Five different representations and associated variation operators are studied in the context of a steady-state evolutionary algorithm (EA) for the multi-dimensional knapsack problem. Four of them are indirect decoder-based techniques, and the fifth is a direct encoding including heuristic initialization, repair, and local improvement. The complex decoders and the local improvement and repair strategies make it practically impossible to completely analyze such EAs in a fully theoretical way. After comparing the general performance of the EA variants on two benchmark suites, we present a hands-on approach for empirically analyzing important aspects of initialization, mutation, and crossover in an isolated fashion. Static, inexpensive measurements based on randomly created solutions are performed in order to quantify and visualize specific properties with respect to heuristic bias, locality, and heritability. These tests shed light onto the complex behavior of such EAs and point out reasons for good or bad performance. In addition, the proposed measures are also examined during actual EA runs, which gives further insight into dynamic aspects of evolutionary search and verifies the validity of the isolated static measurements. All measurements are described in a general way, allowing for an easy adaption to other representations and combinatorial problems.

Abstract. The choice of genetic representation crucially determines the capability of evolutionary processes to find complex solutions in which many variables interact. The question is how good genetic representations can be found and how they can be adapted online to account for what can be learned about the structure of the problem from previous samples. We address these questions in a scenario that we term indirect Estimation-of-Distribution: We consider a decorrelated search distribution (mutational variability) on a variable length genotype space. A one-to-one encoding onto the phenotype space then needs to induce an adapted phenotypic variability incorporating the dependencies between phenotypic variables that have been observed successful previously. Formalizing this in the framework of Estimation-of-Distribution Algorithms, an adapted phenotypic variability can be characterized as minimizing the Kullback-Leibler divergence to a population of previously selected individuals (parents). Our core result is a relation between the Kullback-Leibler divergence and the description length of the encoding in the specific scenario, stating that compact codes provide a way to minimize this divergence. A proposed class of Compression Evolutionary Algorithms and preliminary experiments with an L-system compression scheme illustrate the approach. We also discuss the implications for the self-adaptive evolution of genetic representations on the basis of neutrality (σ-evolution) towards compact codes. 1

Abstract not found

Biological and artificial evolutionary systems exhibit varying degrees of evolvability and different rates of evolution. Such quantities can be affected by various factors. Here, we review some evolutionary mechanisms and discuss new developments in biology that can potentially improve evolvability or accelerate evolution in artificial systems. Biological notions are discussed to the degree they correspond to notions in Evolutionary Computation. We hope that the findings put forward here can be used to design computational models of evolution that produce significant gains in evolvability and evolutionary speed.

This paper presents an investigation into the properties of the optimal communication spanning tree (OCST) problem. The OCST problem finds a spanning tree that connects all nodes and satisfies their communication requirements for a minimum total cost. The paper compares the properties of randomly created solutions to the best solutions that are found using an evolutionary algorithm framework. The results show that on average the distance between the optimal solution and the minimum spanning tree (MST) that is calculated according to the distance weights is significantly smaller than the distance between a randomly created solution and the MST. This means, optimal solutions for the OCST problem are biased towards the MST defined on the distance weights alone. Consequently, the performance of optimization methods for the OCST problem can be increased if the search is biased towards MST-like solutions.

This dissertation concerns the principles and techniques for scalable evolutionary computation to achieve better solutions for larger problems with more computational resources. It suggests that many of the limitations of existent evolutionary algorithms, such as premature convergence, stagnation, loss of diversity, lack of reliability and efficiency, are derived from the fundamental convergent evolution model, the oversimplified “survival of the fittest” Darwinian evolution model. Within this model, the higher the fitness the population achieves, the more the search capability is lost. This is also the case for many other conventional search techniques. The main result of this dissertation is the introduction of a novel sustainable evolution model, the Hierarchical Fair Competition (HFC) model, and corresponding five sustainable evolutionary algorithms (EA) for evolutionary search. By maintaining individuals in hierarchically organized fitness levels and keeping evolution going at all fitness levels, HFC transforms the conventional convergent evolutionary computation model into a sustainable search framework by ensuring a continuous supply and incorporation of low-level building blocks and by culturing and maintaining building blocks of intermediate levels with its

Neutral networks, which occur in fitness landscapes containing neighboring points of equal fitness, have attracted much research interest in recent years. In recent papers [20,21], we have shown that, in the case of simple test functions, the mutation rate of a genetic algorithm is an important factor for improving the speed at which a population moves along a neutral network. Our results also suggested that the benefits of the variable mutation rate strategy used by the operon-GA [5] increase as the ruggedness of the landscapes increases. In this work, we conducted a series of computer simulations with an evolutionary robotics problem in order to investigate whether our previous results are applicable to this problem domain. Two types of GA were used. One was the standard GA, where the mutation rate is constant, and the other was the operon-GA, whose effective mutation rate at each locus changes independently according to the history of the genetic search. The evolutionary dynamics we observed were consistent with those observed in our previous experiments, confirming that the variable mutation rate strategy is also beneficial to this problem.

The edge-set encoding is a direct encoding for trees which directly repre-sents trees as sets of edges. In contrast to indirect representations, where usually standard operators are applied to a list of strings and the re-sulting phenotype is constructed by an appropriate genotype-phenotype mapping, encoding-specic initialization, crossover, and mutation oper-ators have been developed for the edge-set encoding, which are directly applied to trees. There are two dierent variants of operators: heuristic versions that consider the weights of the edges and non-heuristic versions. An investigation into the bias of the dierent variants of the operators shows that the heuristic variants are biased towards the minimum span-ning tree (MST), that means solutions similar to the MST are favored. In contrast, non-heuristic versions are unbiased. The performance of edge-sets is investigated for the optimal communication spanning tree (OCST) problem. Results are presented for randomly created problems as well

Abstract — Search algorithms are subject to the trappings of local optima. Attempts to address the problem are often framed in the context of needing to balance, or trade-off, exploitation against exploration. Ideally, it is best to maximise both simultaneously, but this is usually seen as infeasible in the presence of multi-modal search spaces. This paper investigates the potential for exploration of both neutrality and mutation rate, and argues that the former is the more important. The most interesting result, however, is that the necessity for a trade-off between exploitation and exploration can be avoided within the context of our algorithm for evolving Binary Decision Diagrams. I.

We study the impact of the choice of search space for a GA that learns Bayesian networks from data. The most convenient search space is redundant and therefore allows for multiple representations of the same solution and possibly disruption during crossover. An alternative search space eliminates this redundancy, and potentially allows a more efficient search to be conducted. On the other hand, a non-redundant encoding requires a more complicated implementation. We experimentally compare several plausible approaches (GAs) to study the impact of this and other design decisions.