Runtime analysis of non-elitist populations: from classical optimisation to partial information

Although widely applied in optimisation, relatively little has been proven rigorously about the role and behaviour of populations in randomised search processes. This paper presents a new method to prove upper bounds on the expected optimisation time of population-based randomised search heuristics that use non-elitist selection mechanisms and unary variation operators. Our results follow from a detailed drift analysis of the population dynamics in these heuristics. This analysis shows that the optimisation time depends on the relationship between the strength of the selective pressure and the degree of variation introduced by the variation operator. Given limited variation, a surprisingly weak selective pressure suffices to optimise many functions in expected polynomial time. We derive upper bounds on the expected optimisation time of non-elitist Evolutionary Algorithms (EA) using various selection mechanisms, including fitness proportionate selection. We show that EAs using fitness proportionate selection can optimise standard benchmark functions in expected polynomial time given a sufficiently low mutation rate. As a second contribution, we consider an optimisation scenario with partial information, where fitness values of solutions are only partially available. We prove that non-elitist EAs under a set of specific conditions can optimise benchmark functions in expected polynomial time, even when vanishingly little information about the fitness values of individual solutions or populations is available. To our knowledge, this is the first runtime analysis of randomised search heuristics under partial information

First-Hitting Times Under Additive Drift

For the last ten years, almost every theoretical result concerning the expected run time of a randomized search heuristic used drift theory, making it the arguably most important tool in this domain. Its success is due to its ease of use and its powerful result: drift theory allows the user to derive bounds on the expected first-hitting time of a random process by bounding expected local changes of the process -- the drift. This is usually far easier than bounding the expected first-hitting time directly. Due to the widespread use of drift theory, it is of utmost importance to have the best drift theorems possible. We improve the fundamental additive, multiplicative, and variable drift theorems by stating them in a form as general as possible and providing examples of why the restrictions we keep are still necessary. Our additive drift theorem for upper bounds only requires the process to be nonnegative, that is, we remove unnecessary restrictions like a finite, discrete, or bounded search space. As corollaries, the same is true for our upper bounds in the case of variable and multiplicative drift

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

Artificial Immune Systems can find arbitrarily good approximations for the NP-Hard partition problem

Typical Artificial Immune System (AIS) operators such as hypermutations with mutation potential and ageing allow to efficiently overcome local optima from which Evolutionary Algorithms (EAs) struggle to escape. Such behaviour has been shown for artificial example functions such as Jump, Cliff or Trap constructed especially to show difficulties that EAs may encounter during the optimisation process. However, no evidence is available indicating that similar effects may also occur in more realistic problems. In this paper we perform an analysis for the standard NP-Hard Partition problem from combinatorial optimisation and rigorously show that hypermutations and ageing allow AISs to efficiently escape from local optima where standard EAs require exponential time. As a result we prove that while EAs and Random Local Search may get trapped on 4/3 approximations, AISs find arbitrarily good approximate solutions of ratio ( 1+ϵ ) for any constant ϵ within a time that is polynomial in the problem size and exponential only in 1/ϵ

Not an Ordinary Killer- Just an Ordinary Guy: When men murder an intimate woman partner

The Murder in Britain Study was designed to examine in detail different types of murder. Using a subset of case files from this study, men who murder other men (MM;n = 424) are compared with men who murder an intimate partner (IP;n = 106) to reflect on the relative conventionality of each group. In terms of many of the characteristics of childhood and adulthood, the IP murder group differs from theMMgroup and appears to be more “ordinary” or “conventional.” However, the IP group is less conventional in that they are more likely to have intimate relationships that had broken down, to have used violence against a previous woman partner as well as against the victim they killed, and to “ specialize” in violence against women

Neutrality in evolutionary algorithms... what do we know?

Over the last years, the effects of neutrality have attracted the attention of many researchers in the Evolutionary Algorithms (EAs) community. A mutation from one gene to another is considered as neutral if this modification does not affect the phenotype. This article provides a general overview on the work carried out on neutrality in EAs. Using as a framework the origin of neutrality and its study in different paradigms of EAs (e.g., Genetic Algorithms, Genetic Programming), we discuss the most significant works and findings on this topic. This work points towards open issues, which the community needs to address.Science Foundation Irelandti, ke, ab, li - TS 02.12 12 month EMBARG