Franz Rothlauf

Redundant representations in evolutionary computation

This paper discusses how the use of redundant representations influences the performance of genetic and evolutionary algorithms. Representations are redundant if the number of genotypes exceeds the number of phenotypes. A distinction is made between synonymously and non-synonymously redundant representations. Representations are synonymously redundant if the genotypes that represent the same phenotype are very similar to each other. Non-synonymously redundant representations do not allow genetic operators to work properly and result in a lower performance of evolutionary search. When using synonymously redundant representations, the performance of selectorecombinative genetic algorithms (GAs) depends on the modification of the initial supply. We have developed theoretical models for synonymously redundant representations that show the necessary population size to solve a problem and the number of generations goes with O(2kr/r), where kr is the order of redundancy and r is the number of genotypic building blocks (BB) that represent the optimal phenotypic BB. As a result, uniformly redundant representations do not change the behavior of GAs. Only by increasing r, which means overrepresenting the optimal solution, does GA performance increase. Therefore, non-uniformly redundant representations can only be used advantageously if a-priori information exists regarding the optimal solution. The validity of the proposed theoretical concepts is illustrated for the binary trivial voting mapping and the real-valued link-biased encoding. Our empirical investigations show that the developed population sizing and time to convergence models allow an accurate prediction of the empirical results.

On the locality of grammatical evolution

This paper investigates the locality of the genotype-phenotype mapping (representation) used in grammatical evolution (GE). The results show that the representation used in GE has problems with locality as many neighboring genotypes do not correspond to neighboring phenotypes. Experiments with a simple local search strategy reveal that the GE representation leads to lower performance for mutation-based search approaches in comparison to standard GP representations. The results suggest that locality issues should be considered for further development of the representation used in GE.

Network random keys: a tree representation scheme for genetic and evolutionary algorithms

When using genetic and evolutionary algorithms for network design, choosing a good representation scheme for the construction of the genotype is important for algorithm performance. One of the most common representation schemes for networks is the characteristic vector representation. However, with encoding trees, and using crossover and mutation, invalid individuals occur that are either under or overspecified. When constructing the offspring or repairing the invalid individuals that do not represent a tree, it is impossible to distinguish between the importance of the links that should be used. These problems can be overcome by transferring the concept of random keys from scheduling and ordering problems to the encoding of trees. This paper investigates the performance of a simple genetic algorithm (SGA) using network random keys (NetKeys) for the one-max tree and a real-world problem. The comparison between the network random keys and the characteristic vector encoding shows that despite the effects of stealth mutation, which favors the characteristic vector representation, selectorecombinative SGAs with NetKeys have some advantages for small and easy optimization problems. With more complex problems, SGAs with network random keys significantly outperform SGAs using characteristic vectors. This paper shows that random keys can be used for the encoding of trees, and that genetic algorithms using network random keys are able to solve complex tree problems much faster than when using the characteristic vector. Users should therefore be encouraged to use network random keys for the representation of trees.

Vehicle routing with compartments: applications, modelling and heuristics

Despite the vast amount of literature about vehicle routing problems, only very little attention has been paid to vehicles with compartments that allow transportation of inhomogeneous products on the same vehicle, but in different compartments. We motivate a general vehicle routing problem with compartments that is essential for several industries, like the distribution of food or petrol. We introduce a formal model, an integer program formulation and a benchmark suite of 200 instances. A solver suite of heuristic components is presented, which covers a broad range of alternative approaches for construction, local search, large neighbourhood search and meta-heuristics. The empirical results for the benchmark instances identify effective algorithmic setups as well as essential components for achieving high solution quality. In a comparison on 23 specific and combinatorially less complex instances taken from literature, our algorithm showed to be competitive.

Design of Modern Heuristics

Inevitably, reading is one of the requirements to be undergone. To improve the performance and quality, someone needs to have something new every day. It will suggest you to have more inspirations, then. However, the needs of inspirations will make you searching for some sources. Even from the other people experience, internet, and many books. Books and internet are the recommended media to help you improving your quality and performance.

