Thomas Bäck

Evolutionary computation: comments on the history and current state

Evolutionary computation has started to receive significant attention during the last decade, although the origins can be traced back to the late 1950s. This article surveys the history as well as the current state of this rapidly growing field. We describe the purpose, the general structure, and the working principles of different approaches, including genetic algorithms (GA) (with links to genetic programming (GP) and classifier systems (CS)), evolution strategies (ES), and evolutionary programming (EP) by analysis and comparison of their most important constituents (i.e. representations, variation operators, reproduction, and selection mechanism). Finally, we give a brief overview on the manifold of application domains, although this necessarily must remain incomplete.

An overview of evolutionary algorithms for parameter optimization

Three main streams of evolutionary algorithms (EAs), probabilistic optimization algorithms based on the model of natural evolution, are compared in this article: evolution strategies (ESs), evolutionary programming (EP), and genetic algorithms (GAs). The comparison is performed with respect to certain characteristic components of EAs: the representation scheme of object variables, mutation, recombination, and the selection operator. Furthermore, each algorithm is formulated in a high-level notation as an instance of the general, unifying basic algorithm, and the fundamental theoretical results on the algorithms are presented. Finally, after presenting experimental results for three test functions representing a unimodal and a multimodal case as well as a step function with discontinuities, similarities and differences of the algorithms are elaborated, and some hints to open research questions are sketched.

Selective pressure in evolutionary algorithms: a characterization of selection mechanisms

Due to its independence of the actual search space and its impact on the exploration-exploitation tradeoff, selection is an important operator in any kind of evolutionary algorithm. All important selection operators are discussed and quantitatively compared with respect to their selective pressure. The comparison clarifies that only a few really different and useful selection operators exist: proportional selection (in combination with a scaling method), linear ranking, tournament selection, and (/spl mu/,/spl lambda/)-selection (respectively (/spl mu/+/spl lambda/)-selection). Their selective pressure increases in the order as they are listed here. The theoretical results are confirmed by an experimental investigation using a genetic algorithm with different selection methods on a simple unimodal objective function.<<ETX>>Due to its independence of the actual search space and its impact on the exploration-exploitation tradeoff, selection is an important operator in any kind of evolutionary algorithm. All important selection operators are discussed and quantitatively compared with respect to their selective pressure. The comparison clarifies that only a few really different and useful selection operators exist: proportional selection (in combination with a scaling method), linear ranking, tournament selection, and (/spl mu/,/spl lambda/)-selection (respectively (/spl mu/+/spl lambda/)-selection). Their selective pressure increases in the order as they are listed here. The theoretical results are confirmed by an experimental investigation using a genetic algorithm with different selection methods on a simple unimodal objective function. >

The zero/one multiple knapsack problem and genetic algorithms

A genetic algorithm, GENEsYs, is applied to an NP-complete problem, the 0/1 multiple knapsack problem. The partitioning of the search space resulting from this highly constrained problem may include substantially large infeasible regions. Our implementation allows for the breeding and participation of infeasible strings in the population. Unlike many other GA-based algorithms that are augmented with domainspecific knowledge, GENEsYs uses a simple fitness function that uses a graded penalty term to penalize infeasibly bred strings. We apply our genetic algorithm to problem instances from the literature of well known test problems and report our experimental results. These encouraging results, especially for relatively large test problems, indicate that genetic algorithms can be successfully used as heuristics for finding good solutions for highly constrained NP-complete problems.

Evolutionary computation: an overview

We present an overview of the most important representatives of algorithms gleaned from natural evolution, so-called evolutionary algorithms. Evolution strategies, evolutionary programming, and genetic algorithms are summarized, with special emphasis on the principle of strategy parameter self-adaptation utilized by the first two algorithms to learn their own strategy parameters such as mutation variances and covariances. Some experimental results are presented which demonstrate the working principle and robustness of the self-adaptation methods used in evolution strategies and evolutionary programming. General principles of evolutionary algorithms are discussed, and we identify certain properties of natural evolution which might help to improve the problem solving capabilities of evolutionary algorithms even further.

