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Lower Bounds for the ITC2007 CurriculumBased Course Timetabling Problem
"... This paper describes an approach for generating lower bounds for the Curriculumbased course timetabling problem, which was presented at the International Timetabling Competition (ITC2007, Track 3). So far, several methods based on integer linear programming have been proposed for computing lower bo ..."
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This paper describes an approach for generating lower bounds for the Curriculumbased course timetabling problem, which was presented at the International Timetabling Competition (ITC2007, Track 3). So far, several methods based on integer linear programming have been proposed for computing lower bounds of this minimization problem. We present a new partitionbased approach that is based on the “divide and conquer ” principle. The proposed approach uses Iterative Tabu Search to partition the initial problem into subproblems which are solved with an ILP solver. Computational outcomes show that this approach is able to improve on the current best lower bounds for 12 out of the 21 benchmark instances, and to prove optimality for 6 of them. These new lower bounds are useful to estimate the quality of the upper bounds obtained with various heuristic approaches.
A Twostage Decomposition of High School . . .
, 2013
"... Integer Programming (IP) has been used to model educational timetabling problems since the very early days of Operations Research. It is well recognized that these IP models in general are hard to solve, and this area of research is dominated by heuristic solution approaches. In this paper a TwoS ..."
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Integer Programming (IP) has been used to model educational timetabling problems since the very early days of Operations Research. It is well recognized that these IP models in general are hard to solve, and this area of research is dominated by heuristic solution approaches. In this paper a TwoStage Decomposition of an IP model for a practical case of high school timetabling is shown. This particular timetabling problem consists of assigning lectures to both a timeslot and a classroom, which is modeled using a very large amount of binary variables. The decomposition splits this model into two separate problems (Stage I and Stage II) with far less variables. These two separate problems are solved in sequence, such that the solution for the Stage I model is given as input to the Stage II model, implying that irreversible decisions are made in Stage I. However, the objective of the Stage II model is partly incorporated in the Stage I model by exploiting that Stage II can be seen as a minimum weight maximum matching problem in a bipartite graph. This theoretically strengthens the decomposition in terms of global optimality. The approach relies on Hall's theorem for the existence of matchings in bipartite graphs, which in its basic form yields an exponential amount of constraints in the Stage I model. However, it is shown that only a small subset of these constraints is needed, making the decomposition tractable in practice for IP solvers. To evaluate the decomposition, 100 reallife problem instances from the database of the high school ERP system Lectio are used. Computational results show that the decomposition performs significantly better than solving the original IP, in terms of both found solutions and bounds.
EXPLOITING STRUCTURE IN INTEGER PROGRAMS
, 2011
"... This dissertation argues the case for exploiting certain structures in integer linear programs. Integer linear programming is a wellknown optimisation problem, which seeks the optimum of a linear function of variables, whose values are required to be integral as well as to satisfy certain linear eq ..."
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This dissertation argues the case for exploiting certain structures in integer linear programs. Integer linear programming is a wellknown optimisation problem, which seeks the optimum of a linear function of variables, whose values are required to be integral as well as to satisfy certain linear equalities and inequalities. The state of the art in solvers for this problem is the “branch and bound ” approach. The performance of such solvers depends crucially on four types of inbuilt heuristics: primal, improvement, branching, and cutseparation or, more generally, bounding heuristics. Such heuristics in generalpurpose solvers have not, until recently, exploited structure in integer linear programs beyond the recognition of certain types of singlerow constraints. Many alternative approaches to integer linear programming can be cast in the following, novel framework. “Structure” in any integer linear program
Performance Analysis of Diversity Measure with Crossover Operators in Genetic Algorithm M.Nandhini
"... The goal of nphard Combinatorial Optimization is finding the best possible solution from the set of feasible solutions. In this paper, we establish an approach using genetic algorithm with various selection and crossover operators with repair function for an institute course timetabling problem. It ..."
