2,818 research outputs found
Optimizing egalitarian performance in the side-effects model of colocation for data center resource management
In data centers, up to dozens of tasks are colocated on a single physical
machine. Machines are used more efficiently, but tasks' performance
deteriorates, as colocated tasks compete for shared resources. As tasks are
heterogeneous, the resulting performance dependencies are complex. In our
previous work [18] we proposed a new combinatorial optimization model that uses
two parameters of a task - its size and its type - to characterize how a task
influences the performance of other tasks allocated to the same machine.
In this paper, we study the egalitarian optimization goal: maximizing the
worst-off performance. This problem generalizes the classic makespan
minimization on multiple processors (P||Cmax). We prove that
polynomially-solvable variants of multiprocessor scheduling are NP-hard and
hard to approximate when the number of types is not constant. For a constant
number of types, we propose a PTAS, a fast approximation algorithm, and a
series of heuristics. We simulate the algorithms on instances derived from a
trace of one of Google clusters. Algorithms aware of jobs' types lead to better
performance compared with algorithms solving P||Cmax.
The notion of type enables us to model degeneration of performance caused by
using standard combinatorial optimization methods. Types add a layer of
additional complexity. However, our results - approximation algorithms and good
average-case performance - show that types can be handled efficiently.Comment: Author's version of a paper published in Euro-Par 2017 Proceedings,
extends the published paper with addtional results and proof
Scheduling Bidirectional Traffic on a Path
We study the fundamental problem of scheduling bidirectional traffic along a
path composed of multiple segments. The main feature of the problem is that
jobs traveling in the same direction can be scheduled in quick succession on a
segment, while jobs in opposing directions cannot cross a segment at the same
time. We show that this tradeoff makes the problem significantly harder than
the related flow shop problem, by proving that it is NP-hard even for identical
jobs. We complement this result with a PTAS for a single segment and
non-identical jobs. If we allow some pairs of jobs traveling in different
directions to cross a segment concurrently, the problem becomes APX-hard even
on a single segment and with identical jobs. We give polynomial algorithms for
the setting with restricted compatibilities between jobs on a single and any
constant number of segments, respectively
Meta-RaPS Algorithm for the Aerial Refueling Scheduling Problem
The Aerial Refueling Scheduling Problem (ARSP) can be defined as determining the refueling completion times for each fighter aircraft (job) on multiple tankers (machines). ARSP assumes that jobs have different release times and due dates, The total weighted tardiness is used to evaluate schedule's quality. Therefore, ARSP can be modeled as a parallel machine scheduling with release limes and due dates to minimize the total weighted tardiness. Since ARSP is NP-hard, it will be more appropriate to develop a ppro~imate or heuristic algorithm to obtain solutions in reasonable computation limes. In this paper, Meta-Raps-ATC algorithm is implemented to create high quality solutions. Meta-RaPS (Meta-heuristic for Randomized Priority Search) is a recent and promising meta heuristic that is applied by introducing randomness to a construction heuristic. The Apparent Tardiness Rule (ATC), which is a good rule for scheduling problems with tardiness objective, is used to construct initial solutions which are improved by an exchanging operation. Results are presented for generated instances
A DECOMPOSITION-BASED HEURISTIC ALGORITHM FOR PARALLEL BATCH PROCESSING PROBLEM WITH TIME WINDOW CONSTRAINT
This study considers a parallel batch processing problem to minimize the makespan under constraints of arbitrary lot sizes, start time window and incompatible families. We first formulate the problem with a mixed-integer programming model. Due to the NP-hardness of the problem, we develop a decomposition-based heuristic to obtain a near-optimal solution for large-scale problems when computational time is a concern. A two-dimensional saving function is introduced to quantify the value of time and capacity space wasted. Computational experiments show that the proposed heuristic performs well and can deal with large-scale problems efficiently within a reasonable computational time. For the small-size problems, the percentage of achieving optimal solutions by the DH is 94.17%, which indicates that the proposed heuristic is very good in solving small-size problems. For large-scale problems, our proposed heuristic outperforms an existing heuristic from the literature in terms of solution quality
Optimization Models and Approximate Algorithms for the Aerial Refueling Scheduling and Rescheduling Problems
