Analyzing different variants of immune inspired somatic contiguous hypermutations

Abstract

Jansen, T., Zarges, C. (2011). Analyzing different variants of immune inspired somatic contiguous hypermutations. Theoretical Computer Science, 412 (6), 517-533.Artificial immune systems can be applied to a variety of very different tasks including function optimization. There are even artificial immune systems tailored specifically for this task. In spite of their successful application there is little knowledge and hardly any theoretical investigation about how and why they perform well. Here rigorous analyses for a specific class of mutation operators introduced for function optimization called somatic contiguous hypermutation is presented. Different concrete instantiations of this operator are considered and shown to behave quite differently in general. While there are serious limitations to the performance of this type of operator even for simple optimization tasks it is proven that for some types of optimization problems it performs much better than standard bit mutations most often used in evolutionary algorithms. (C) 2010 Elsevier B.V. All rights reserved.Peer reviewe

On Easiest Functions for Mutation Operators in Bio-Inspired Optimisation

“…As done in previous work (see, e. g., [17]), we only consider the extreme case here and set r = 1. CHM is formally defined in Algorithm 3.…”

“…It is well known that CHM (Algorithm 3) can be trapped in local optima when the parameter r is set to r = 1 [2] (see [17, p. 521] for a concrete example demonstrating this effect). Setting r = 1, however, reveals properties of the hypermutation operator in the clearest way and this is the reason we stick to this choice (compare [17]). This implies that analysing hardest functions for (1+1) CHM does not make much sense because it is easy to find functions where there is a positive probability that the algorithm gets stuck in a local optimum so that, consequently, the expected optimisation time is not finite.…”

“…One such example is the somatic contiguous hypermutation (CHM) operator from the B-cell algorithm (BCA) [23], 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 [14,17,18], the expected solution quality after a pre-defined number of steps [21], and in dynamic environments [22]. 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 non-contiguous bits [17].…”

A Multi-Learning Immune Algorithm for Numerical Optimization

“…1. From this figure, it is clear that the quality of mutated populations is determined by the capacity of learning operators [31], [40], thus directly influencing the performance of the algorithm. Many researchers have designed and investigated an amount of learning operators, some of which are widely used in evolutionary algorithms [32], [33], while others are specifically designed based on the mechanisms in biological immune systems [34], [36], [41].…”

Enhancing the learning capacity of immunological algorithms: a comprehensive study of learning operators

“…Compared with other bio-inspired algorithms, such as the well-known evolutionary computation (Yao and Xu, 2006), IAs still greatly suffer from the issues of stagnation and slow convergence. The reason seems to be that the learning capacity (involving hypermutation and receptor editing) has not been fully exploited, i.e., no sophisticated learning operator can be found in the literature (Jansen and Zarges, 2011). Based on the above consideration, we review and analyze the existing learning operators commonly used in IAs, and propose a new search direction based learning operator (L sd ) to encourage the antibodies to utilize the information of its surrounding antibodies, by means of moving the antibody toward the nearby antibodies with higher affinities and meanwhile away from the antibody with lower affinities.…”