Effective Fitness as an Alternative Paradigm for Evolutionary Computation I: General Formalism

In evolutionary computation the concept of a fitness landscape has played an important role, evolution itself being portrayed as a hill-climbing process on a rugged landscape. In this article we review the recent development of an alternative paradigm for evolution on a fitness landscape—effective fitness. It is shown that in general, in the presence of other genetic operators such as mutation and recombination, hill-climbing is the exception rather than the rule; a discrepancy that has its origin in the different ways in which the concept of fitness appears—as a measure of the number of fit offspring, or as a measure of the probability to reach reproductive age. Effective fitness models the former not the latter and gives an intuitive way to understand population dynamics as flows on an effective fitness landscape when genetic operators other than reproductive selection play an important role. Additionally, we will show that when the genotype-phenotype map is degenerate, i.e. there exists a synonym symmetry, it can be used to quantify the degree of symmetry breaking of the map, thus allowing for a quantitative explanation of phenomena such as self-adaptation, bloat and evolutionary robustness.     

Where Are the Niches? Dynamic Fitness Sharing

The problem of locating all the optima within a multimodal fitness landscape has been widely addressed in evolutionary computation, and many solutions, based on a large variety of different techniques, have been proposed in the literature. Among them, fitness sharing (FS) is probably the best known and the most widely used. The main criticisms to FS concern both the lack of an explicit mechanism for identifying or providing any information about the location of the peaks in the fitness landscape, and the definition of species implicitly assumed by FS. We present a mechanism of FS, i.e., dynamic fitness sharing, which has been devised in order to overcome these limitations. The proposed method allows an explicit, dynamic identification of the species discovered at each generation, their localization on the fitness landscape, the application of the sharing mechanism to each species separately, and a species elitist strategy. The proposed method has been tested on a set of standard functions largely adopted in the literature to assess the performance of evolutionary algorithms on multimodal functions. Experimental results confirm that our method performs significantly better than FS and other methods proposed in the literature without requiring any further assumption on the fitness landscape than those assumed by the FS itself.     

Chaotic populations in genetic algorithms

We set two objectives for this study: one is to emulate chaotic natural populations in GA (Genetic Algorithms) populations by utilizing the Logistic Chaos map model, and the other is to analyze the population fitness distribution by utilizing insect spatial distribution theory. Natural populations are so dynamic that one of the first experimental evidences of Chaos in nature was discovered by a theoretical ecologist, May (1976, Nature, 261,459–467)[30], in his analysis of insect population dynamics. In evolutionary computing, perhaps influenced by the stable or infinite population concepts in population genetics, the status quo of population settings has dominantly been the fixed-size populations. In this paper, we propose to introduce dynamic populations controlled by the Logistic Chaos map model to Genetic Algorithms (GA), and test the hypothesis – whether or not the dynamic populations that emulate chaotic populations in nature will have an advantage over traditional fixed-size populations.The Logistic Chaos map model, arguably the simplest nonlinear dynamics model, has surprisingly rich dynamic behaviors, ranging from exponential, sigmoid growth, periodic oscillations, and aperiodic oscillations, to complete Chaos. What is even more favorable is that, unlike many other population dynamics models, this model can be expressed as a single parameter recursion equation, which makes it very convenient to control the dynamic behaviors and therefore easy to apply to evolutionary computing. The experiments show result values in terms of the fitness evaluations and memory storage requirements. We further conjecture that Chaos may be helpful in breaking neutral space in the fitness landscape, similar to the argument in ecology that Chaos may help the exploration and/or exploitation of environment heterogeneity and therefore enhance a species’ survival or fitness.     

On the role of population size and niche radius in fitness sharing

We propose a characterization of the dynamic behavior of an evolutionary algorithm (EA) with fitness sharing as a function of both the niche radius and the population size. Such a characterization, given in terms of the mean and the standard deviation of the number of niches found during the evolution, can be applied to any EA employing a proportional selection mechanism and does not make any assumption on either the fitness landscape or the internal parameters of the EA itself. On the basis of the proposed characterization, a method for estimating the optimal values for the population size and the niche radius without any a priori information on the fitness landscape is presented and tested on a standard set of functions. The proposed method also provides the best solution for the problem at hand, i.e., the solution obtained in correspondence of such optimal values, at no additional cost.     

