Abstract
Evolutionary algorithms with a self-adaptive step control mechanism like evolution strategies (ES) often suffer from premature fitness stagnation on constrained numerical optimization problems. When the optimum lies on the constraint boundary or even in a vertex of the feasible search space, a disadvantageous success probability results in premature step size reduction. We introduce three new constraint-handling methods for ES on constrained continuous search spaces. The death penalty step control evolution strategy (DSES) is based on the controlled reduction of a minimum step size depending on the distance to the infeasible search space. The two sexes evolution strategy (TSES) is inspired by the biological concept of sexual selection and pairing. At last, the nested angle evolution strategy (NAES) is an approach in which the angles of the correlated mutation of the inner ES are adapted by the outer ES. All methods are experimentally evaluated on four selected test problems and compared with existing penalty-based constraint-handling methods.
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Abbreviations
- EA:
-
evolutionary algorithm
- ES:
-
evolution strategy
- NLP:
-
nonlinear programming
- DSES:
-
death penalty step control evolution strategy
- TSES:
-
two sexes evolution strategy
- NAES:
-
nested angle evolution strategy
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Kramer, O., Schwefel, HP. On three new approaches to handle constraints within evolution strategies. Nat Comput 5, 363–385 (2006). https://doi.org/10.1007/s11047-006-0001-x
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DOI: https://doi.org/10.1007/s11047-006-0001-x