The Aerial Refueling Scheduling Problem (ARSP) can be defined as determining the refueling completion times for fighter aircrafts (jobs) on multiple tankers (machines) to minimize the total weighted tardiness. ARSP can be modeled as a parallel machine scheduling with release times and due date-to-deadline window. ARSP assumes that the jobs have different release times, due dates, and due date-to-deadline windows between the refueling due date and a deadline to return without refueling. The Aerial Refueling Rescheduling Problem (ARRP), on the other hand, can be defined as updating the existing AR schedule after being disrupted by job related events including the arrival of new aircrafts, departure of an existing aircrafts, and changes in aircraft priorities. ARRP is formulated as a multiobjective optimization problem by minimizing the total weighted tardiness (schedule quality) and schedule instability. Both ARSP and ARRP are formulated as mixed integer programming models. The objective function in ARSP is a piecewise tardiness cost that takes into account due date-to-deadline windows and job priorities. Since ARSP is NP-hard, four approximate algorithms are proposed to obtain solutions in reasonable computational times, namely (1) apparent piecewise tardiness cost with release time rule (APTCR), (2) simulated annealing starting from random solution (SArandom ), (3) SA improving the initial solution constructed by APTCR (SAAPTCR), and (4) Metaheuristic for Randomized Priority Search (MetaRaPS). Additionally, five regeneration and partial repair algorithms (MetaRE, BestINSERT, SEPRE, LSHIFT, and SHUFFLE) were developed for ARRP to update instantly the current schedule at the disruption time. The proposed heuristic algorithms are tested in terms of solution quality and CPU time through computational experiments with randomly generated data to represent AR operations and disruptions. Effectiveness of the scheduling and rescheduling algorithms are compared to optimal solutions for problems with up to 12 jobs and to each other for larger problems with up to 60 jobs. The results show that, APTCR is more likely to outperform SArandom especially when the problem size increases, although it has significantly worse performance than SA in terms of deviation from optimal solution for small size problems. Moreover CPU time performance of APTCR is significantly better than SA in both cases. MetaRaPS is more likely to outperform SAAPTCR in terms of average error from optimal solutions for both small and large size problems. Results for small size problems show that MetaRaPS algorithm is more robust compared to SAAPTCR. However, CPU time performance of SA is significantly better than MetaRaPS in both cases. ARRP experiments were conducted with various values of objective weighting factor for extended analysis. In the job arrival case, MetaRE and BestINSERT have significantly performed better than SEPRE in terms of average relative error for small size problems. In the case of job priority disruption, there is no significant difference between MetaRE, BestINSERT, and SHUFFLE algorithms. MetaRE has significantly performed better than LSHIFT to repair job departure disruptions and significantly superior to the BestINSERT algorithm in terms of both relative error and computational time for large size problems
Total Completion Time Minimization for Scheduling with Incompatibility Cliques
This paper considers parallel machine scheduling with incompatibilities
between jobs. The jobs form a graph and no two jobs connected by an edge are
allowed to be assigned to the same machine. In particular, we study the case
where the graph is a collection of disjoint cliques. Scheduling with
incompatibilities between jobs represents a well-established line of research
in scheduling theory and the case of disjoint cliques has received increasing
attention in recent years. While the research up to this point has been focused
on the makespan objective, we broaden the scope and study the classical total
completion time criterion. In the setting without incompatibilities, this
objective is well known to admit polynomial time algorithms even for unrelated
machines via matching techniques. We show that the introduction of
incompatibility cliques results in a richer, more interesting picture.
Scheduling on identical machines remains solvable in polynomial time, while
scheduling on unrelated machines becomes APX-hard. Furthermore, we study the
problem under the paradigm of fixed-parameter tractable algorithms (FPT). In
particular, we consider a problem variant with assignment restrictions for the
cliques rather than the jobs. We prove that it is NP-hard and can be solved in
FPT time with respect to the number of cliques. Moreover, we show that the
problem on unrelated machines can be solved in FPT time for reasonable
parameters, e.g., the parameter pair: number of machines and maximum processing
time. The latter result is a natural extension of known results for the case
without incompatibilities and can even be extended to the case of total
weighted completion time. All of the FPT results make use of n-fold Integer
Programs that recently have received great attention by proving their
usefulness for scheduling problems
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