23 research outputs found
Beam search heuristics for the single machine scheduling problem with linear earliness and quadratic tardiness costs
In this paper, we consider the single machine scheduling problem with linear earliness and quadratic tardiness costs, and no machine idle time. We present heuristic algorithms based on the beam search technique. These algorithms include classic beam search procedures, as well as the filtered and recovering variants. Several dispatching rules are considered as evaluation functions, in order to analyse the effect of different rules on the effectiveness of the beam search algorithms. The computational results show that using better rules indeed improves the performance of the beam search heuristics. The detailed, filtered and recovering beam search procedures outperform the best existing heuristic. The best results are given by the recovering and detailed variants, which provide objective function values that are quite close to the optimum. For small to medium size instances, either of these procedures can be used. For larger instances, however, the detailed beam search algorithm requires excessive computation times, and the recovering beam search procedure then becomes the heuristic of choice.scheduling, single machine, linear earliness, quadratic tardiness, beam search, heuristics
Greedy randomized dispatching heuristics for the single machine scheduling problem with quadratic earliness and tardiness penalties
In this paper, we present greedy randomized dispatching heuristics for the single machine scheduling problem with quadratic earliness and tardiness costs, and no machine idle time. The several heuristic versions differ, on the one hand, on the strategies involved in the construction of the greedy randomized schedules. On the other hand, these versions also differ on whether they employ only a final improvement step, or perform a local search after each greedy randomized construction. The proposed heuristics were compared with existing procedures, as well as with optimum solutions for some instance sizes. The computational results show that the proposed procedures clearly outperform their underlying dispatching heuristic, and the best of these procedures provide results that are quite close to the optimum. The best of the proposed algorithms is the new recommended heuristic for large instances, as well as a suitable alternative to the best existing procedure for the larger of the middle size instances.scheduling, single machine, early/tardy, quadratic penalties, greedy randomized dispatching rules
Just-in-time preemptive single machine problem with costs of earliness/tardiness, interruption and work-in-process
This paper considers preemption and idle time are allowed in a single machine scheduling problem with just-in-time (JIT) approach. It incorporates Earliness/Tardiness (E/T) penalties, interruption penalties and holding cost of jobs which are waiting to be processed as work-in-process (WIP). Generally in non-preemptive problems, E/T penalties are a function of the completion time of the jobs. Then, we introduce a non-linear preemptive scheduling model where the earliness penalty depends on the starting time of a job. The model is liberalized by an elaborately–designed procedure to reach the optimum solution. To validate and verify the performance of proposed model, computational results are presented by solving a number of numerical examples
A new hybrid meta-heuristic algorithm for solving single machine scheduling problems
A dissertation submitted in partial ful lment of the
degree of Master of Science in Engineering (Electrical) (50/50)
in the
Faculty of Engineering and the Built Environment
Department of Electrical and Information Engineering
May 2017Numerous applications in a wide variety of elds has resulted in a rich history of research
into optimisation for scheduling. Although it is a fundamental form of the problem, the
single machine scheduling problem with two or more objectives is known to be NP-hard.
For this reason we consider the single machine problem a good test bed for solution
algorithms. While there is a plethora of research into various aspects of scheduling
problems, little has been done in evaluating the performance of the Simulated Annealing
algorithm for the fundamental problem, or using it in combination with other techniques.
Speci cally, this has not been done for minimising total weighted earliness and tardiness,
which is the optimisation objective of this work.
If we consider a mere ten jobs for scheduling, this results in over 3.6 million possible
solution schedules. It is thus of de nite practical necessity to reduce the search space in
order to nd an optimal or acceptable suboptimal solution in a shorter time, especially
when scaling up the problem size. This is of particular importance in the application
area of packet scheduling in wireless communications networks where the tolerance for
computational delays is very low. The main contribution of this work is to investigate
the hypothesis that inserting a step of pre-sampling by Markov Chain Monte Carlo
methods before running the Simulated Annealing algorithm on the pruned search space
can result in overall reduced running times.
The search space is divided into a number of sections and Metropolis-Hastings Markov
Chain Monte Carlo is performed over the sections in order to reduce the search space for
Simulated Annealing by a factor of 20 to 100. Trade-o s are found between the run time
and number of sections of the pre-sampling algorithm, and the run time of Simulated
Annealing for minimising the percentage deviation of the nal result from the optimal
solution cost. Algorithm performance is determined both by computational complexity
and the quality of the solution (i.e. the percentage deviation from the optimal). We
nd that the running time can be reduced by a factor of 4.5 to ensure a 2% deviation
from the optimal, as compared to the basic Simulated Annealing algorithm on the full
search space. More importantly, we are able to reduce the complexity of nding the
optimal from O(n:n!) for a complete search to O(nNS) for Simulated Annealing to
O(n(NMr +NS)+m) for the input variables n jobs, NS SA iterations, NM Metropolis-
Hastings iterations, r inner samples and m sections.MT 201
Common due date early
Ankara : The Department of Industrial Engineering and the Graduate School of Engineering and Science of Bilkent University, 2013.Thesis (Master's) -- Bilkent University, 2013.Includes bibliographical references leaves 91-96.This study considers a scheduling problem with position-dependent deteriorating jobs
and a maintenance activity in a single machine. Even in the absence of maintenance activity
and deterioration problem is NP-hard. A solution comprises the following: (i) positions of
jobs, (ii) the position of the maintenance activity, (iii) starting time of the first job in the
schedule. After the maintenance activity, machine will revert to its initial condition and
deterioration will start anew. The objective is to minimize the total weighted earliness and
tardiness costs. Jobs scheduled before (after) the due-date are penalized according to their
earliness (tardiness) value. Polynomial (O(n log n)) time solutions are provided for some
special cases. No polynomial solution exists for instances with tight due-dates. We propose a
mixed integer programming model and efficient algorithms for the cases where mathematical
formulation is not efficient in terms of computational time requirements. Computational
results show that the proposed algorithms perform well in terms of both solution quality and
computation time.Şirvan, FatmaM.S
Solving Weighted Number of Operation Plus Processing Time Due-Date Assignment, Weighted Scheduling and Process Planning Integration Problem Using Genetic and Simulated Annealing Search Methods
Traditionally, the three important manufacturing functions, which are process planning, scheduling and due-date assignment, are performed separately and sequentially. For couple of decades, hundreds of studies are done on integrated process planning and scheduling problems and numerous researches are performed on scheduling with due date assignment problem, but unfortunately the integration of these three important functions are not adequately addressed. Here, the integration of these three important functions is studied by using genetic, random-genetic hybrid, simulated annealing, random-simulated annealing hybrid and random search techniques. As well, the importance of the integration of these three functions and the power of meta-heuristics and of hybrid heuristics are studied