Drift conditions for estimating the first hitting times of evolutionary algorithms

For the global optimization problems with continuous variables, evolutionary algorithms (EAs) are often used to find the approximate solutions. The number of generations for an EA to find the approximate solutions, called the first hitting time, is an important index to measure the performance of the EA. However, calculating the first hitting time is still difficult in theory. This paper proposes some new drift conditions that are used to estimate the upper bound of the first hitting times of EAs for finding the approximate solutions. Two case studies are given to show how to apply these conditions to estimate the first hitting times.     

A new hybrid method using evolutionary algorithms to train Fuzzy Cognitive Maps

A novel hybrid method based on evolutionary computation techniques is presented in this paper for training Fuzzy Cognitive Maps. Fuzzy Cognitive Maps is a soft computing technique for modeling complex systems, which combines the synergistic theories of neural networks and fuzzy logic. The methodology of developing Fuzzy Cognitive Maps relies on human expert experience and knowledge, but still exhibits weaknesses in utilization of learning methods and algorithmic background. For this purpose, we investigate a coupling of differential evolution algorithm and unsupervised Hebbian learning algorithm, using both the global search capabilities of Evolutionary strategies and the effectiveness of the nonlinear Hebbian learning rule. The use of differential evolution algorithm is related to the concept of evolution of a number of individuals from generation to generation and that of nonlinear Hebbian rule to the concept of adaptation to the environment by learning. The hybrid algorithm is introduced, presented and applied successfully in real-world problems, from chemical industry and medicine. Experimental results suggest that the hybrid strategy is capable to train FCM effectively leading the system to desired states and determining an appropriate weight matrix for each specific problem.     

Expected runtimes of evolutionary algorithms for the Eulerian cycle problem

Evolutionary algorithms are randomized search heuristics, which are applied to problems whose structure is not well understood, as well as to problems in combinatorial optimization. They have successfully been applied to different kinds of arc routing problems. To start the analysis of evolutionary algorithms with respect to the expected optimization time on these problems, we consider the Eulerian cycle problem. We show that a variant of the well-known (1+1)$(1+1)$ EA working on the important encoding of permutations is able to find an Eulerian tour of an Eulerian graph in expected polynomial time. Altering the operator used for mutation in the considered algorithm, the expected optimization time changes from polynomial to exponential.     

Time Complexity of Evolutionary Algorithms for Combinatorial Optimization： A Decade of Results

Computational time complexity analyzes of evolutionary algorithms (EAs) have been performed since the mid-nineties. The first results were related to very simple algorithms,such as the (1 1)-EA,on toy problems.These efforts produced a deeper understanding of how EAs perform on different kinds of fitness landscapes and general mathematical tools that may be extended to the analysis of more complicated EAs on more realistic problems.In fact,in recent years,it has been possible to analyze the (1 1)-EA on combinatorial optimization problems with practical applications and more realistic population-baeed EAs on structured toy problems. This paper presents a survey of the results obtained in the last decade along these two research lines.The most common mathematical techniques are introduced,the basic ideas behind them are discussed and their elective applications are highlighted.Solved problems that were still open are enumerated as are those still awaiting for a solution.New questions and problems arisen in the meantime are also considered.     

Rethinking the design of real-coded evolutionary algorithms: Making discrete choices in continuous search domains

Although real-coded evolutionary algorithms (EAs) have been applied to optimization problems for over thirty years, the convergence properties of these methods remain poorly understood. We discuss the use of discrete random variables to perform search in real-valued EAs. Although most real-valued EAs perform mutation with continuous random variables, we argue that EAs using discrete random variables for mutation can be much easier to analyze. In particular, we present and analyze two simple EAs that make discrete choices of mutation steps.     

A note on the expected time required to construct the outer layer

The expected time E(T) of the standard divide-and-conquer algorithm for finding the outer layer of a set of points in the plane depends upon the distribution of the points. Under the mild assumption that the points are independent random vectors and have a common bounded density with compact support, it is shown that E(T) = O(n).     

A population dynamics model to describe gene frequencies in evolutionary algorithms

The performance of evolutionary algorithms (EAs) may heavily depend severely on a suitable choice of parameters such as mutation and crossover rates. Several methods to adjust those parameters have been developed in order to enhance EA performance. For this purpose, it is important to understand the EA dynamics, i.e., to appreciate the behavior of the population. Hence, this paper presents a new model of population dynamics to describe and predict the diversity in any particular generation. The formulation is based on selecting the probability density function of each individual. The population dynamics proposed is modeled for a generational population. The model was tested in several case studies of different population sizes. The results suggest that the prediction error decreases as the population size increases.     

