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Brown, R. G., Chinneck, J.W. and Karam, G. "Optimization with Constraint Programming Systems" in Impact of Recent Computer Advances on Operations Research, North Holland, January 1989.

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Extending Prolog with Constraint Arithmetic on Real Intervals - Older, Vellino (1990)   (36 citations)  (Correct)

....is evaluated and is the function that returns the intersection of two intervals. It follows from this definition of relational addition that the evaluation of a relational equation may well narrow all the intervals in it. For example evaluating the equation X Y = Z, for initial values X=[3,7], Y= 2,8] and Z= 4,6] narrows all three intervals: X to [3,4] Y to [2,3] and Z to [5,6] 1 . 2.4 Critical Path Analysis The following example solves a simple critical path analysis (PERT) problem. Let the time required to complete an activity, the activity time, be the difference between the ....

....of two intervals. It follows from this definition of relational addition that the evaluation of a relational equation may well narrow all the intervals in it. For example evaluating the equation X Y = Z, for initial values X= 3,7] Y= 2,8] and Z= 4,6] narrows all three intervals: X to [3,4], Y to [2,3] and Z to [5,6] 1 . 2.4 Critical Path Analysis The following example solves a simple critical path analysis (PERT) problem. Let the time required to complete an activity, the activity time, be the difference between the start time and the finish time. Let the slack time be the ....

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Brown, R. G., Chinneck, J.W. and Karam, G. "Optimization with Constraint Programming Systems" in Impact of Recent Computer Advances on Operations Research, North Holland, January 1989.


Constraint Arithmetic on Real Intervals - Older (1993)   (66 citations)  (Correct)

....search algorithms, or dealing with problems that have both combinatorial and continuous aspects. A more complete description of the surface syntax and operational appearance of constraint interval arithmetic can be found in [10] which also includes examples illustrating various features and [1] which compares BNR Prolog with other CLP systems. 3.2 Comparisons It is helpful to contrast constraint interval arithmetic both with other constraint satisfaction techniques and with conventional methods. In the following subsections we note the differences from symbolic methods, procedural ....

Brown, R. G., Chinneck, J.W. and Karam, G. "Optimization with Constraint Programming Systems" in Impact of Recent Computer Advances on Operations Research, North Holland, January 1989.

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