}

Binary parameters are used in a similar way to boolean variables (in Matlab, C, etc) and logical variables (Fortran). If a binary parameter has the value 0 this is equivalent to false, and 1 is equivalent to true. Binary parameters can be used with conditional expressions to hold a true/false result from a logical expression:

\begin{verbatim} param isGreater binary;

let isGreater := if 4 > 5 then 1 else 0; # isGreater = 0 (false) let isGreater := if 6 > 5 then 1; # else 0 is the default, isGreater = 1 (true) \end{verbatim}

so the syntax is

\begin{verbatim} \end{verbatim} or as the condition in a conditional statement or conditional structure. They are very useful for building complex conditional statements or structures:

\begin{verbatim} Some example from depth first searching or column generation \end{verbatim}

and controlling loops.

Logical Operators

<\tt not} {\tt and} {\tt or}

Conditional Expressions

A conditional expression is very much like the IF function in Excel: param ifvalue := if then [else ];

If the logical expression is true then ifvalue will be set to , otherwise it is set to 0 (by default) or, if the else part of the expression is present, . Note that if the else keyword is present, then no ; needs to be included after .

Conditional Structures

A conditional structure is the same as the classical if-then-else statement in programming languages like MATLAB, Fortran, Visual Basic and C++: if then ; [else ;] Note here that even if the else keyword is present you need to end with ;. If you want to include more than one statement within the conditional structures you can use { and } to enclose your statements. if then { } [else { }]

Logic in AMPL

Coming soon!

-- TWikiAdminGroup - 18 Mar 2008