Self-adaptation of mutation operator and probability for permutation representations in genetic algorithms

The choice of mutation rate is a vital factor in the success of any genetic algorithm (GA), and for permutation representations this is compounded by the availability of several alternative mutation operators. It is now well understood that there is no one "optimal choice"; rather, the situation changes per problem instance and during evolution. This paper examines whether this choice can be left to the processes of evolution via selfadaptation, thus removing this nontrivial task fromtheGAuser and reducing the risk of poor performance arising from (inadvertent) inappropriate decisions. Self-adaptation has been proven successful for mutation step sizes in the continuous domain, and for the probability of applying bitwise mutation to binary encodings; here we examine whether this can translate to the choice and parameterisation of mutation operators for permutation encodings. We examine one method for adapting the choice of operator during runtime, and several different methods for adapting the rate at which the chosen operator is applied. In order to evaluate these algorithms, we have used a range of benchmark TSP problems. Of course this paper is not intended to present a state of the art in TSP solvers; rather, we use this well known problem as typical of many that require a permutation encoding, where our results indicate that self-adaptation can prove beneficial. The results show that GAs using appropriate methods to self-adapt their mutation operator and mutation rate find solutions of comparable or lower cost than algorithms with "static" operators, even when the latter have been extensively pretuned. Although the adaptive GAs tend to need longer to run, we show that is a price well worth paying as the time spent finding the optimal mutation operator and rate for the nonadaptive versions can be considerable. Finally, we evaluate the sensitivity of the self-adaptive methods to changes in the implementation, and to the choice of other genetic operators and population models. The results show that the methods presented are robust, in the sense that the performance benefits can be obtained in a wide range of host algorithms. © 2010 by the Massachusetts Institute of Technology

Estimating meme fitness in adaptive memetic algorithms for combinatorial problems

Among the most promising and active research areas in heuristic optimisation is the field of adaptive memetic algorithms (AMAs). These gain much of their reported robustness by adapting the probability with which each of a set of local improvement operators is applied, according to an estimate of their current value to the search process. This paper addresses the issue of how the current value should be estimated. Assuming the estimate occurs over several applications of a meme, we consider whether the extreme or mean improvements should be used, and whether this aggregation should be global, or local to some part of the solution space. To investigate these issues, we use the well-established COMA framework that coevolves the specification of a population of memes (representing different local search algorithms) alongside a population of candidate solutions to the problem at hand. Two very different memetic algorithms are considered: the first using adaptive operator pursuit to adjust the probabilities of applying a fixed set of memes, and a second which applies genetic operators to dynamically adapt and create memes and their functional definitions. For the latter, especially on combinatorial problems, credit assignment mechanisms based on historical records, or on notions of landscape locality, will have limited application, and it is necessary to estimate the value of a meme via some form of sampling. The results on a set of binary encoded combinatorial problems show that both methods are very effective, and that for some problems it is necessary to use thousands of variables in order to tease apart the differences between different reward schemes. However, for both memetic algorithms, a significant pattern emerges that reward based on mean improvement is better than that based on extreme improvement. This contradicts recent findings from adapting the parameters of operators involved in global evolutionary search. The results also show that local reward schemes outperform global reward schemes in combinatorial spaces, unlike in continuous spaces. An analysis of evolving meme behaviour is used to explain these findings. © 2012 by the Massachusetts Institute of Technology

Adaptation and self-organization in evolutionary algorithms

The objective of Evolutionary Computation is to solve practical problems (e.g.optimization, data mining) by simulating the mechanisms of natural evolution. This thesis addresses several topics related to adaptation and self-organization in evolving systems with the overall aims of improving the performance of Evolutionary Algorithms (EA), understanding its relation to natural evolution, and incorporating new mechanisms for mimicking complex biological systems. Part I of this thesis presents a new mechanism for allowing an EA to adapt its behavior in response to changes in the environment. Using the new approach, adaptation of EA behavior (i.e. control of EA design parameters) is driven by an analysis of population dynamics, as opposed to the more traditional use of fitness measurements. Comparisons with a number of adaptive control methods from the literature indicate substantial improvements in algorithm performance for a range of artificial and engineering design problems. Part II of this thesis involves a more thorough analysis of EA behavior based on the methods derived in Part 1. In particular, several properties of EA population dynamics are measured and compared with observations of evolutionary dynamics in nature. The results demonstrate that some large scale spatial and temporal features of EA dynamics are remarkably similar to their natural counterpart. Compatibility of EA with the Theory of Self-Organized Criticality is also discussed. Part III proposes fundamentally new directions in EA research which are inspired by the conclusions drawn in Part II. These changes involve new mechanisms which allow self-organization of the EA to occur in ways which extend beyond its common convergence in parameter space. In particular, network models for EA populations are developed where the network structure is dynamically coupled to EA population dynamics. Results indicate strong improvements in algorithm performance compared to cellular Genetic Algorithms and non-distributed EA designs. Furthermore, topological analysis indicates that the population network can spontaneously evolve to display similar characteristics to the interaction networks of complex biological systems