115,854 research outputs found
Efficient algorithms to solve scheduling problems with a variety of optimization criteria
La programmation par contraintes est une technique puissante pour rĂ©soudre, entre autres, des problĂšmes d'ordonnancement de grande envergure. L'ordonnancement vise Ă allouer dans le temps des tĂąches Ă des ressources. Lors de son exĂ©cution, une tĂąche consomme une ressource Ă un taux constant. GĂ©nĂ©ralement, on cherche Ă optimiser une fonction objectif telle la durĂ©e totale d'un ordonnancement. RĂ©soudre un problĂšme d'ordonnancement signifie trouver quand chaque tĂąche doit dĂ©buter et quelle ressource doit l'exĂ©cuter. La plupart des problĂšmes d'ordonnancement sont NP-Difficiles. ConsĂ©quemment, il n'existe aucun algorithme connu capable de les rĂ©soudre en temps polynomial. Cependant, il existe des spĂ©cialisations aux problĂšmes d'ordonnancement qui ne sont pas NP-Complet. Ces problĂšmes peuvent ĂȘtre rĂ©solus en temps polynomial en utilisant des algorithmes qui leur sont propres. Notre objectif est d'explorer ces algorithmes d'ordonnancement dans plusieurs contextes variĂ©s. Les techniques de filtrage ont beaucoup Ă©voluĂ© dans les derniĂšres annĂ©es en ordonnancement basĂ© sur les contraintes. La proĂ©minence des algorithmes de filtrage repose sur leur habilitĂ© Ă rĂ©duire l'arbre de recherche en excluant les valeurs des domaines qui ne participent pas Ă des solutions au problĂšme. Nous proposons des amĂ©liorations et prĂ©sentons des algorithmes de filtrage plus efficaces pour rĂ©soudre des problĂšmes classiques d'ordonnancement. De plus, nous prĂ©sentons des adaptations de techniques de filtrage pour le cas oĂč les tĂąches peuvent ĂȘtre retardĂ©es. Nous considĂ©rons aussi diffĂ©rentes propriĂ©tĂ©s de problĂšmes industriels et rĂ©solvons plus efficacement des problĂšmes oĂč le critĂšre d'optimisation n'est pas nĂ©cessairement le moment oĂč la derniĂšre tĂąche se termine. Par exemple, nous prĂ©sentons des algorithmes Ă temps polynomial pour le cas oĂč la quantitĂ© de ressources fluctue dans le temps, ou quand le coĂ»t d'exĂ©cuter une tĂąche au temps t dĂ©pend de t.Constraint programming is a powerful methodology to solve large scale and practical scheduling problems. Resource-constrained scheduling deals with temporal allocation of a variety of tasks to a set of resources, where the tasks consume a certain amount of resource during their execution. Ordinarily, a desired objective function such as the total length of a feasible schedule, called the makespan, is optimized in scheduling problems. Solving the scheduling problem is equivalent to finding out when each task starts and which resource executes it. In general, the scheduling problems are NP-Hard. Consequently, there exists no known algorithm that can solve the problem by executing a polynomial number of instructions. Nonetheless, there exist specializations for scheduling problems that are not NP-Complete. Such problems can be solved in polynomial time using dedicated algorithms. We tackle such algorithms for scheduling problems in a variety of contexts. Filtering techniques are being developed and improved over the past years in constraint-based scheduling. The prominency of filtering algorithms lies on their power to shrink the search tree by excluding values from the domains which do not yield a feasible solution. We propose improvements and present faster filtering algorithms for classical scheduling problems. Furthermore, we establish the adaptions of filtering techniques to the case that the tasks can be delayed. We also consider distinct properties of industrial scheduling problems and solve more efficiently the scheduling problems whose optimization criteria is not necessarily the makespan. For instance, we present polynomial time algorithms for the case that the amount of available resources fluctuates over time, or when the cost of executing a task at time t is dependent on t
A new solution approach to polynomial LPV system analysis and synthesis
Based on sum-of-squares (SOS) decomposition, we propose a new solution approach for polynomial LPV system analysis and control synthesis problems. Instead of solving matrix variables over a positive definite cone, the SOS approach tries to find a suitable decomposition to verify the positiveness of given polynomials. The complexity of the SOS-based numerical method is polynomial of the problem size. This approach also leads to more accurate solutions to LPV systems than most existing relaxation methods. Several examples have been used to demonstrate benefits of the SOS-based solution approach
Optimal Composition Ordering Problems for Piecewise Linear Functions
In this paper, we introduce maximum composition ordering problems. The input
is real functions and a constant
. We consider two settings: total and partial compositions. The
maximum total composition ordering problem is to compute a permutation
which maximizes , where .
The maximum partial composition ordering problem is to compute a permutation
and a nonnegative integer which maximize
.
We propose time algorithms for the maximum total and partial
composition ordering problems for monotone linear functions , which
generalize linear deterioration and shortening models for the time-dependent
scheduling problem. We also show that the maximum partial composition ordering
problem can be solved in polynomial time if is of form
for some constants , and . We
finally prove that there exists no constant-factor approximation algorithm for
the problems, even if 's are monotone, piecewise linear functions with at
most two pieces, unless P=NP.Comment: 19 pages, 4 figure
A greedy heuristic approach for the project scheduling with labour allocation problem
Responding to the growing need of generating a robust project scheduling, in this article we present a greedy algorithm to generate the project baseline schedule. The robustness achieved by integrating two dimensions of the human resources flexibilities. The first is the operatorsâ polyvalence, i.e. each operator has one or more secondary skill(s) beside his principal one, his mastering level being characterized by a factor we call âefficiencyâ. The second refers to the working time modulation, i.e. the workers have a flexible time-table that may vary on a daily or weekly basis respecting annualized working strategy. Moreover, the activity processing time is a non-increasing function of the number of workforce allocated to create it, also of their heterogynous working efficiencies. This modelling approach has led to a nonlinear optimization model with mixed variables. We present: the problem under study, the greedy algorithm used to solve it, and then results in comparison with those of the genetic algorithms
Parameterized complexity of machine scheduling: 15 open problems
Machine scheduling problems are a long-time key domain of algorithms and
complexity research. A novel approach to machine scheduling problems are
fixed-parameter algorithms. To stimulate this thriving research direction, we
propose 15 open questions in this area whose resolution we expect to lead to
the discovery of new approaches and techniques both in scheduling and
parameterized complexity theory.Comment: Version accepted to Computers & Operations Researc
Necessary and sufficient conditions for robust gain scheduling
Recent results in the design of controllers for parameter dependent systems are extended to systems with plant uncertainty. The solution takes the form of an affine matrix
inequality (AMI), which is both a necessary and sufficient condition for the posed problem to have a solution. The results in this paper may be used for the design of gain scheduled controllers for a class of uncertain systems
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