
Project Title: "Evolution Strategies for Constrained Optimization" FWF Project Number: P29651N32
Project
Summary:
This research project was aiming at the analysis and design of algorithms
for optimization problems in realvalued 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
socalled Evolution Strategies (ESs) has proven itself as an alternative
especially wellsuited for difficult nonlinear 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, socalled constraints, as they are often
prevalent in realworld applications, has only been done in an ad hoc
and nonsystematic 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 innerpoint behavior.
That is, the solutions generated during the evolutionary improvement
process are always valid (i.e. feasible). This is especially desirable
in simulationbased 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 stateoftheart, 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 RealParameter Optimization in CEC'18:
IEEE Congress on Evolutionary Computation; pp.
749756; 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.
335342; 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 KleeMinty Problem in TPNC2018:
7th International Conference on the Theory and
Practice of Natural Computing; pp.
139151; 2018; DOI: 10.1007/9783030040703_11; [pdf]
4. Spettel, P. and Beyer, H.G.: Analysis of the
(1, lambda)sigmaSelfAdaptation Evolution
Strategy with Repair by Projection Applied to a
Conically Constrained Problem in Journal of Theoretical
Computer Science; pp.
3045; 2018; DOI: 10.1016/j.tcs.2018.10.036; [pdf]
5. Spettel, P. and Beyer, H.G. and Hellwig, M.: A Covariance Matrix SelfAdaptation Evolution
Strategy for Linear Constrained Optimization in IEEE Transactions on Evolutionary Computation 23(3); pp.
514524; 2019; DOI: 10.1109/TEVC.2018.2871944; [pdf]
6. Hellwig, M. and Beyer, H.G.: Benchmarking evolutionary algorithms for single
objective realvalued constrained optimization  A critical review in Swarm and Evolutionary Computation 44; pp.
927944; 2019; DOI: 10.1016/j.swevo.2018.10.002; [pdf]
7. Spettel, P. and Beyer, H.G.: A multirecombinative active matrix adaptation
evolution strategy for constrained optimization in Soft Computing 23(16); pp.
68476869; 2019; DOI: 10.1007/s0050001803736z; [pdf]
8. Spettel, P. and Beyer, H.G.: Matrix Adaptation Evolution Strategies for
Optimization Under Nonlinear Equality Constraints in Swarm and Evolutionary Computation; Vol. 54, May 2020; DOI: 10.1016/j.swevo.2020; [pdf]
9. Spettel, P. and Beyer, H.G.: Analysis of the
(mu/muI, lambda)sigmaSelfAdaptation
Evolution Strategy with Repair by Projection
Applied to a Conically Constrained Problem in IEEE Transactions on Evolutionary Computation 24(3); pp.
593602; 2020; DOI: 10.1109/TEVC.2019.2930316; [pdf]
10. Hellwig, M. and Beyer, H.G.: Analysis of a MetaES on a Conically Constrained Problem
in GECCO'19: Proceedings of the Genetic and Evolutionary Computation Conference;
pp. 673681; 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 KleeMinty Problem
in GECCO'19: Proceedings of the Genetic and Evolutionary Computation Conference;
pp. 673681; 2019; DOI: 10.1145/3319619.3326805; [pdf]
12. Spettel, P. and Beyer, H.G.: Analysis of the (mu/muI,lambda)CSAES with
Repair by Projection Applied to a Conically
Constrained Problem
in Evolutionary Computation 28(3);
pp. 463488; 2020; DOI: 10.1162/EVCO_a_00261; [pdf]
13. Spettel, P. and Beyer, H.G. and Hellwig, M.: Steady State Analysis of a MultiRecombinative
MetaES on a Conically Constrained Problem with
Comparison to sigmaSA and CSA
in Foundations of Genetic Algorithms XV, pp. 4357, 2019;
DOI: 10.1145/3299904.3340306; [pdf]
14. Hellwig, M. and Beyer, H.G.: A Modified Matrix Adaptation Evolution Strategy
with Restarts for Constrained RealWorld Problems in CEC'20:
IEEE Congress on Evolutionary Computation; pp.
18; 2020; DOI: 10.1109/CEC48606.2020.9185566; [pdf]
15. Spettel, P. and Beyer, H.G.: A Matrix Adaptation Evolution Strategy for
Optimization on General Quadratic Manifolds
in GECCO'21: Proceedings of the Genetic and Evolutionary Computation Conference;
pp. 537545; 2021; DOI: 10.1145/3449639.3459282; [pdf]
16. Spettel, P. and Beyer, H.G.: On the Design of a Matrix Adaptation Evolution
Strategy for Optimization on General Quadratic Manifolds
in ACM Transactions on Evolutionary Learning and
Optimization (TELO) ?(?);
pp. ??????; 2022; DOI: 10.1145/3551394
17. Hellwig, M. and Beyer, H.G.: Benchmarking epsilonMAgES and
BPepsilonMAgES on the bbobconstrained
Testbed
in GECCO'22: Proceedings of the Genetic and Evolutionary Computation Conference;
pp. 17171724; 2022; DOI: 10.1145/3520304.3534010; [pdf]
