4 research outputs found
Evolutionary Algorithms with Self-adjusting Asymmetric Mutation
Evolutionary Algorithms (EAs) and other randomized search heuristics are
often considered as unbiased algorithms that are invariant with respect to
different transformations of the underlying search space. However, if a certain
amount of domain knowledge is available the use of biased search operators in
EAs becomes viable. We consider a simple (1+1) EA for binary search spaces and
analyze an asymmetric mutation operator that can treat zero- and one-bits
differently. This operator extends previous work by Jansen and Sudholt (ECJ
18(1), 2010) by allowing the operator asymmetry to vary according to the
success rate of the algorithm. Using a self-adjusting scheme that learns an
appropriate degree of asymmetry, we show improved runtime results on the class
of functions OneMax describing the number of matching bits with a fixed
target .Comment: 16 pages. An extended abstract of this paper will be published in the
proceedings of PPSN 202
Artificial immune systems can find arbitrarily good approximations for the NP-hard number partitioning problem
Typical artificial immune system (AIS) operators such as hypermutations with mutation potential and ageing allow to efficiently overcome local optima from which evolutionary algorithms (EAs) struggle to escape. Such behaviour has been shown for artificial example functions constructed especially to show difficulties that EAs may encounter during the optimisation process. However, no evidence is available indicating that these two operators have similar behaviour also in more realistic problems. In this paper we perform an analysis for the standard NP-hard Partition problem from combinatorial optimisation and rigorously show that hypermutations and ageing allow AISs to efficiently escape from local optima
where standard EAs require exponential time. As a result we prove that while EAs and random local search (RLS) may get trapped on 4/3 approximations, AISs find arbitrarily
good approximate solutions of ratio (1+) within n(−(2/)−1)(1 − )−2e322/ + 2n322/ + 2n3 function evaluations in expectation. This expectation is polynomial in the problem size and exponential only in 1/
Artificial Immune Systems can find arbitrarily good approximations for the NP-Hard partition problem
Typical Artificial Immune System (AIS) operators such as hypermutations with mutation potential and ageing allow to efficiently overcome local optima from which Evolutionary Algorithms (EAs) struggle to escape. Such behaviour has been shown for artificial example functions such as Jump, Cliff or Trap constructed especially to show difficulties that EAs may encounter during the optimisation process. However, no evidence is available indicating that similar effects may also occur in more realistic problems. In this paper we perform an analysis for the standard NP-Hard Partition problem from combinatorial optimisation and rigorously show that hypermutations and ageing allow AISs to efficiently escape from local optima where standard EAs require exponential time. As a result we prove that while EAs and Random Local Search may get trapped on 4/3 approximations, AISs find arbitrarily good approximate solutions of ratio ( 1+ϵ ) for any constant ϵ within a time that is polynomial in the problem size and exponential only in 1/ϵ