Intelligent Mutation Rate Control in Canonical Genetic Algorithms

The role of the mutation rate in canonical genetic algorithms is investigated by comparing a constant setting, a deterministically varying, time-dependent mutation rate schedule, and a self-adaptation mechanism for individual mutation rates following the principle of self-adaptation as used in evolution strategies. The power of the self-adaptation mechanism is illustrated by a time-varying optimization problem, where mutation rates have to adapt continuously in order to follow the optimum. The strengths of the proposed deterministic schedule and the self-adaptation method are demonstrated by a comparison of their performance on difficult combinatorial optimization problems (multiple knapsack, maximum cut and maximum independent set in graphs). Both methods are shown to perform significantly better than the canonical genetic algorithm, and the deterministic schedule yields the best results of all control mechanisms compared.

Metamodel-Assisted Evolution Strategies

This paper presents various Metamodel-Assisted Evolution Strategies which reduce the computational cost of optimisation problems involving time-consuming function evaluations. The metamodel is built using previously evaluated solutions in the search space and utilized to predict the fitness of new candidate solutions. In addition to previous works by the authors, the new metamodel takes also into account the error associated with each prediction, by correlating neighboring points in the search space. A mathematical problem and the problem of designing an optimal airfoil shape under viscous flow considerations have been worked out. Both demonstrate the noticeable gain in computational time one might expect from the use of metamodels in Evolution Strategies.

Empirical investigation of multiparent recombination operators in evolution strategies

An extension of evolution strategies to multiparent recombination involving a variable number of parents to create an offspring individual is proposed. The extension is experimentally evaluated on a test suite of functions differing in their modality and separability and the regular/irregular arrangement of their local optima. Multiparent diagonal crossover and uniform scanning crossover and a multiparent version of intermediary recombination are considered in the experiments. The performance of the algorithm is observed to depend on the particular combination of recombination operator and objective function. In most of the cases a significant increase in performance is observed as the number of parents increases. However, there might also be no significant impact of recombination at all, and for one of the unimodal objective functions, the performance is observed to deteriorate over the course of evolution for certain choices of the recombination operator and the number of parents. Additional experiments with a skewed initialization of the population clarify that intermediary recombination does not cause a search bias toward the origin of the coordinate system in the case of domains of variables that are symmetric around zero.

An evolutionary approach to combinatorial optimization problems

The paper reports on the application of genetic algorithms, probabilistic search algorithms based on the model of organic evolution, to NP-complete combinatorial optimization problems. In particular, the subset sum, maximum cut, and minimum tardy task problems are considered. Except for the fitness function, no problem-specific changes of the genetic algorithm are required in order to achieve results of high quality even for the problem instances of size 100 used in the paper. For constrained problems, such as the subset sum and the minimum tardy task, the constraints are taken into account by incorporating a graded penalty term into the fitness function. Even for large instances of these highly multimodal optimization problems, an iterated application of the genetic algorithm is observed to find the global optimum within a number of runs. As the genetic algorithm samples only a tiny fraction of the search space, these results are quite encouraging.

Robust design of multilayer optical coatings by means of evolutionary algorithms

Robustness is an important requirement for almost all kinds of products. This article shows how evolutionary algorithms can be applied for robust design based on the approach of Taguchi. To achieve a better understanding of the consequences of this approach, we first present some analytical results gained from a toy problem. As a nontrivial industrial application we consider the design of multilayer optical coatings (MOCs) most frequently used for optical filters. An evolutionary algorithm based on a parallel diffusion model and extended for mixed-integer optimization was able to compete with or even outperform traditional methods of robust MOC design. With respect to chromaticity, the MOC designs found by the evolutionary algorithm are substantially more robust to parameter variations than a reference design and therefore perform much better in the average case. In most cases, however, this advantage has to be paid for by a reduction in the average reflectance. The robust design approach outlined in this paper should be easily adopted to other application domains.