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Project Title:

"Evolution Strategies for Constrained Optimization"

FWF Project Number: P29651-N32

Project Summary:

This research project was aiming at the analysis and design of algorithms for optimization problems in real-valued search spaces as they occur in many applications in engineering, natural sciences, and economy. While there are various approaches to tackle such optimization problems, the use of so-called Evolution Strategies (ESs) has proven itself as an alternative especially well-suited for difficult non-linear problems. The ES algorithms are gleaned from nature mimicking the process of Darwinian evolution by improving initial candidate solutions gradually - as in nature - by applying small mutations, recombination of solutions and selection, thus, getting better and better solutions. However, up until now, the incorporation of restrictions, so-called constraints, as they are often prevalent in real-world applications, has only been done in an ad hoc and non-systematic manner.

This project has significantly changed the situation for Evolution Strategies. Being based on a thorough theoretically grounded analysis, ESs have been developed that are able to handle equality as well as inequality constraints. Unlike most of other evolutionary algorithms, the methods developed are also able to realize an inner-point behavior. That is, the solutions generated during the evolutionary improvement process are always valid (i.e. feasible). This is especially desirable in simulation-based optimization problems where leaving the domain of admissible parameters often results in abnormal terminations of the simulation software. This is also an issue in financial applications where balance equations must be exactly fulfilled.

Besides the development of ES algorithms that are simpler, on par with, and are often better performing then the state-of-the-art, also the border of the theory of these probabilistic algorithms has been pushed forward. This is important because understanding these algorithms, which are difficult to be analyzed, is a prerequisite for developing even better performing algorithms.

 

Publications

1.  Hellwig, M. and Beyer, H.-G.: A Matrix Adaptation Evolution Strategy for Constrained Real-Parameter Optimization in CEC'18: IEEE Congress on Evolutionary Computation; pp. 749-756; 2018; DOI: 10.1109/CEC.2018.8477950; [pdf]

2.  Spettel, P. and Beyer, H.-G.: A Simple Approach for Constrained Optimization - An Evolution Strategy that Evolves Rays in CEC'18: IEEE Congress on Evolutionary Computation; pp. 335-342; 2018; DOI: 10.1109/CEC.2018.8477753; [pdf]

3.  Hellwig, M. and Beyer, H.-G.: A Linear Constrained Optimization Benchmark for Probabilistic Search Algorithms: The Rotated Klee-Minty Problem in TPNC2018: 7th International Conference on the Theory and Practice of Natural Computing; pp. 139-151; 2018; DOI: 10.1007/978-3-030-04070-3_11; [pdf]

4.  Spettel, P. and Beyer, H.-G.: Analysis of the (1, lambda)-sigma-Self-Adaptation Evolution Strategy with Repair by Projection Applied to a Conically Constrained Problem in Journal of Theoretical Computer Science; pp. 30-45; 2018; DOI: 10.1016/j.tcs.2018.10.036; [pdf]

5.  Spettel, P. and Beyer, H.-G. and Hellwig, M.: A Covariance Matrix Self-Adaptation Evolution Strategy for Linear Constrained Optimization in IEEE Transactions on Evolutionary Computation 23(3); pp. 514-524; 2019; DOI: 10.1109/TEVC.2018.2871944; [pdf]

6.  Hellwig, M. and Beyer, H.-G.: Benchmarking evolutionary algorithms for single objective real-valued constrained optimization - A critical review in Swarm and Evolutionary Computation 44; pp. 927-944; 2019; DOI: 10.1016/j.swevo.2018.10.002; [pdf]

7.  Spettel, P. and Beyer, H.-G.: A multi-recombinative active matrix adaptation evolution strategy for constrained optimization in Soft Computing 23(16); pp. 6847-6869; 2019; DOI: 10.1007/s00500-018-03736-z; [pdf]

8.  Spettel, P. and Beyer, H.-G.: Matrix Adaptation Evolution Strategies for Optimization Under Nonlinear Equality Constraints in Swarm and Evolutionary Computation; accepted; pp. ??-??; 2020; DOI: 10.1016/j.swevo.2020; [pdf]

9.  Spettel, P. and Beyer, H.-G.: Analysis of the (mu/muI, lambda)-sigma-Self-Adaptation Evolution Strategy with Repair by Projection Applied to a Conically Constrained Problem in IEEE Transactions on Evolutionary Computation ??(?); pp. ??-??; 2020; DOI: 10.1109/TEVC.2019.2930316; [pdf]

10.  Hellwig, M. and Beyer, H.-G.: Analysis of a Meta-ES on a Conically Constrained Problem in GECCO'19: Proceedings of the Genetic and Evolutionary Computation Conference; pp. 673-681; 2019; DOI: 10.1145/3321707.3321824; [pdf]

11.  Hellwig, M. and Spettel, P. and Beyer, H.-G.: Comparison of Contemporary Evolutionary Algorithms on the Rotated Klee-Minty Problem in GECCO'19: Proceedings of the Genetic and Evolutionary Computation Conference; pp. 673-681; 2019; DOI: 10.1145/3319619.3326805; [pdf]

12.  Spettel, P. and Beyer, H.-G.: Analysis of the (mu/muI,lambda)-CSA-ES with Repair by Projection Applied to a Conically Constrained Problem in Evolutionary Computation ??(?); pp. ??-??; 2019; DOI: 10.1162/EVCO_a_00261; [pdf]

13.  Spettel, P. and Beyer, H.-G. and Hellwig, M.: Steady State Analysis of a Multi-Recombinative Meta-ES on a Conically Constrained Problem with Comparison to sigmaSA and CSA in Foundations of Genetic Algorithms XV, pp. 43-57, 2019; pp. ??-??; 2019; DOI: 10.1145/3299904.3340306; [pdf]



last change: 03.02.2020