Relational operators are used to compare two expressions. They are most commonly used in constraints, but not exclusively. The relational operators are:
Expression | Meaning |
---|---|
< | Less than |
<= | Less than or equal to |
> | Greater than |
>= | Greater than or equal to |
>= | Equal to |
<> | Not equal to |
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:
Expression | Result |
---|---|
not <expression> |
True if <expression> is false, false if <expression> is true |
<e1> and <e2> |
True if <e1> and <e2> are both true, otherwise false |
<e1> or <e2> |
True if either <e1> or <e2> are true, otherwise false |
Logical expressions are expressions that will evaluate to either true or false. Logical expressions are usually defined in terms of the relational operators:
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:
<e> in <SET>
is true if <e>
is a member of <SET>
;
<e>
is a member of <SET>
;
exists {<e> in <SET>} <expression>
is true if some <e>
in <SET>
has <expression>
being true;
forall {<e> in <SET>} <expression>
is true if all <e>
in <SET>
have <expression>
being true;
<SUBSET> within <SET>
is true if all the elements in <SUBSET>
are in <SET>
;
<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.
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>
.
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> }]
In AMPL we can create binary parameters by using the binary
keyword in the parameter declaration:
param stillSearching binary;
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:
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)so the syntax is
let <binary parameter> := if <expression> then 1;
You can also set binary parameters within conditional structures
binary <binary parameter>; if <expression> then let <binary parameter> := 1; else let <binary parameter> := 0;
Binary parameters may be used in logical expressions or as the condition in a conditional statement or conditional structure. They are very useful for building complex conditional statements or structures:
Some example from depth first searching or column generationComing soon! and controlling conditional loops:
Some example from depth first searching or column generationComing soon!
-- TWikiAdminGroup - 18 Mar 2008