Computing Longest Common Subsequences with the B-Cell Algorithm

Jansen, Thomas; Zarges, Christine

doi:10.1007/978-3-642-33757-4_9

Cited by 17 publications

(15 citation statements)

References 29 publications

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“…Such studies have been extensively performed for the contiguous somatic hypermutation operator employed by the B-Cell algorithm [8,9], the inversely proportional hypermutation operator of Clonalg [10,11] and the ageing operator used by Opt-IA [12,13,14]. These studies formed a foundational basis which allowed the subsequent analysis of the complete B-Cell algorithm as used in practice for standard combinatorial optimisation [15,16].…”

Section: Introductionmentioning

confidence: 99%

When hypermutations and ageing enable artificial immune systems to outperform evolutionary algorithms

Corus

Oliveto

Yazdani

2020

Theoretical Computer Science

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We present a time complexity analysis of the Opt-IA artificial immune system (AIS). We first highlight the power and limitations of its distinguishing operators (i.e., hypermutations with mutation potential and ageing) by analysing them in isolation. Recent work has shown that ageing combined with local mutations can help escape local optima on a dynamic optimisation benchmark function. We generalise this result by rigorously proving that, compared to evolutionary algorithms (EAs), ageing leads to impressive speed-ups on the standard Cliff d benchmark function both when using local and global mutations. Unless the stop at first constructive mutation (FCM) mechanism is applied, we show that hypermutations require exponential expected runtime to optimise any function with a polynomial number of optima. If instead FCM is used, the expected runtime is at most a linear factor larger than the upper bound achieved for any random local search algorithm using the artificial fitness levels method. Nevertheless, we prove that algorithms using hypermutations can be considerably faster than EAs at escaping local optima. An analysis of the complete Opt-IA reveals that it is efficient on the previously considered functions and highlights problems where the use of the full algorithm is crucial. We complete the picture by presenting a class of functions for which Opt-IA fails with overwhelming probability while standard EAs are efficient.

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Section: Introductionmentioning

confidence: 99%

When hypermutations and ageing enable artificial immune systems to outperform evolutionary algorithms

Corus

Oliveto

Yazdani

2020

Theoretical Computer Science

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“…One such example is the somatic contiguous hypermutation (CHM) operator from the B-cell algorithm (BCA) [15], where large contiguous blocks of a bit string are flipped simultaneously. Previous theoretical work on comparing SBM and CHM has contributed to the understanding of their benefits and drawbacks in the context of its runtime on different problems [8,10,11], the expected solution quality after a pre-defined number of steps [14] and in dynamic environments [12]. It is easy to see that hardest functions for CHM with respect to expected optimisation times are those where the algorithm gets trapped with positive probability such that the optimisation time is not finite, e. g., if there exists a second best search point for which all direct mutations to the optimum involve noncontiguous bits [10].…”

Section: Introductionmentioning

confidence: 99%

On Easiest Functions for Somatic Contiguous Hypermutations And Standard Bit Mutations

Corus

Jansen

et al. 2015

Proceedings of the 2015 Annual Conference on Genetic and Evolutionary Computation

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Understanding which function classes are easy and which are hard for a given algorithm is a fundamental question for the analysis and design of bio-inspired search heuristics. A natural starting point is to consider the easiest and hardest functions for an algorithm. For the (1+1) EA using standard bit mutation it is well known that OneMax is an easiest function with unique optimum while Trap is a hardest.In this paper we extend the analysis of easiest function classes to the contiguous somatic hypermutation (CHM) operator used in artificial immune systems. We define a function MinBlocks and prove that it is an easiest function for the (1+1) EA using CHM, presenting both a runtime and a fixed budget analysis. Since MinBlocks is, up to a factor of 2, a hardest function for standard bit mutations, we consider the effects of combining both operators into a hybrid algorithm. We show that an easiest function for the hybrid algorithm is not just a trivial weighted combination of the respective easiest functions for each operator. Nevertheless, by combining the advantages of both operators, the hybrid algorithm has optimal asymptotic performance on both OneMax and MinBlocks.

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“…All these works considered the hypermutation operators within a very simple algorithmic framework on simple example problems to understand the power and limitations of the operators. Concerning CSM, the work was a basis which enabled the analysis of the full BCA for standard combinatorial optimisation problems such as vertex cover [10] and the longest common subsequence problem [14].…”

Section: Introductionmentioning

confidence: 99%

On the runtime analysis of stochastic ageing mechanisms

Oliveto

Sudholt

2014

Proceedings of the 2014 Annual Conference on Genetic and Evolutionary Computation

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Ageing operators are applied in the field of artificial immune systems (AIS) to increase the diversity of the population during the optimization process. Previous theoretical analyses have shown how static ageing operators can successfully escape local optima by implicitly performing a restart of the algorithm. However, showing naturally that ageing in an AIS is more effective than a conceptually simpler restart strategy has proved to be a hard task. We present a rigorous analysis of stochastic ageing mechanisms and show that superior performance compared to just simple restarts can be achieved. Since standard stochastic pure ageing is only effective for small population sizes, we present a hybrid pure ageing operator that achieves the same performance independent of the population size. For a benchmark function used in dynamic optimisation we rigorously prove that hybrid pure ageing allows to escape local optima beyond restarts while static pure ageing is inefficient. The results also apply to the non-dynamic setting. An analytical general framework for the analysis of standard stochastic pure ageing is presented along the way.

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Computing Longest Common Subsequences with the B-Cell Algorithm

Cited by 17 publications

References 29 publications

When hypermutations and ageing enable artificial immune systems to outperform evolutionary algorithms

When hypermutations and ageing enable artificial immune systems to outperform evolutionary algorithms

On Easiest Functions for Somatic Contiguous Hypermutations And Standard Bit Mutations

On the runtime analysis of stochastic ageing mechanisms

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