Analysis of Estimation of Distribution Algorithms and Genetic Algorithms on NK Landscapes
Missouri Estimation of Distribution Algorithms Laboratory (MEDAL)（密苏里分布估计算法实验室（MEDAL））；Department of Mathematics and Computer Science（数学与计算机科学系）；University of Missouri–St. Louis（密苏里大学圣路易斯分校）
This study analyzes performance of several genetic and evolutionary algorithms on randomly generated NK fitness landscapes with various values of n and k. A large number of NK problem instances are first generated for each n and k, and the global optimum of each instance is obtained using the branch-and-bound algorithm. Next, the hierarchical Bayesian optimization algorithm (hBOA), the univariate marginal distribution algorithm (UMDA), and the simple genetic algorithm (GA) with uniform and two-point crossover operators are applied to all generated instances. Performance of all algorithms is then analyzed and compared, and the results are discussed.
In this paper, we employ genetic algorithms to explore the landscape of type IIB flux vacua. We show that genetic algorithms can efficiently scan the landscape for viable solutions satisfying various criteria. More specifically, we consider a symmetric $T^{6}$ as well as the conifold region of a Calabi-Yau hypersurface. We argue that in both cases genetic algorithms are powerful tools for finding flux vacua with interesting phenomenological properties. We also compare genetic algorithms to algorithms based on different breeding mechanisms as well as random walk approaches.
Genetic programming is an often-used technique for symbolic regression: finding symbolic expressions that match data from an unknown function. To make the symbolic regression more efficient, one can also use dimensionally-aware genetic programming that constrains the physical units of the equation. Nevertheless, there is no formal analysis of how much dimensionality awareness helps in the regression process. In this paper, we conduct a fitness landscape analysis of dimensionallyaware genetic programming search spaces on a subset of equations from Richard Feynmans well-known lectures. We define…
Most real-world optimization problems are difficult to solve with traditional statistical techniques or with metaheuristics. The main difficulty is related to the existence of a considerable number of local optima, which may result in the premature convergence of the optimization process. To address this problem, we propose a novel heuristic method for constructing a smooth surrogate model of the original function. The surrogate function is easier to optimize but maintains a fundamental property of the original rugged fitness landscape: the location of the global optimum. To create such a surr…
Multi-Representation Genetic Programming: A Case Study on Tree-based and Linear Representations
Centre for Data Science and Artificial Intelligence & School of Engineering and Computer Science, Victoria University of Wellington（数据科学与人工智能中心及工程与计算机科学学院，维多利亚大学）
Accelerating Evolution: Integrating PSO Principles into Real-Coded Genetic Algorithm Crossover
Xiaobo Jin School of Information Engineering Taizhou Vocational College of Science & Technology（金晓波 学校信息工程学院 太zhou 职业科技学院）；Traditional Chinese Medicine department Taizhou First People’s Hospital（传统中医部门 太zhou 第一人民医院）
This paper concerns applications of genetic algorithms and genetic programming to tasks for which it is difficult to find a representation that does not map to a highly complex and discontinuous fitness landscape. In such cases the standard algorithm is prone to getting trapped in local extremes. The paper proposes several adaptive mechanisms that are useful in preventing the search from getting trapped.
Universidad Nacional de Tucumán（图库曼国立大学）；Universidad Tecnológica Nacional（国家技术大学）
Variable selection problems generally present more than a single solution and, sometimes, it is worth to find as many solutions as possible. The use of Evolutionary Algorithms applied to this kind of problem proves to be one of the best methods to find optimal solutions. Moreover, there are variants designed to find all or almost all local optima, known as Niching Genetic Algorithms (NGA). There are several different NGA methods developed in order to achieve this task. The present work compares the behavior of eight different niching techniques, applied to a climatic database of four weather s…
Universidade de Lisboa（里斯本大学）；NOVA Information Management School (NOVA IMS)（新里斯本大学信息管理学院）；Universidade Nova de Lisboa（新里斯本大学）
Fitness landscapes are a useful concept to study the dynamics of meta-heuristics. In the last two decades, they have been applied with success to estimate the optimization power of several types of evolutionary algorithms, including genetic algorithms and genetic programming. However, so far they have never been used to study the performance of machine learning algorithms on unseen data, and they have never been applied to neuroevolution. This paper aims at filling both these gaps, applying for the first time fitness landscapes to neuroevolution and using them to infer useful information about…
The search ability of an Evolutionary Algorithm (EA) depends on the variation among the individuals in the population [3, 4, 8]. Maintaining an optimal level of diversity in the EA population is imperative to ensure that progress of the EA search is unhindered by premature convergence to suboptimal solutions. Clearer understanding of the concept of population diversity, in the context of evolutionary search and premature convergence in particular, is the key to designing efficient EAs. To this end, this paper first presents a brief analysis of the EA population diversity issues. Next we presen…
We continue the study of Genetic Algorithms (GA) on combinatorial optimization problems where the candidate solutions need to satisfy a balancedness constraint. It has been observed that the reduction of the search space size granted by ad-hoc crossover and mutation operators does not usually translate to a substantial improvement of the GA performances. There is still no clear explanation of this phenomenon, although it is suspected that a balanced representation might yield a more irregular fitness landscape, where it could be more difficult for GA to converge to a global optimum. In this pa…
The search ability of an Evolutionary Algorithm (EA) depends on the variation among the individuals in the population. Maintaining an optimal level of diversity in the EA population is imperative to ensure that progress of the EA search is unhindered by premature convergence to suboptimal solutions. Clearer understanding of the concept of population diversity, in the context of evolutionary search and premature convergence in particular, is the key to designing efficient EAs. To this end, this paper first presents a comprehensive analysis of the EA population diversity issues. Next we present …
From Understanding Genetic Drift to a Smart-Restart Mechanism for Estimation-of-Distribution Algorithms
Southern University of Science and Technology（南方科技大学）；Harbin Institute of Technology（哈尔滨工业大学）；Laboratoire d’Informatique (LIX)（信息学实验室（LIX））；École Polytechnique（巴黎综合理工学院）；CNRS（法国国家科学研究中心）；Institut Polytechnique de Paris（巴黎理工学院）
This study proposes a data condensation method for multivariate kernel density estimation by genetic algorithm. First, our proposed algorithm generates multiple subsamples of a given size with replacement from the original sample. The subsamples and their constituting data points are regarded as $\it{chromosome}$ and $\it{gene}$, respectively, in the terminology of genetic algorithm. Second, each pair of subsamples breeds two new subsamples, where each data point faces either $\it{crossover}$, $\it{mutation}$, or $\it{reproduction}$ with a certain probability. The dominant subsamples in terms …
The compact genetic algorithm (cGA) is an non-elitist estimation of distribution algorithm which has shown to be able to deal with difficult multimodal fitness landscapes that are hard to solve by elitist algorithms. In this paper, we investigate the cGA on the CLIFF function for which it has been shown recently that non-elitist evolutionary algorithms and artificial immune systems optimize it in expected polynomial time. We point out that the cGA faces major difficulties when solving the CLIFF function and investigate its dynamics both experimentally and theoretically around the cliff. Our ex…
Reversible Cellular Automata (RCA) are a particular kind of shift-invariant transformations characterized by a dynamics composed only of disjoint cycles. They have many applications in the simulation of physical systems, cryptography and reversible computing. In this work, we formulate the search of a specific class of RCA -- namely, those whose local update rules are defined by conserved landscapes -- as an optimization problem to be tackled with Genetic Algorithms (GA) and Genetic Programming (GP). In particular, our experimental investigation revolves around three different research questio…
