High-Quality Algorithms for Makespan Minimization

  • Forschungsthema:Makespan Minimization, Parallel Algorithms
  • Typ:Bachelor-/Masterarbeit
  • Betreuung:

    Nikolai Maas


Job scheduling problems arise in various application areas, for example manufac-
turing systems and data centers. The makespan minimization problem on identical
parallel machines (also denoted by P||C_max ) asks for a distribution of n jobs to
m machines. Each job has a processing time and the goal is to minimize the
completion time of the latest job.
Makespan minimization is a classical NP-complete problem and there are several
known approximation algorithms, such as the Longest Processing Time (LPT)
algorithm. For small instances, techniques such as ILP or SAT-encoding allow to
find an optimal solution. In addition, makespan minimization permits efficient appro-
ximation schemes (EPTAS). However, despite recent advances in the practicability
of PTAS approaches it is still expensive to run a PTAS with higher precision than
simple approximation algorithms. In practice, the results might be worse for some
instances while requiring a high running time. Thus, the engineering of practical
high-quality algorithms is still an open question.
The goal of this thesis is to combine ideas from approximation algorithms, PTAS
and local search heuristics to achieve high quality in practice (note that the focus
is not on worst case guarantees). A promising approach is to use a portfolio of
different solvers that can run in parallel and exchange information about machine
configurations with small span. The algorithm then maintains a set of configurations
that can be recombined to find better solutions. This allows to explore the solution
space heuristically, hopefully resulting in significantly better running times than
PTAS algorithms. In addition to the generation, selection and combination of machi-
ne configurations, there are multiple related areas that could be explored. These
include heuristics for improving known solutions, reducing the size of the search
space and solving a small set of machines with high quality. The results should
be evaluated on a comprehensive benchmark set and compared with competing


  • Interest in optimization algorithms and parallel algorithms
  • Good programming knowledge in either (modern) C++ or Rust
  • Willingness to do a detailed experimental evaluation