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The goal of nphard Combinatorial Optimization is finding the best possible solution from the set of feasible solutions. In this paper, we establish an approach using genetic algorithm with various selection and crossover operators with repair function for an institute course timetabling problem. It employs a constructive heuristic approach to find the feasible timetable, fitness value calculation, selection operators, crossover operators and repair function. The performance of proposed and existing selection and crossover operators are compared and shown by keeping diversity in the fitness value of population.
Semidefinite Programming Relaxations in Timetabling (Abstract)
 PATAT 2010
, 2010
"... Semidefinite programming has recently gained much attention as a powerful method for deriving both strong lower bounds and approximation algorithms in combinatorial optimisation. There have not been, however, any applications to timetabling. We show one reason to believe that this could well change ..."
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Semidefinite programming has recently gained much attention as a powerful method for deriving both strong lower bounds and approximation algorithms in combinatorial optimisation. There have not been, however, any applications to timetabling. We show one reason to believe that this could well change, ultimately. Definitions In linear programming (LP), the task is to optimise a linear combination cT x subject to linear constraints Ax = b, together with the constraint that each in vector x of n variables is nonnegative. The nonnegativity of x, x ∈ (R+) n, can be seen be seen as a restriction of the variables to lie in the convex cone of the positive orthant. Using interior point methods, linear programming can be solved to any fixed precision in polynomial time. These methods also work for other symmetric convex cones. Semidefinite programming (SDP, Bellman & Fan, 1963; Alizadeh, 1995; Wolkowicz, Saigal, & Vandenberghe, 2000) is a generalisation of linear programming, replacing the vector variable with a square symmetric matrix variable and the polyhedral symmetric convex cone of the positive
MIC 2015: The XI Metaheuristics International Conference id–1 A Research Agenda for Metaheuristic Standardization
"... We propose that the development of standardized, explicit, machinereadable descriptions of metaheuristics will greatly advance scientific progress in the field. In particular, we advocate a purely functional description of metaheuristics — separate from any metaphors that inspire them and with no ..."
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We propose that the development of standardized, explicit, machinereadable descriptions of metaheuristics will greatly advance scientific progress in the field. In particular, we advocate a purely functional description of metaheuristics — separate from any metaphors that inspire them and with no hidden mechanisms. A recent policy statement in the Journal of Heuristics1 highlights the need for improved
A Decomposition of the Maxmin Fair Curriculumbased Course Timetabling Problem∗ The Impact of Solving Subproblems to Optimality
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Under consideration for publication in Theory and Practice of Logic Programming 1 Answer Set Programming as a Modeling Language for Course Timetabling
, 2003
"... The course timetabling problem can be generally dened as the task of assigning a number of lectures to a limited set of timeslots and rooms, subject to a given set of hard and soft constraints. The modeling language for course timetabling is required to be expressive enough to specify a wide variety ..."
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The course timetabling problem can be generally dened as the task of assigning a number of lectures to a limited set of timeslots and rooms, subject to a given set of hard and soft constraints. The modeling language for course timetabling is required to be expressive enough to specify a wide variety of soft constraints and objective functions. Furthermore, the resulting encoding is required to be extensible for capturing new constraints and for switching them between hard and soft, and to be
exible enough to deal with different formulations. In this paper, we propose to make effective use of ASP as a modeling language for course timetabling. We show that our ASPbased approach can naturally satisfy the above requirements, through an ASP encoding of the curriculumbased course timetabling problem proposed in the third track of the second international timetabling competition (ITC2007). Our encoding is compact and humanreadable, since each constraint is individually expressed by either one or two rules. Each hard constraint is expressed by using integrity constraints and aggregates of ASP. Each soft constraint S is expressed by rules in which the head is the form of penalty(S,V,C), and a violation V and its penalty cost C are detected and calculated respectively in the body. We carried out experiments on four different benchmark sets with ve different formulations. We succeeded either in improving the bounds or producing the same bounds for many combinations of problem instances and formulations, compared with the previous best known bounds.