Identification of influential vertices in complex networks: A hitting time-based approach

Unravelling the dynamics of network vertices is pivotal, and traditional centrality measures have limitations in adapting to structural changes, directed and weighted networks, and temporal analyses. This paper introduces a ground breaking approach - hitting time-based centrality. Utilizing network matrix notations and a random walk model on a connected network , we establish a Markov chain to quantify the hitting time, hitting distance, and hitting centrality, providing a nuanced measure prioritizing central vertices. Through extensive experiments using Kendall's tau coefficient, the paper evaluates the method's correlation with actual influence in the Susceptible-Infectious (SI) model, showcasing superior performance across diverse network sizes and structures. The hitting centrality method exhibits sensitivity to connectivity dynamics, effective incorporation of temporal dynamics, and robust handling of weighted and directed networks. Positive Kendall's tau coefficients underline the method's proficiency in prioritizing influential vertices by correlating hitting centrality values with actual infection ability. The demonstrated robustness to structural changes enhances its utility for dynamic network analysis. In conclusion, our hitting time-based centrality approach emerges as a promising method, mitigating the shortcomings of traditional measures. By integrating information propagation speed, accommodating network dynamics, and enabling time-dependent analyses, it offers a comprehensive tool for evaluating vertex importance and influence in complex networks.     

进化算法漂移分析基本定理的改进与证明

漂移分析的基本定理存在缺陷：条件过严、证明有误且不够严格等, 而这些缺陷一直未见指出。鉴于该定理是漂移分析的核心和理论基础, 很有必要加以严格化。指出了该定理的不足之处, 以测度论为工具, 对该定理进行了适当的修正与改进, 并且给出了一个新的严格的证明。     

On limits on the computational power of data-accumulating algorithms

In the data-accumulating paradigm, inputs arrive continuously in real time, and the computation terminates when all the already received data are processed before another datum arrives. Previous research states that a constant upper bound on the running time of a successful algorithm within this paradigm exists only for particular forms of the data arrival law. This contradicts our recent conjecture that those problems that are solvable in real time are included in the class of logarithmic space-bounded computations. However, we prove that such an upper bound does exist in fact in both the parallel and sequential cases and for any polynomial arrival law, thus strengthening the mentioned conjecture. Then, we analyze an example of a non-continuous data arrival law. We find similar properties for the sorting algorithm under such a law, namely the existence of an upper bound on the running time, suggesting that such properties do not depend on the form of the arrival law.     

Design and analysis of evolutionary bit-length optimization algorithms for floating to fixed-point conversion

Hardware designs need to obey constraints of resource utilization, minimum clock frequency, power consumption, computation precision and data range, which are all affected by the data type representation. Floating and fixed-point representations are the most common data types to work with real numbers where arithmetic hardware units for fixed-point format can improve performance and reduce energy consumption when compared to floating point solution. However, the right bit-lengths estimation for fixed-point is a time-consuming task since it is a combinatorial optimization problem of minimizing the accumulative arithmetic computation error. This work proposes two evolutionary approaches to accelerate the process of converting algorithms from floating to fixed-point format. The first is based on a classic evolutionary algorithm and the second one introduces a compact genetic algorithm, with theoretical evidence that a near-optimal performance, to find a solution, has been reached. To validate the proposed approaches, they are applied to three computing intensive algorithms from the mobile robotic scenario, where data error accumulated during execution is influenced by sensor noise and navigation environment characteristics. The proposed compact genetic algorithm accelerates the conversion process up to 10.2× against the state of art methods reaching similar bit precision and robustness.     

Convergence of multi-objective evolutionary algorithms to a uniformly distributed representation of the Pareto front

In evolutionary multi-objective optimization (EMO), the convergence to the Pareto set of a multi-objective optimization problem (MOP) and the diversity of the final approximation of the Pareto front are two important issues. In the existing definitions and analyses of convergence in multi-objective evolutionary algorithms (MOEAs), convergence with probability is easily obtained because diversity is not considered. However, diversity cannot be guaranteed. By combining the convergence with diversity, this paper presents a new definition for the finite representation of a Pareto set, the B-Pareto set, and a convergence metric for MOEAs. Based on a new archive-updating strategy, the convergence of one such MOEA to the B-Pareto sets of MOPs is proved. Numerical results show that the obtained B-Pareto front is uniformly distributed along the Pareto front when, according to the new definition of convergence, the algorithm is convergent.     

Improving the prediction of the clinical outcome of breast cancer using evolutionary algorithms

There exist several methods for binary classification of gene expression data sets. However, in the majority of published methods, little effort has been made to minimize classifier complexity. In view of the small number of samples available in most gene expression data sets, there is a strong motivation for minimizing the number of free parameters that must be fitted to the data. In this paper, a method is introduced for evolving (using an evolutionary algorithm) simple classifiers involving a minimal subset of the available genes. The classifiers obtained by this method perform well, reaching 97% correct classification of clinical outcome on training samples from the breast cancer data set published by van't Veer, and up to 89% correct classification on validation samples from the same data set, easily outperforming previously published results.     

