The CLP Procedure
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Overview
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Getting Started
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Syntax
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Details
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ExamplesLogic-Based PuzzlesAlphabet Blocks ProblemWork-Shift Scheduling ProblemA Nonlinear Optimization ProblemCar Painting ProblemScene Allocation ProblemCar Sequencing ProblemRound-Robin ProblemResource-Constrained Scheduling with Nonstandard Temporal ConstraintsScheduling with Alternate Resources10×10 Job Shop Scheduling ProblemScheduling a Major Basketball ConferenceBalanced Incomplete Block DesignProgressive Party ProblemStatement and Option Cross-Reference Table
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The CLP Procedure
The CLP procedure is a finite-domain constraint programming solver for CSPs. In the context of the CLP procedure, CSPs can be classified into the following two types, which are determined by specification of the relevant output data set:
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A standard CSP is characterized by integer variables, linear constraints, array-type constraints, global constraints, and reify constraints. In other words, X is a finite set of integer variables, and C can contain linear, array, global, or logical constraints. Specifying the OUT= option in the PROC CLP statement indicates to the CLP procedure that the CSP is a standard-type CSP. As such, the procedure expects only VARIABLE , ALLDIFF , ELEMENT , GCC , LEXICO , LINCON , PACK , REIFY , ARRAY , and FOREACH statements. You can also specify a
Constraintdata set by using the CONDATA= option in the PROC CLP statement instead of, or in combination with, VARIABLE and LINCON statements. -
A scheduling CSP is characterized by activities, temporal constraints, and resource requirement constraints. In other words, X is a finite set of activities, and C is a set of temporal constraints and resource requirement constraints. Specifying one of the SCHEDULE= , SCHEDRES= , or SCHEDTIME= options in the PROC CLP statement indicates to the CLP procedure that the CSP is a scheduling-type CSP. As such, the procedure expects only ACTIVITY , RESOURCE , REQUIRES , and SCHEDULE statements. You can also specify an
Activitydata set by using the ACTDATA= option in the PROC CLP statement instead of, or in combination with, the ACTIVITY , RESOURCE , and REQUIRES statements. You can define activities by using theActivitydata set or the ACTIVITY statement. Precedence relationships between activities must be defined using the ACTDATA= data set. You can define resource requirements of activities by using theActivitydata set or the RESOURCE and REQUIRES statements.
The output data sets contain any solutions determined by the CLP procedure. For more information about the format and layout of the output data sets, see the sections Solution Data Set and Schedule Data Set.
Consistency Techniques
The CLP procedure features a full look-ahead algorithm for standard CSPs that follows a strategy of maintaining a version of generalized arc consistency that is based on the AC-3 consistency routine (Mackworth 1977). This strategy maintains consistency between the selected variables and the unassigned variables and also maintains consistency between unassigned variables. For the scheduling CSPs, the CLP procedure uses a forward-checking algorithm, an arc-consistency routine for maintaining consistency between unassigned activities, and energetic-based reasoning methods for resource-constrained scheduling that feature the edge-finder algorithm (Applegate and Cook 1991). You can elect to turn off some of these consistency techniques in the interest of performance.
Selection Strategy
A search algorithm for CSPs searches systematically through the possible assignments of values to variables. The order in which a variable is selected can be based on a static ordering, which is determined before the search begins, or on a dynamic ordering, in which the choice of the next variable depends on the current state of the search. The VARSELECT= option in the PROC CLP statement defines the variable selection strategy for a standard CSP. The default strategy is the dynamic MINR strategy, which selects the variable with the smallest range. The ACTSELECT= option in the SCHEDULE statement defines the activity selection strategy for a scheduling CSP. The default strategy is the RAND strategy, which selects an activity at random from the set of activities that begin prior to the earliest early finish time. This strategy was proposed by Nuijten (1994).
Assignment Strategy
After a variable or an activity has been selected, the assignment strategy dictates the value that is assigned to it. For variables, the assignment strategy is specified with the VARASSIGN= option in the PROC CLP statement. The default assignment strategy selects the minimum value from the domain of the selected variable. For activities, the assignment strategy is specified with the ACTASSIGN= option in the SCHEDULE statement. The default strategy of RAND assigns the time to the earliest start time, and the resources are chosen randomly from the set of resource assignments that support the selected start time.