Level-Based Analysis of Genetic Algorithms and Other Search Processes

The fitness-level technique is a simple and old way to derive upper bounds for the expected runtime of simple elitist evolutionary algorithms (EAs). Recently, the technique has been adapted to deduce the runtime of algorithms with non-elitist populations and unary variation operators [2,8]. In this paper, we show that the restriction to unary variation operators can be removed. This gives rise to a much more general analytical tool which is applicable to a wide range of search processes. As introductory examples, we provide simple runtime analyses of many variants of the Genetic Algorithm on well-known benchmark functions, such as OneMax, LeadingOnes, and the sorting problem

Towards a Runtime Comparison of Natural and Artificial Evolution

Evolutionary algorithms (EAs) form a popular optimisation paradigm inspired by natural evolution. In recent years the field of evolutionary computation has developed a rigorous analytical theory to analyse the runtimes of EAs on many illustrative problems. Here we apply this theory to a simple model of natural evolution. In the Strong Selection Weak Mutation (SSWM) evolutionary regime the time between occurrences of new mutations is much longer than the time it takes for a mutated genotype to take over the population. In this situation, the population only contains copies of one genotype and evolution can be modelled as a stochastic process evolving one genotype by means of mutation and selection between the resident and the mutated genotype. The probability of accepting the mutated genotype then depends on the change in fitness. We study this process, SSWM, from an algorithmic perspective, quantifying its expected optimisation time for various parameters and investigating differences to a similar evolutionary algorithm, the well-known (1+1) EA. We show that SSWM can have a moderate advantage over the (1+1) EA at crossing fitness valleys and study an example where SSWM outperforms the (1+1) EA by taking advantage of information on the fitness gradient

Parental rearing and psychopathology in mothers of adolescents with and without borderline personality symptoms

<p>Abstract</p> <p>Background</p> <p>A combination of multiple factors, including a strong genetic predisposition and environmental factors, are considered to contribute to the developmental pathways to borderline personality disorder (BPD). However, these factors have mostly been investigated retrospectively, and hardly in adolescents. The current study focuses on maternal factors in BPD features in adolescence.</p> <p>Methods</p> <p>Actual parenting was investigated in a group of referred adolescents with BPD features (N = 101) and a healthy control group (N = 44). Self-reports of perceived concurrent parenting were completed by the adolescents. Questionnaires on parental psychopathology (both Axis I and Axis II disorders) were completed by their mothers.</p> <p>Results</p> <p>Adolescents reported significantly less emotional warmth, more rejection and more overprotection from their mothers in the BPD-group than in the control group. Mothers in the BPD group reported significantly more parenting stress compared to mothers in the control group. Also, these mothers showed significantly more general psychopathology and clusters C personality traits than mothers in the control group. Contrary to expectations, mothers of adolescents with BPD features reported the same level of cluster B personality traits, compared to mothers in the control group. Hierarchical logistic regression revealed that parental rearing styles (less emotional warmth, and more overprotection) and general psychopathology of the mother were the strongest factors differentiating between controls and adolescents with BPD symptoms.</p> <p>Conclusions</p> <p>Adolescents with BPD features experience less emotional warmth and more overprotection from their mothers, while the mothers themselves report more symptoms of anxiety and depression. Addition of family interventions to treatment programs for adolescents might increase the effectiveness of such early interventions, and prevent the adverse outcome that is often seen in adult BPD patients.</p

Speeding Up Evolutionary Algorithms through Asymmetric Mutation Operators

Successful applications of evolutionary algorithms show that certain variation operators can lead to good solutions much faster than other ones. We examine this behavior observed in practice from a theoretical point of view and investigate the effect of an asymmetric mutation operator in evolutionary algorithms with respect to the runtime behavior. Considering the Eulerian cycle problem we present runtime bounds for evolutionary algorithms using an asymmetric operator which are much smaller than the best upper bounds for a more general one. In our analysis it turns out that a plateau which both algorithms have to cope with changes its structure in a way that allows the algorithm to obtain an improvement much faster. In addition, we present a lower bound for the general case which shows that the asymmetric operator speeds up computation by at least a linear factor.Benjamin Doerr, Nils Hebbinghaus, and Frank Neuman

Speeding up evolutionary algorithms through restricted mutation operators

Also published as a journal article: Lecture Notes in Computer Science, 2006; 4193:978-987We investigate the effect of restricting the mutation operator in evolutionary algorithms with respect to the runtime behavior. For the Eulerian cycle problem; we present runtime bounds on evolutionary algorithms with a restricted operator that are much smaller than the best upper bounds for the general case. It turns out that a plateau that both algorithms have to cope with is left faster by the new algorithm. In addition, we present a lower bound for the unrestricted algorithm which shows that the restricted operator speeds up computation by at least a linear factor.Benjamin Doerr, Nils Hebbinghaus, and Frank Neuman

Towards a Theory of Randomized Search Heuristics

There is a well-developed theory about the algorithmic complexity of optimization problems. Complexity theory provides negative results which typically are based on assumptions like NP#=P or NP#=RP