Michael Hellwig

David Hutter, Thomas Steinberger, Michael Hellwig

This paper addresses the Flexible Job Shop Scheduling Problem and its extension with Worker Flexibility, which integrates workforce assignment into machine-operation scheduling. Diverse solvers have been proposed across multiple optimization domains including Mathematical Programming, Constraint Programming, and Simulation-Based Optimization, or Simulation-based Optimization. These are often tailored to narrow use cases and validated on limited test problem sets, hindering cross-domain comparison. To overcome this, a comprehensive benchmarking environment built on 402 standardized Flexible Job Shop Scheduling Problem instances is introduced and systematically extended to include worker flexibility. This creates a hitherto unique collection of ready-to-use worker flexibility instances. The benchmark suite features several metrics for algorithm performance assessment, the visualization of algorithmic results, as well as state-of-the-art baseline results. This enables rigorous, reproducible, and comparable performance analysis between solvers and scheduling problem subdomains. Through the simulation-based integration of uncertainties in processing times as well as resource availabilities, the environment supports the development and evaluation of robust optimization strategies. The present work lays a foundation for targeted algorithm development and consistent performance evaluation in production scheduling research.

Michael Hellwig, Hans-Georg Beyer

The development, assessment, and comparison of randomized search algorithms heavily rely on benchmarking. Regarding the domain of constrained optimization, the number of currently available benchmark environments bears no relation to the number of distinct problem features. The present paper advances a proposal of a scalable linear constrained optimization problem that is suitable for benchmarking Evolutionary Algorithms. By comparing two recent EA variants, the linear benchmarking environment is demonstrated.

Patrick Spettel, Hans-Georg Beyer, Michael Hellwig

This paper addresses the development of a covariance matrix self-adaptation evolution strategy (CMSA-ES) for solving optimization problems with linear constraints. The proposed algorithm is referred to as Linear Constraint CMSA-ES (lcCMSA-ES). It uses a specially built mutation operator together with repair by projection to satisfy the constraints. The lcCMSA-ES evolves itself on a linear manifold defined by the constraints. The objective function is only evaluated at feasible search points (interior point method). This is a property often required in application domains such as simulation optimization and finite element methods. The algorithm is tested on a variety of different test problems revealing considerable results.

Michael Hellwig, Hans-Georg Beyer

Benchmarking plays an important role in the development of novel search algorithms as well as for the assessment and comparison of contemporary algorithmic ideas. This paper presents common principles that need to be taken into account when considering benchmarking problems for constrained optimization. Current benchmark environments for testing Evolutionary Algorithms are reviewed in the light of these principles. Along with this line, the reader is provided with an overview of the available problem domains in the field of constrained benchmarking. Hence, the review supports algorithms developers with information about the merits and demerits of the available frameworks.