基于共同进化计算模型的基因连锁问题求解

针对传统单种群进化类算法(conventional evolutionary algorithms,简称CEAs)求解基因连锁问题的不足,基于生物界共同进化机制提出求解NK基因连锁问题的合作式共同进化算法(Coevolutionary algorithm,简称CoEA),探讨其子种群的合作方式与个体适应值的计算方法,并从数学上分析该算法的性能,指出共同进化算法中高于平均适应值模式的递增指数高于传统单种群进化算法.仿真结果证实了理论分析.结果表明,共同进化算法比传统单种群进化算法对求解基因连锁问题的效力和效     

Darwinian, Lamarckian, and Baldwinian (Co)Evolutionary Approaches for Feature Weighting in $K$-means-Based Algorithms

Feature weighting is an aspect of increasing importance in clustering because data are becoming more and more complex. In this paper, we propose new feature weighting methods based on genetic algorithms. These methods use the cost function defined in LKM as a fitness function. We present new methods based on Darwinian, Lamarckian, and Baldwinian evolution. For each one of them, we describe evolutionary and coevolutionary versions. We compare classical hill-climbing optimization with these six genetic algorithms on different datasets. The results show that the proposed methods, except Darwinian methods, are always better than the LKM algorithm.     

Evolutionary consequences of coevolving targets

Most evolutionary optimization models incorporate a fitness evaluation that is based on a predefined static set of test cases or problems. In the natural evolutionary process, selection is of course not based on a static fitness evaluation. Organisms do not have to combat every existing disease during their lifespan; organisms of one species may live in different or changing environments; different species coevolve. This leads to the question of how information is integrated over many generations. This study focuses on the effects of different fitness evaluation schemes on the types of genotypes and phenotypes that evolve. The evolutionary target is a simple numerical function. The genetic representation is in the form of a program (i.e., a functional representation, as in genetic programming). Many different programs can code for the same numerical function. In other words, there is a many-to-one mapping between "genotypes" (the programs) and "phenotypes". We compare fitness evaluation based on a large static set of problems and fitness evaluation based on small coevolving sets of problems. In the latter model very little information is presented to the evolving programs regarding the evolutionary target per evolutionary time step. In other words, the fitness evaluation is very sparse. Nevertheless the model produces correct solutions to the complete evolutionary target in about half of the simulations. The complete evaluation model, on the other hand, does not find correct solutions to the target in any of the simulations. More important, we find that sparse evaluated programs are better generalizable compared to the complete evaluated programs when they are evaluated on a much denser set of problems. In addition, the two evaluation schemes lead to programs that differ with respect to mutational stability; sparse evaluated programs are less stable than complete evaluated programs.     

基于定向爬山的遗传算法

爬山法是一种局部搜索能力相当好的算法,主要是因为它是通过个体的优劣信息来引导搜索的。而传统的遗传算法作为一种全局搜索算法,在搜索过程中却没有考虑个体间的信息,而仅依靠个体适应度来引导搜索,使得算法的收敛性受到限制。将定向爬山机制应用于遗传算法,提出了一种基于定向爬山的遗传算法（OHCGA）。该算法结合了爬山法与遗传算法的优点,通过比较个体的优劣,使用定向爬山操作引导算法向更优秀的解区域进行搜索。实验结果表明,与传统遗传算法（TGA）相比,OHCGA较大地提高了算法的收敛速度和搜索最优解的能力。     

基于改进遗传算法的船舶管路布局设计

针对船舶管路布局设计中的路径规划问题提出一种改进型遗传算法求解方法。建立船舶管路布局设计问题的模型空间、约束条件和优化目标;提出一种基于连接点网格的定长编码方法,结合该编码方法设计了适合改进遗传算法应用的适应度函数和交叉、变异算子,定长编码可降低遗传算子设计复杂度和非法个体修补代价;提出在进化流程中嵌入以“去折弯”和“改模式”两种改善型变异方法构建的爬山操作,以提升算法收敛性和寻优能力。通过仿真实验验证所提算法具有可行性和先进性。     

Type-2 fuzzy mathematical modeling and analysis of the dynamical behaviors of complex ecosystems

