Average Drift Analysis and Population Scalability

This paper aims to study how the population size affects the computation time of evolutionary algorithms in a rigorous way. The computation time of an evolutionary algorithm can be measured by either the expected number of generations (hitting time) or the expected number of fitness evaluations (running time) to find an optimal solution. Population scalability is the ratio of the expected hitting time between a benchmark algorithm and an algorithm using a larger population size. Average drift analysis is presented for comparing the expected hitting time of two algorithms and estimating lower and upper bounds on population scalability. Several intuitive beliefs are rigorously analysed. It is prove that (1) using a population sometimes increases rather than decreases the expected hitting time; (2) using a population cannot shorten the expected running time of any elitist evolutionary algorithm on unimodal functions in terms of the time-fitness landscape, but this is not true in terms of the distance-based fitness landscape; (3) using a population cannot always reduce the expected running time on fully-deceptive functions, which depends on the benchmark algorithm using elitist selection or random selection

On the Easiest and Hardest Fitness Functions

The hardness of fitness functions is an important research topic in the field of evolutionary computation. In theory, the study can help understanding the ability of evolutionary algorithms. In practice, the study may provide a guideline to the design of benchmarks. The aim of this paper is to answer the following research questions: Given a fitness function class, which functions are the easiest with respect to an evolutionary algorithm? Which are the hardest? How are these functions constructed? The paper provides theoretical answers to these questions. The easiest and hardest fitness functions are constructed for an elitist (1+1) evolutionary algorithm to maximise a class of fitness functions with the same optima. It is demonstrated that the unimodal functions are the easiest and deceptive functions are the hardest in terms of the time-fitness landscape. The paper also reveals that the easiest fitness function to one algorithm may become the hardest to another algorithm, and vice versa

A Comparison of GAs Penalizing Infeasible Solutions and Repairing Infeasible Solutions on the 0-1 Knapsack Problem

Constraints exist in almost every optimization problem. Different constraint handling techniques have been incorporated with genetic algorithms (GAs), however most of current studies are based on computer experiments. An example is Michalewicz\u27s comparison among GAs using different constraint handling techniques on the 0-1 knapsack problem. The following phenomena are observed in experiments: 1) the penalty method needs more generations to find a feasible solution to the restrictive capacity knapsack than the repair method; 2) the penalty method can find better solutions to the average capacity knapsack. Such observations need a theoretical explanation. This paper aims at providing a theoretical analysis of Michalewicz\u27s experiments. The main result of the paper is that GAs using the repair method are more efficient than GAs using the penalty method on both restrictive capacity and average capacity knapsack problems. This result of the average capacity is a little different from Michalewicz\u27s experimental results. So a supplemental experiment is implemented to support the theoretical claim. The results confirm the general principle pointed out by Coello: a better constraint-handling approach should tend to exploit specific domain knowledge

Fast Estimations of Hitting Time of Elitist Evolutionary Algorithms from Fitness Levels

The fitness level method is an easy-to-use tool for estimating the hitting time of elitist EAs. Recently, general linear lower and upper bounds from fitness levels have been constructed. However, the construction of these bounds requires recursive computation, which makes them difficult to use in practice. We address this shortcoming with a new directed graph (digraph) method that does not require recursive computation and significantly simplifies the calculation of coefficients in linear bounds. In this method, an EA is modeled as a Markov chain on a digraph. Lower and upper bounds are directly calculated using conditional transition probabilities on the digraph. This digraph method provides straightforward and explicit expressions of lower and upper time bound for elitist EAs. In particular, it can be used to derive tight lower bound on both fitness landscapes without and with shortcuts. This is demonstrated through four examples: the (1+1) EA on OneMax, FullyDeceptive, TwoMax1 and Deceptive. Our work extends the fitness level method from addressing simple fitness functions without shortcuts to more realistic functions with shortcuts

Transport properties of dense deuterium-tritium plasmas

Consistent descriptions of the equation of states, and information about transport coefficients of deuterium-tritium mixture are demonstrated through quantum molecular dynamic (QMD) simulations (up to a density of 600 g/cm$^{3}$ and a temperature of $10^{4}$ eV). Diffusion coefficients and viscosity are compared with one component plasma model in different regimes from the strong coupled to the kinetic one. Electronic and radiative transport coefficients, which are compared with models currently used in hydrodynamic simulations of inertial confinement fusion, are evaluated up to 800 eV. The Lorentz number is also discussed from the highly degenerate to the intermediate region.Comment: 4 pages, 3 figure

A new framework for analysis of coevolutionary systems:Directed graph representation and random walks

Studying coevolutionary systems in the context of simplified models (i.e. games with pairwise interactions between coevolving solutions modelled as self plays) remains an open challenge since the rich underlying structures associated with pairwise comparison-based fitness measures are often not taken fully into account. Although cyclic dynamics have been demonstrated in several contexts (such as intransitivity in coevolutionary problems), there is no complete characterization of cycle structures and their effects on coevolutionary search. We develop a new framework to address this issue. At the core of our approach is the directed graph (digraph) representation of coevolutionary problem that fully captures structures in the relations between candidate solutions. Coevolutionary processes are modelled as a specific type of Markov chains ? random walks on digraphs. Using this framework, we show that coevolutionary problems admit a qualitative characterization: a coevolutionary problem is either solvable (there is a subset of solutions that dominates the remaining candidate solutions) or not. This has an implication on coevolutionary search. We further develop our framework that provide the means to construct quantitative tools for analysis of coevolutionary processes and demonstrate their applications through case studies. We show that coevolution of solvable problems corresponds to an absorbing Markov chain for which we can compute the expected hitting time of the absorbing class. Otherwise, coevolution will cycle indefinitely and the quantity of interest will be the limiting invariant distribution of the Markov chain. We also provide an index for characterizing complexity in coevolutionary problems and show how they can be generated in a controlled mannerauthorsversionPeer reviewe

Differential responses of two rubber tree clones to chilling stress

Chilling stress is one of the most important environmental factors that limit the growth, distribution and yield of rubber tree in China. The effects of chilling stress on the grated plants of two rubber trees clones, GT1 and Wenchang217, were studied by physiological methods in controlled light chamber in order to explore the physiological mechanism of cold tolerance in rubber tree. Our results show a significant change in the tested physiological parameters after chilling treatment between two rubber clones. In comparison with the case of rubber tree clone GT1, the level of malondialdehyde (MDA) increased while superoxide dismutase, especially peroxidase and catalase decreased significantly in the seedlings of rubber tree clone Wenchang217 in response to chilling stress. As the cold tolerance ability of rubber tree clone GT1 is stronger than that of rubber tree clone Wenchang217, activation of oxidative quenching enzyme system should be one of the important factors that determine the cold tolerance of rubber tree.Keywords: Chilling stress, cold tolerance, Hevea brasiliensis Muell. Arg., physiological parameter, seedlin