Behaviour of UMDA/sub c/ with truncation selection on monotonous functions

Of late, much progress has been made in developing estimation of distribution algorithms (EDA), algorithms that use probabilistic modelling of high quality solutions to guide their search. While experimental results on EDA behaviour are widely available, theoretical results are still rare. This is especially the case for continuous EDA. In this article, we develop theory that predicts the behaviour of the univariate marginal distribution algorithm in the continuous domain (UMDA/sub c/) with truncation selection on monotonous fitness functions. Monotonous functions are commonly used to model the algorithm behaviour far from the optimum. Our result includes formulae to predict population statistics in a specific generation as well as population statistics after convergence. We find that population statistics develop identically for monotonous functions. We show that if assuming monotonous fitness functions, the distance that UMDA/sub c/ travels across the search space is bounded and solely relies on the percentage of selected individuals and not on the structure of the fitness landscape. This can be problematic if this distance is too small for the algorithm to find the optimum. Also, by wrongly setting the selection intensity, one might not be able to explore the whole search space.

Pruefer Numbers and Genetic Algorithms: A Lesson on How the Low Locality of an Encoding Can Harm the Performance of GAs

When handling tree networks, researchers have sometimes tried using the Pruefer number representation for encoding networks, however GAs often degraded when used on this encoding. This paper investigates the locality of the Pruefer number and its affect on the performance of a Genetic Algorithm (GA). The locality describes how the neighborhood of the genotype is preserved when constructing the phenotype (the tree) from the genotype (the Pruefer number). It is shown that the locality of the Pruefer number is highly irregular on the entire solution space, and that the performance of a GA depends on the structure of the optimal solution. A GA is able to perform well only for networks that have a high locality (stars). For all other types of networks (lists, trees) the locality is low and a GA fails to find the best list or tree. Using a GA with the Pruefer number encoding can be useful, when the best solution tends to be a star. The locality of an encoding could have a strong influence on the performance of a GA. When choosing encodings for optimization problems, researchers should be aware of this and be careful with low locality encodings. If the locality of the encoding is low, a failure of the GA is often unavoidable.

Approaches to Collaborative Software Development

Software development is becoming more and more complex. Traditionally and to date, the software development process rather corresponds to job-shop manufacturing. Therefore, the ever growing demands for different kinds of software as well as the ongoing globalization require more efficient development processes. Both scientific literature and practical experience hence postulate a necessary industrialization of software development and design of novel forms of specialization, task distribution, and collaboration. Existing approaches to collaborative software development can be classified and analyzed according to multiple categories. By evaluating these, current deficiencies are identified and discussed for further investigation.

On Optimal Solutions for the Optimal Communication Spanning Tree Problem

This paper presents an experimental investigation into the properties of the optimal communication spanning tree (OCST) problem. The OCST problem seeks a spanning tree that connects all the nodes and satisfies their communication requirements at a minimum total cost. The paper compares the properties of random trees to the properties of the best solutions for the OCST problem that are found using an evolutionary algorithm. The results show, on average, that the optimal solution and the minimum spanning tree (MST) share a higher number of links than the optimal solution and a random tree. Furthermore, optimal solutions for OCST problems with randomly chosen distance weights share a higher number of links with an MST than OCST problems with Euclidean distance weights. This intuitive similarity between optimal solutions and MSTs suggests that some heuristic optimization methods for OCST problems might be improved by starting with an MST. Using an MST as a starting solution for a greedy search in the tested cases either improves median running time up to a factor of 10 while finding solutions of the same quality, or increases solution quality up to a factor of 100 while using the same number of search steps in comparison to starting the greedy search from a random tree. Starting a local search, a simulated annealing approach and a genetic algorithm from an MST increases solution quality up to a factor of three in comparison to starting from a random solution.

Evolution Strategies, Network Random Keys, and the One-Max Tree Problem

Evolution strategies (ES)are efficient optimization methods for continuous problems. However, many combinatorial optimization methods can not be represented by using continuous representations. The development of the network random key representation which represents trees by using real numbers allows one to use ES for combinatorial tree problems.In this paper we apply ES to tree problems using the network random key representation. We examine whether existing recommendations regarding optimal parameter settings for ES, which were developed for the easy sphere and corridor model, are also valid for the easy one-max tree problem.The results show that the 1/5-success rule for the (1+1)-ES results in low performance because the standard deviation is continuously reduced and we get early convergence. However, for the (µ+?)-ES and the (µ, ?)-ES the recommendations from the literature are confirmed for the parameters of mutation ?1 and ?2 and the ratio µ/?. This paper illustrates how existing theory about ES is helpful in finding good parameter settings for new problems like the one-max tree problem.