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The constraint solver library contains a local search based framework that allows
modeling of a problem using constraint programming primitives (variables, values, constraints).
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/**
* University Course Timetabling: Heuristics.
*
*
* The quality of a solution is expressed as a weighted sum combining
* soft time and classroom preferences, satisfied soft group constrains
* and the total number of student conflicts. This allows us to express
* the importance of different types of soft constraints. The following
* weights are considered in the sum:
*
* -
* weight of a student conflict,
*
-
* weight of a time preference of a placement,
*
-
* weight of a classroom preference of a placement,
*
-
* weight of a preference of a satisfied soft group constraint,
*
-
* weight of a distance instructor preference of a placement (it is
* discouraged if there are two subsequent classes taught by the
* same instructor but placed in different buildings not far than
* 50 meters, strongly discouraged if the buildings are more than
* 50 meters but less than 200 meters far)
*
-
* weight of the overall department balancing penalty (number of
* the time units used over initial allowances summed over all
* times and departments)
*
-
* weight of an useless half-hour (empty half-hour time segments
* between classes, such half-hours cannot be used since all
* events require at least one hour)
*
-
* weight of a too large classrooms (weight for each classroom
* that has more than 50% excess seats)
*
*
* Note that preferences of all time, classroom and group soft
* constraints go from -2 (strongly preferred) to 2 (strongly
* discouraged). So, for instance, the value of the weighted sum is
* increased when there is a discouraged time or room selected or a
* discouraged group constraint satisfied. Therefore, if there are two
* solutions, the better solution of them has the lower weighted sum of
* the above criteria.
*
*
* The termination condition stops the search when the solution is
* complete and good enough (expressed as the number of perturbations and
* the solution quality described above). It also allows for the solver
* to be stopped by the user. Characteristics of the current and the best
* achieved solution, describing the number of assigned variables, time
* and classroom preferences, the total number of student conflicts,
* etc., are visible to the user during the search.
*
*
* The solution comparator prefers a more complete solution (with a
* smaller number of unassigned variables) and a solution with a smaller
* number of perturbations among solutions with the same number of
* unassigned variables. If both solutions have the same number of
* unassigned variables and perturbations, the solution of better quality
* is selected.
*
*
* If there are one or more variables unassigned, the variable selection
* criterion picks one of them randomly. We have tried several approaches
* using domain sizes, number of previous assignments, numbers of
* constraints in which the variable participates, etc., but there was no
* significant improvement in this timetabling problem towards the random
* selection of an unassigned variable. The reason is, that it is easy to
* go back when a wrong variable is picked - such a variable is
* unassigned when there is a conflict with it in some of the subsequent
* iterations.
*
*
* When all variables are assigned, an evaluation is made for each
* variable according to the above described weights. The variable with
* the worst evaluation is selected. This variable promises the best
* improvement in optimization.
*
*
* We have implemented a hierarchical handling of the value selection
* criteria. There are three levels of comparison. At each level a
* weighted sum of the criteria described below is computed. Only
* solutions with the smallest sum are considered in the next level. The
* weights express how quickly a complete solution should be found. Only
* hard constraints are satisfied in the first level sum. Distance from
* the initial solution (MPP), and a weighting of major preferences
* (including time, classroom requirements and student conflicts), are
* considered in the next level. In the third level, other minor criteria
* are considered. In general, a criterion can be used in more than one
* level, e.g., with different weights.
*
*
* The above sums order the values lexicographically: the best value
* having the smallest first level sum, the smallest second level sum
* among values with the smallest first level sum, and the smallest third
* level sum among these values. As mentioned above, this allows
* diversification between the importance of individual criteria.
*
*
* Furthermore, the value selection heuristics also support some limits
* (e.g., that all values with a first level sum smaller than a given
* percentage Pth above the best value [typically 10%] will go to the
* second level comparison and so on). This allows for the continued
* feasibility of a value near to the best that may yet be much better in
* the next level of comparison. If there is more than one solution after
* these three levels of comparison, one is selected randomly. This
* approach helped us to significantly improve the quality of the
* resultant solutions.
*
*
* In general, there can be more than three levels of these weighted
* sums, however three of them seem to be sufficient for spreading
* weights of various criteria for our problem.
*
*
* The value selection heuristics also allow for random selection of a
* value with a given probability (random walk, e.g., 2%) and, in the
* case of MPP, to select the initial value (if it exists) with a given
* probability (e.g., 70%).
*
*
* Criteria used in the value selection heuristics can be divided into
* two sets. Criteria in the first set are intended to generate a
* complete assignment:
*
* -
* Number of hard conflicts
*
-
* Number of hard conflicts, weighted by their previous occurrences
* (see conflict-based statistics)
*
* Additional criteria allow better results to be achieved during
* optimization:
*
* -
* Number of student conflicts caused by the value if it is assigned to
* the variable
*
-
* Soft time preference caused by a value if it is assigned to the
* variable
*
-
* Soft classroom preference caused by a value if it is assigned to
* the variable (combination of the placement's building, room, and
* classroom equipment compared with preferences)
*
-
* Preferences of satisfied soft group constraints caused by the
* value if it is assigned to the variable
*
-
* Difference in the number of assigned initial values if the value
* is assigned to the variable: -1 if the value is initial, 0
* otherwise, increased by the number of initial values assigned to
* variables with hard conflicts with the value.
*
-
* Distance instructor preference caused by a value if it is
* assigned to the variable (together with the neighbour classes)
*
-
* Difference in department balancing penalty
*
-
* Difference in the number of useless half-hours (number of
* empty half-hour time segments between classes that arise,
* minus those which disappear if the value is selected)
*
-
* Classroom is too big: 1 if the selected classroom has more
* than 50% excess seats
*
*
* Let us emphasize that the criteria from the second group are needed
* for optimization only, i.e., they are not needed to find a feasible
* solution. Furthermore, assigning a different weight to a particular
* criteria influences the value of the corresponding objective function.
*
* @author Tomas Muller
* @version IFS 1.4 (Instructor Sectioning)
* Copyright (C) 2024 Tomas Muller
* [email protected]
* http://muller.unitime.org
*
* This library is free software; you can redistribute it and/or modify
* it under the terms of the GNU Lesser General Public License as
* published by the Free Software Foundation; either version 3 of the
* License, or (at your option) any later version.
*
* This library is distributed in the hope that it will be useful, but
* WITHOUT ANY WARRANTY; without even the implied warranty of
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
* Lesser General Public License for more details.
*
* You should have received a copy of the GNU Lesser General Public
* License along with this library; if not see
* http://www.gnu.org/licenses/.
*/
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