It is very complex to model, study and analyze the dynamical behavior of the complex ecosystems. Many ecological theoretical problems are based on niche. The niche one species occupies and the relation between niches of different species will directly influence the species’ dynamical behavior. The discussion of niche has been very important to an ecosystem. Fuzzy set theory gave a new creative method to form the niche of a species. Based on broadband effect inherent in membership function of type-2 fuzzy set, the dynamic niche model of fuzzy niche theory is proposed. It is applied to explain the relationship between niches’ separating degree and competition of species and study the dynamical behavior emerging in the competition bio-system. It also analyses the case of the biological synergism in a simulate Lotka–Volterra competition bio-system based on niches.     

Comparing evolutionary algorithms to the (1+1) -EA

In this paper, we study the conditions in which the random hill-climbing algorithm (1 + 1)-EA compares favorably to other evolutionary algorithms (EAs) in terms of fitness function distribution at a given iteration and with respect to the average optimization time. Our approach is applicable when the reproduction operator of an evolutionary algorithm is dominated by the mutation operator of the (1 + 1)-EA. In this case one can extend the lower bounds obtained for the expected optimization time of the (1 + 1)-EA to other EAs based on the dominated reproduction operator. This method is demonstrated on the sorting problem with HAM landscape and the exchange mutation operator. We consider several simple examples where the (1 + 1)-EA is the best possible search strategy in the class of the EAs.     

Exploring the fitness landscape and the run-time behaviour of an iterated local search algorithm for cost-based abduction

Cost-based abduction (CBA) is an important problem in reasoning under uncertainty, and can be considered a generalization of belief revision. CBA is known to be NP-hard and has been a subject of considerable research over the past decade. In this paper, we investigate the fitness landscape for CBA, by looking at fitness–distance correlation for local minima and at landscape ruggedness. Our results indicate that stochastic local search techniques would be promising on this problem. We go on to present an iterated local search algorithm based on hill-climbing, tabu search, and simulated annealing. We compare the performance of our algorithm to simulated annealing, and to Santos' integer linear programming method for CBA.     

Bacterially inspired evolving system with an application to time series prediction

This paper explores the synergies between evolutionary computation and synthetic biology, developing an in silico evolutionary system that is inspired by the behavior of bacterial populations living in continuously changing environments. This system creates a 3D environment seeded with a simulated population of bacteria that eat, reproduce, interact with each other and with the environment and eventually die. This provides a 3D framework implementing an evolutionary process. The subject of the evolution is each bacterium's internal process, defining its interactions with the environment. The evolutionary goal is the survival of the population under successive, continuously changing environmental conditions. The key advantage of this bacterial evolutionary system is its decentralized, asynchronous, parallel and self-adapting general-purpose evolutionary process. We describe this system and present the results of an application to the evolution of a bacterial population that learns how to predict the presence or absence of food in the environment by analyzing three input signals from the environment. The resulting populations successfully evolve by continuously improving their fitness under different environmental conditions, demonstrating their adaptability to a fluctuating medium.     

Barricade construction by primitive termites: task allocation and evolutionary perspectives

The collective activities of social insects often result in the formation of complex structures. Previous studies have revealed the building mechanisms of various species, where sophisticated colony-level structures emerge from the interactions among individuals. However, little is known about the building behaviors of primitive species, which would give us an insight into the evolutionary processes that gave rise to collective building of sophisticated structures. Therefore, in this study, I investigated the building behavior of the primitive termite Zootermopsis nevadensis, which constructs simple barricades to plug the openings to its nests. Observation of the time course of barricade construction showed that the building dynamics followed a logistic pattern, suggesting that their collective building involves an amplification phase, which plays an important role in self-organized building activities in social insects. Moreover, this species exhibited highly skewed task allocation during construction. Together, these results suggest that this primitive species possesses building mechanisms similar to species with more sophisticated collective behaviors.     

