Hans-Paul Schwefel

Evolution strategies –A comprehensive introduction

This article gives a comprehensive introduction into one of the main branches of evolutionary computation – the evolution strategies (ES) the history of which dates back to the 1960s in Germany. Starting from a survey of history the philosophical background is explained in order to make understandable why ES are realized in the way they are. Basic ES algorithms and design principles for variation and selection operators as well as theoretical issues are presented, and future branches of ES research are discussed.

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.

Parallel Problem Solving from Nature - PPSN VIII

Two ideas taken from Bayesian optimization and classifier systems are presented for personnel scheduling based on choosing a suitable scheduling rule from a set for each person’s assignment. Unlike our previous work of using genetic algorithms whose learning is implicit, the learning in both approaches is explicit, i.e. we are able to identify building blocks directly. To achieve this target, the Bayesian optimization algorithm builds a Bayesian network of the joint probability distribution of the rules used to construct solutions, while the adapted classifier system assigns each rule a strength value that is constantly updated according to its usefulness in the current situation. Computational results from 52 real data instances of nurse scheduling demonstrate the success of both approaches. It is also suggested that the learning mechanism in the proposed approaches might be suitable for other scheduling problems.

Parallel Problem Solving from Nature PPSN VI

Spatially structured evolutionary algorithms (EAs) have shown to be endowed with useful features for global optimization. Distributed EAs (dEA) and cellular EAs (cEA) are two of the most widely known types of structured algorithms. In this paper we deal with cellular EAs. Two important parameters guiding the search in a cEA are the population topology and the neighborhood defined on it. Here we first review some theoretical results which show that a cEA with a 2D grid can be easily tuned to shift from exploration to exploitation. We initially make a study on the relationship between the topology and the neighborhood by defining a ratio measure between they two. Then, we encompass a set of tests aimed at discovering the performance that different ratio values have on different classes of problems. We find out that, with the same neighborhood, rectangular grids have some advantages in multimodal and epistatic problems, while square ones are more efficient for solving deceptive problems and for simple function optimization. Finally, we propose and study a cEA in which the ratio is dynamically changed.

Parallel Problem Solving from Nature — PPSN VII

Dynamic optimization is frequently cited as a prime application area for evolutionary algorithms. In contrast to static optimization, the objective in dynamic optimization is to continuously adapt the solution to a changing environment – a task that evolutionary algorithms are believed to be good at. At the time being, however, almost all knowledge with regard to the performance of evolutionary algorithms in dynamic environments is of an empirical nature. In this paper, tools devised originally for the analysis in static environments are applied to study the performance of a popular type of recombinative evolution strategy with cumulative mutation strength adaptation on a dynamic problem. With relatively little effort, scaling laws that quite accurately describe the behavior of the strategy and that greatly contribute to its understanding are derived and their implications are discussed.

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.

Contemporary Evolution Strategies

After an outline of the history of evolutionary algorithms, a new (μ, κ, λ, ρ) variant of the evolution strategies is introduced formally. Though not comprising all degrees of freedom, it is richer in the number of features than the meanwhile old (μ, λ) and (μ+λ) versions. Finally, all important theoretically proven facts about evolution strategies are briefly summarized and some of many open questions concerning evolutionary algorithms in general are pointed out.

A Spatial Predator-Prey Approach to Multi-objective Optimization: A Preliminary Study

This paper presents a novel evolutionary approach of approximating the shape of the Pareto-optimal set of multi-objective optimization problems. The evolutionary algorithm (EA) uses the predator-prey model from ecology. The prey are the usual individuals of an EA that represent possible solutions to the optimization task. They are placed at vertices of a graph, remain stationary, reproduce, and are chased by predators that traverse the graph. The predators chase the prey only within its current neighborhood and according to one of the optimization criteria. Because there are several predators with different selection criteria, those prey individuals, which perform best with respect to all objectives, are able to produce more descendants than inferior ones. As soon as a vertex for the prey becomes free, it is refilled by descendants from alive parents in the usual way of EA, i.e., by inheriting slightly altered attributes. After a while, the prey concentrate at Pareto-optimal positions. The main objective of this preliminary study is the answer to the question whether the predator-prey approach to multi-objective optimization works at all. The performance of this evolutionary algorithm is examined under several step-size adaptation rules.

How to analyse evolutionary algorithms

Many variants of evolutionary algorithms have been designed and applied. The experimental knowledge is immense. The rigorous analysis of evolutionary algorithms is difficult, but such a theory can help to understand, design, and teach evolutionary algorithms. In this survey, first the history of attempts to analyse evolutionary algorithms is described and then new methods for continuous as well as discrete search spaces are presented and discussed.