An empirical time analysis of evolutionary algorithms as C programs

This article presents an empirical study devoted to characterize the computational efficiency behavior of an evolutionary algorithm (usually called canonical) as a C program. The study analyzes the effects of several implementation decisions on the execution time of the resulting evolutionary algorithm. The implementation decisions studied include: memory utilization (using dynamic vs. static variables and local vs. global variables), methods for ordering the population, code substitution mechanisms, and the routines for generating pseudorandom numbers within the evolutionary algorithm. The results obtained in the experimental analysis allow us to conclude that significant improvements in efficiency can be gained by applying simple guidelines to best program an evolutionary algorithm in C. Copyright © 2013 John Wiley & Sons, Ltd.     

A case study on using evolutionary algorithms to optimize bakery production planning

The production of bakery goods is strictly time sensitive due to the complex biochemical processes during dough fermentation, which leads to special requirements for production planning and scheduling. Instead of mathematical methods scheduling is often completely based on the practical experience of the responsible employees in bakeries. This sometimes inconsiderate scheduling approach often leads to sub-optimal performance of companies. This paper presents the modeling of the production in bakeries as a kind of no-wait hybrid flow-shop following the definitions in Scheduling Theory, concerning the constraints and frame conditions given by the employed processes properties. Particle Swarm Optimization and Ant Colony Optimization, two widely used evolutionary algorithms for solving scheduling problems, were adapted and used to analyse and optimize the production planning of an example bakery. In combination with the created model both algorithms proved capable to provide optimized results for the scheduling operation within a predefined runtime of 15 min.     

Distributed evolutionary algorithms and their models: A survey of the state-of-the-art

The increasing complexity of real-world optimization problems raises new challenges to evolutionary computation. Responding to these challenges, distributed evolutionary computation has received considerable attention over the past decade. This article provides a comprehensive survey of the state-of-the-art distributed evolutionary algorithms and models, which have been classified into two groups according to their task division mechanism. Population-distributed models are presented with master-slave, island, cellular, hierarchical, and pool architectures, which parallelize an evolution task at population, individual, or operation levels. Dimension-distributed models include coevolution and multi-agent models, which focus on dimension reduction. Insights into the models, such as synchronization, homogeneity, communication, topology, speedup, advantages and disadvantages are also presented and discussed. The study of these models helps guide future development of different and/or improved algorithms. Also highlighted are recent hotspots in this area, including the cloud and MapReduce-based implementations, GPU and CUDA-based implementations, distributed evolutionary multiobjective optimization, and real-world applications. Further, a number of future research directions have been discussed, with a conclusion that the development of distributed evolutionary computation will continue to flourish.     

An experimental study on the applicability of evolutionary algorithms to craniofacial superimposition in forensic identification

Photographic supra-projection is a forensic process that aims to identify a missing person from a photograph and a skull found. One of the crucial tasks throughout all this process is the craniofacial superimposition which tries to find a good fit between a 3D model of the skull and the 2D photo of the face. This photographic supra-projection stage is usually carried out manually by forensic anthropologists. It is thus very time consuming and presents several difficulties. In this paper, we aim to demonstrate that real-coded evolutionary algorithms are suitable approaches to tackle craniofacial superimposition. To do so, we first formulate this complex task in forensic identification as a numerical optimization problem. Then, we adapt three different evolutionary algorithms to solve it: two variants of a real-coded genetic algorithm and the state of the art evolution strategy CMA-ES. We also consider an existing binary-coded genetic algorithm as a baseline. Results on several superimposition problems of real-world identification cases solved by the Physical Anthropology lab at the University of Granada (Spain) are considered to test our proposals.     

A new approach to generate weighted fuzzy rules using genetic algorithms for estimating null values

In this paper, we present a new method to generate weighted fuzzy rules using genetic algorithms for estimating null values in relational database systems, where there are negative functional dependency relationships between attributes. The proposed method can get higher average estimated accuracy rates than the method presented in [Chen, S. M., & Huang, C. M. (2003). Generating weighted fuzzy rules from relational database systems for estimating null values using genetic algorithms. IEEE Transactions on Fuzzy Systems, 11(4), 495–506].     

A review of procedures to evolve quantum algorithms

There exist quantum algorithms that are more efficient than their classical counterparts; such algorithms were invented by Shor in 1994 and then Grover in 1996. A lack of invention since Grover’s algorithm has been commonly attributed to the non-intuitive nature of quantum algorithms to the classically trained person. Thus, the idea of using computers to automatically generate quantum algorithms based on an evolutionary model emerged. A limitation of this approach is that quantum computers do not yet exist and quantum simulation on a classical machine has an exponential order overhead. Nevertheless, early research into evolving quantum algorithms has shown promise. This paper provides an introduction into quantum and evolutionary algorithms for the computer scientist not familiar with these fields. The exciting field of using evolutionary algorithms to evolve quantum algorithms is then reviewed.