# Re: [eclipse-clp-users] Correct use of minimize to find a globally minimal solution

From: Joachim Schimpf <jschimpf_at_...311...>
Date: Fri, 01 Mar 2013 00:14:33 +0100
On 27/02/2013 19:30, Misha Aizatulin wrote:
> hi all,
>
>    I'm having trouble understanding how to use minimize(). Attached is a
> simple example that tries to find an allocation of dance lessons to
> dance couples (satisfying requests), and then choose the one with the
> minimal cost. Unfortunately, minimize() does not find the globally
> minimal solution. What is the correct way to use that?

A constraint program has to follow a certain structure, in order to
make sense (http://www.eclipseclp.org/doc/tutorial/tutorial055.html)

solve(Variables) :-
setup_constraints(Data, Variables),
labeling(Variables).

An essential point is that the constraint setup code must not contain
"choices" or "alternatives", except in the form of alternative values
for variables (i.e. their domain).  In your code, the cost/3 predicate
represents such choices, and must be replaced.  In the following, I
have used element/3 constraints to do that:

:- lib(ic).
:- lib(branch_and_bound).

%------- the data ---------

ncouples(2).

% request(Couple, PossibleLessons)
request(1, [0,1,2]).
request(2, [0,2,3]).

% Lesson 0 1 2 3
cost(1, [1,0,0,0]).	% Couple 1
cost(2, [0,0,1,1]).	% Couple 2

% ----- the constraint model ---------

schedule(Allocation) :-
ncouples(NCouples),
(
for(I, 1, NCouples),
foreach(Lesson, Allocation),
foreach(Cost, Costs)
do
request(I, PossibleLessons), % get data
Lesson :: PossibleLessons,   % create variable
cost(I, LessonCostsForI),    % get data
Lesson1 #=Lesson+1,          % create constraints
element(Lesson1, LessonCostsForI, Cost)
),
alldifferent(Allocation),        % more constraints
TotalCost #= sum(Costs),

% ---- the search ----
minimize(labeling(Allocation), TotalCost).

-- Joachim
Received on Fri Mar 01 2013 - 00:16:44 CET

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