Escaping Local Optima Using Crossover with Emergent Diversity

Population diversity is essential for avoiding premature convergence in Genetic Algorithms and for the effective use of crossover. Yet the dynamics of how diversity emerges in populations are not well understood. We use rigorous run time analysis to gain insight into population dynamics and Genetic Algorithm performance for the (μ+1) Genetic Algorithm and the Jump test function. We show that the interplay of crossover followed by mutation may serve as a catalyst leading to a sudden burst of diversity. This leads to significant improvements of the expected optimisation time compared to mutation-only algorithms like the (1+1) Evolutionary Algorithm. Moreover, increasing the mutation rate by an arbitrarily small constant factor can facilitate the generation of diversity, leading to even larger speedups. Experiments were conducted to complement our theoretical findings and further highlight the benefits of crossover on the function class

Emergence of Diversity and its Benefits for Crossover in Genetic Algorithms

Population diversity is essential for avoiding premature convergence in Genetic Algorithms (GAs) and for the effective use of crossover. Yet the dynamics of how diversity emerges in populations are not well understood. We use rigorous runtime analysis to gain insight into population dynamics and GA performance for a standard (µ+1) GA and the Jumpk test function. By studying the stochastic process underlying the size of the largest collection of identical genotypes we show that the interplay of crossover followed by mutation may serve as a catalyst leading to a sudden burst of diversity. This leads to improvements of the expected optimisation time of order Ω(n/ log n) compared to mutationonly algorithms like the (1+1) EA

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

Disentangling astroglial physiology with a realistic cell model in silico

Electrically non-excitable astroglia take up neurotransmitters, buffer extracellular K+ and generate Ca2+ signals that release molecular regulators of neural circuitry. The underlying machinery remains enigmatic, mainly because the sponge-like astrocyte morphology has been difficult to access experimentally or explore theoretically. Here, we systematically incorporate multi-scale, tri-dimensional astroglial architecture into a realistic multi-compartmental cell model, which we constrain by empirical tests and integrate into the NEURON computational biophysical environment. This approach is implemented as a flexible astrocyte-model builder ASTRO. As a proof-of-concept, we explore an in silico astrocyte to evaluate basic cell physiology features inaccessible experimentally. Our simulations suggest that currents generated by glutamate transporters or K+ channels have negligible distant effects on membrane voltage and that individual astrocytes can successfully handle extracellular K+ hotspots. We show how intracellular Ca2+ buffers affect Ca2+ waves and why the classical Ca2+ sparks-and-puffs mechanism is theoretically compatible with common readouts of astroglial Ca2+ imaging

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

Determining the neurotransmitter concentration profile at active synapses

Establishing the temporal and concentration profiles of neurotransmitters during synaptic release is an essential step towards understanding the basic properties of inter-neuronal communication in the central nervous system. A variety of ingenious attempts has been made to gain insights into this process, but the general inaccessibility of central synapses, intrinsic limitations of the techniques used, and natural variety of different synaptic environments have hindered a comprehensive description of this fundamental phenomenon. Here, we describe a number of experimental and theoretical findings that has been instrumental for advancing our knowledge of various features of neurotransmitter release, as well as newly developed tools that could overcome some limits of traditional pharmacological approaches and bring new impetus to the description of the complex mechanisms of synaptic transmission

Glutamate Uptake Triggers Transporter-Mediated GABA Release from Astrocytes

Background: Glutamate (Glu) and c-aminobutyric acid (GABA) transporters play important roles in regulating neuronal activity. Glu is removed from the extracellular space dominantly by glial transporters. In contrast, GABA is mainly taken up by neurons. However, the glial GABA transporter subtypes share their localization with the Glu transporters and their expression is confined to the same subpopulation of astrocytes, raising the possibility of cooperation between Glu and GABA transport processes. Methodology/Principal Findings: Here we used diverse biological models both in vitro and in vivo to explore the interplay between these processes. We found that removal of Glu by astrocytic transporters triggers an elevation in the extracellular level of GABA. This coupling between excitatory and inhibitory signaling was found to be independent of Glu receptor-mediated depolarization, external presence of Ca2+ and glutamate decarboxylase activity. It was abolished in the presence of non-transportable blockers of glial Glu or GABA transporters, suggesting that the concerted action of these transporters underlies the process. Conclusions/Significance: Our results suggest that activation of Glu transporters results in GABA release through reversal of glial GABA transporters. This transporter-mediated interplay represents a direct link between inhibitory and excitatory neurotransmission and may function as a negative feedback combating intense excitation in pathological conditions such as epilepsy or ischemia

Astrocytes convert network excitation to tonic inhibition of neurons

<p>Abstract</p> <p>Background</p> <p>Glutamate and γ-aminobutyric acid (GABA) transporters play important roles in balancing excitatory and inhibitory signals in the brain. Increasing evidence suggest that they may act concertedly to regulate extracellular levels of the neurotransmitters.</p> <p>Results</p> <p>Here we present evidence that glutamate uptake-induced release of GABA from astrocytes has a direct impact on the excitability of pyramidal neurons in the hippocampus. We demonstrate that GABA, synthesized from the polyamine putrescine, is released from astrocytes by the reverse action of glial GABA transporter (GAT) subtypes GAT-2 or GAT-3. GABA release can be prevented by blocking glutamate uptake with the non-transportable inhibitor DHK, confirming that it is the glutamate transporter activity that triggers the reversal of GABA transporters, conceivably by elevating the intracellular Na⁺concentration in astrocytes. The released GABA significantly contributes to the tonic inhibition of neurons in a network activity-dependent manner. Blockade of the Glu/GABA exchange mechanism increases the duration of seizure-like events in the low-[Mg²⁺] <it>in vitro </it>model of epilepsy. Under <it>in vivo </it>conditions the increased GABA release modulates the power of gamma range oscillation in the CA1 region, suggesting that the Glu/GABA exchange mechanism is also functioning in the intact hippocampus under physiological conditions.</p> <p>Conclusions</p> <p>The results suggest the existence of a novel molecular mechanism by which astrocytes transform glutamat<it>ergic </it>excitation into GABA<it>ergic </it>inhibition providing an adjustable, <it>in situ </it>negative feedback on the excitability of neurons.</p