To formulate and solve a problem in ECLiPSe the standard pattern is as follows:
Very often, however, the constraints involve logical implications or disjunctions, as in the case of the noclash constraint above. Such constraints are most naturally formulated in a way that would introduce choice points during the constraint posting phase. The two ECLiPSe clauses defining noclash, above, are a case in point.
There are two major disadvantages of introducing choice points during constraint posting:
Propia and CHR’s support the separation of constraint setup and search behaviour, by allowing constraints to be formulated naturally without their execution setting up any choice points.
The effect on performance is illustrated by the following small
The aim is to choose a set of 9 products (
identified by their product number 101-109) to
manufacture, with a
limited quantity of raw materials (
so as to achieve a profit (
Profit) of over
The amount of raw materials (of two kinds) needed to produce
each product is listed in a table, together with its profit.
product_plan(Products) :- length(Products,9), Raw1 #=< 95, Raw2 #=< 95, Profit #>= 40, sum(Products,Raw1,Raw2,Profit), labeling(Products). product( 101,1,19,1). product( 102,2,17,2). product( 103,3,15,3). product( 104,4,13,4). product( 105,10,8,5). product( 106,16,4,4). product( 107,17,3,3). product( 108,18,2,2). product( 109,19,1,1). sum(Products,Raw1,Raw2,Profit) :- ( foreach(Item,Products), foreach(R1,R1List), foreach(R2,R2List), foreach(P,PList) do product(Item,R1,R2,P) ), Raw1 #= sum(R1List), Raw2 #= sum(R2List), Profit #= sum(PList).
The drawback of this program is that the
sum constraint calls
product which chooses an item and leaves a choice point at each
Thus the setup of the
sum constraint leaves 9 choice points.
Try running it, and the program
fails to terminate within a reasonable amount of time.
Now to make the program run efficiently, we can simply annotate the call
product as a Propia constraint making:
product(Item,R1,R2,P) infers most.
This program leaves no choice points during constraint setup, and
finds a solution in a fraction of a second.
In the remainder of this chapter we show how to use Propia and CHR’s, give some examples, and outline their implementation.
Propia and CHRs can be used to build clear problem models that have no (hidden) choice points.