多目标优化的演化算法

近年来．多目标优化问题求解已成为演化计算的一个重要研究方向，而基于Pareto最优概念的多目标演化算法则是当前演化计算的研究热点．多目标演化算法的研究目标是使算法种群快速收敛并均匀分布于问题的非劣最优域．该文在比较与分析多目标优化的演化算法发展的历史基础上，介绍基于Pareto最优概念的多目标演化算法中的一些主要技术与理论结果，并具体以多目标遗传算法为代表，详细介绍了基于偏好的个体排序、适应值赋值以及共享函数与小生境等技术．此外，指出并阐释了值得进一步研究的相关问题．     

多模态函数优化的拥挤聚类遗传算法

对多模态函数优化问题，分析了各种小生境策略；将拥挤模型与聚类算法相结合，提出了一种拥挤聚类遗传算法．拥挤模型在适应值曲面上形成多个小生境，聚类算法消除了每个小生境内部的基因漂移现象．理论分析证明了算法的收敛性能．数值实例表明，拥挤聚类模型在多极值搜索的数量、质量和精度上都优于拥挤模型与确定性拥挤模型．将拥挤聚类遗传算法应用于国家同步辐射实验室变间距全息光栅的设计，取得了满意的效果．     

Bag of local landscape features for fitness landscape analysis

Evolutionary computation is a research field dealing with black-box and complex optimization problems whose fitness landscapes are usually unknown in advance. It is difficult to select an appropriate evolutionary algorithm and parameters for a given problem due to the black-box setting although many evolutionary algorithms have been developed. In this context, several landscape features have been proposed and their usefulness examined for understanding the problem. In this paper, we propose a novel feature vector by focusing on the local landscape in order to characterize the fitness landscape. The proposed landscape features are a vector form and composed of a histogram of quantized local landscape features. We introduce two implementation methods of this concept, called the bag of local landscape patterns (BoLLP) and the bag of evolvability (BoEvo). The BoLLP uses the fitness pattern of the neighbors of a certain candidate solution, and the BoEvo uses the number of better candidate solutions in the neighbors as the local landscape features. Furthermore, the hierarchical versions of the BoLLP and the BoEvo, concatenated feature vectors with different sample sizes, are considered to capture the landscape characteristic with various resolutions. We extract the proposed landscape feature vectors from well-known continuous optimization benchmark functions and the BBOB benchmark function set to investigate their properties; the visualization of the proposed landscape features, clustering and running time prediction experiments are conducted. Then the effectiveness of the proposed landscape features for the fitness landscape analysis is discussed based on the experimental results.     

Decomposition of the maximum entropy niche function – A step beyond modelling species distribution

Some algorithms used to model species' distributions are often only considered as black boxes; coefficients of the underlying niche functions are often not interpreted ecologically. Here, we focus on the maximum entropy approach that is commonly and successfully applied in order to model species' distribution. By means of an eigenanalysis, we decompose the niche function into independent factors that can be interpreted separately. In addition, we derive parameters that can be used to characterize the species' niche, especially considering the steepness of the modelled niche function and the sensitivity of the considered species against changes in certain environmental conditions. On the example of three well-studied Taiga forest tree species we illustrate the capability and scope of our approach. Given the easy availability of environmental data and species occurrences, the presented approach seems to be a feasible way to gain deeper insights into the factors that are related to species' distributions.     

An interactive genetic algorithm with the interval arithmetic based on hesitation and its application to achieve customer collaborative product configuration design

Complex product configuration design requires rapid and accurate response to customers’ demand. The participation of customers in product design will be a very effective solution to achieve this. The traditional interactive genetic algorithm (IGA) can solve the above problem to some extent by a computer-aided user interface. However, it is difficult to adopt an accurate number to express an individual's fitness because the customers’ cognition of evolutionary population is uncertain, and to solve the users’ fatigue problem in IGA. Thus, an interactive genetic algorithm with interval individual fitness based on hesitancy (IGA-HIIF) is proposed in this paper. In IGA-HIIF, the interval number derived from users’ evaluation time is adopted to express an individual's fitness, and the evolutionary individuals are compared according to the interval probability dominant strategy proposed in this paper. Then, the genetic operations are applied to generate offspring population and the evolutionary process doesn’t stop until it meets the termination conditions of the evolution or user manually terminates the evolution process. The IGA-HIIF is applied into the design system of the car console configuration, and compared to the other two kinds of IGA. The extensive experiment results are provided to demonstrate that our proposed algorithm is correct and efficient.