Abstract
We propose an evolutionary approach to constrained optimization where the objective function is considered a black box, but the constraint functions are assumed to be known. The approach can be considered a stochastic active-set method. It labels constraints as either active or inactive and projects candidate solutions onto the subspace of the feasible region that is implied by rendering active inequality constraints equalities. We implement the approach in a \((1+1)\)-ES and evaluate its performance using a commonly used set of test problems.
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Notes
- 1.
See Hansen et al. [7] for an introduction to evolution strategy terminology.
- 2.
The ConstraintTolerance parameter of fmincon is set to its default value of \(10^{-6}\) for the runs with target accuracy \(\epsilon =10^{-4}\). For target accuracy \(\epsilon =10^{-8}\) we used ConstraintTolerance \(10^{-9} \) instead as some runs for problem g03 terminate unsuccessfully if the default accuracy is used.
- 3.
Multimodal problems and those with equality constraints were not considered in that paper, leaving only problems g06, g07, g09, and g10.
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This research was supported by the Natural Sciences and Engineering Research Council of Canada (NSERC).
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Arnold, D.V. (2016). An Active-Set Evolution Strategy for Optimization with Known Constraints. In: Handl, J., Hart, E., Lewis, P., López-Ibáñez, M., Ochoa, G., Paechter, B. (eds) Parallel Problem Solving from Nature – PPSN XIV. PPSN 2016. Lecture Notes in Computer Science(), vol 9921. Springer, Cham. https://doi.org/10.1007/978-3-319-45823-6_18
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