Simple Estimation Of Distribution Algorithms Research Articles

An investigation of the selection strategies impact on MOEDAs: CMA-ES and UMDA

Researchers have acknowledged the importance of the selection, replacement, and archiving strategies in the behavior of evolutionary algorithms (EAs). However, these important relationships have not been deeply investigated in terms of Estimation of Distribution algorithms (EDAs). In a preliminary research, we focused on UMDA, a simple EDA that uses univariate Gaussian factorizations. Experimental results confirm that the choice of the selection method can provoke probabilistic modeling to be more effective for some classes of functions. Motivated by these results, this study is extended by evaluating several variants of selection strategies and probabilistic modeling approaches. The aim is to detect possible interactions between these two important components of evolutionary algorithms. Specifically, we use the selection strategies as defined for NSGA2, SPEA2, and IBEA algorithms, and the probabilistic models implemented as part of UMDA and CMA-ES, and a simple crossover operator (SBX). The recently introduced COCO framework comprising 55 bi-objective functions is used as the benchmark for the analysis. The results show that probabilistic modeling has an advantage over the classical genetic operator regardless of the selection method applied. Nevertheless, the results also show that some selection methods have a better performance when applied together with EDAs.

The Compact Genetic Algorithm is Efficient under Extreme Gaussian Noise

Practical optimization problems frequently include uncertainty about the quality measure, for example, due to noisy evaluations. Thus, they do not allow for a straightforward application of traditional optimization techniques. In these settings, randomized search heuristics such as evolutionary algorithms are a popular choice because they are often assumed to exhibit some kind of resistance to noise. Empirical evidence suggests that some algorithms, such as estimation of distribution algorithms (EDAs) are robust against a scaling of the noise intensity, even without resorting to explicit noise-handling techniques such as resampling. In this paper, we want to support such claims with mathematical rigor. We introduce the concept of graceful scaling in which the run time of an algorithm scales polynomially with noise intensity. We study a monotone fitness function over binary strings with additive noise taken from a Gaussian distribution. We show that myopic heuristics cannot efficiently optimize the function under arbitrarily intense noise without any explicit noise-handling. Furthermore, we prove that using a population does not help. Finally, we show that a simple EDA called the compact genetic algorithm can overcome the shortsightedness of mutation-only heuristics to scale gracefully with noise. We conjecture that recombinative genetic algorithms also have this property.

Novel dynamic diversity controlling EAs for coevolving optimal negotiation strategies

Finding optimal strategies for negotiation with incomplete information is a challenging issue in agent-based automated negotiation research. Although there are some previous works on finding the strategies through coevolutionary learning using evolutionary algorithms (EAs), their coevolving strategies tend to converge to non-global optima (which bring about ineffective negotiation outcomes for participating agents) due to biased coevolution and failures in coevolution. To cope with these drawbacks, this work introduces and compares novel genetic algorithms (GAs) and estimation of distribution algorithms (EDAs) that have additional capability of dynamic diversity control: (1) the dynamic diversity controlling GA (D2C-GA), (2) the dynamic diversity controlling EDA (D2C-EDA), (3) the improved D2C-GA (ID2C-GA) and (4) the improved D2C-EDA (ID2C-EDA). While D2C-GA and D2C-EDA adopt the novel diversification and refinement (DR) procedure, ID2C-GA and ID2C-EDA adopt the modified and enhanced DR (mDR) procedure with two additional local heuristics population repair and local neighborhood search. An extensive series of experiments were carried out to compare and evaluate the performance of the simple GA (S-GA), the simple EDA (S-EDA), and the novel GAs and EDAs in coevolving effective negotiation strategies of two self-interested negotiation agents for their various deadline combinations. Favorable empirical results showed that (i) ID2C-EDA could coevolve (near-)optimal negotiation strategies for all the considered cases due to its good generalization performance and (ii) it also generally outperformed S-GA, S-EDA, D2C-GA, D2C-EDA and ID2C-GA in terms of solution accuracy, coevolutionary search capability and average coevolution restart ratio. Interestingly, it was also found that the coevolution performance of ID2C-GA and ID2C-EDA is complementary in that ID2C-GA and ID2C-EDA generally achieved better results in the cases of equal and different deadlines, respectively.

On the Taxonomy of Optimization Problems Under Estimation of Distribution Algorithms

Understanding the relationship between a search algorithm and the space of problems is a fundamental issue in the optimization field. In this paper, we lay the foundations to elaborate taxonomies of problems under estimation of distribution algorithms (EDAs). By using an infinite population model and assuming that the selection operator is based on the rank of the solutions, we group optimization problems according to the behavior of the EDA. Throughout the definition of an equivalence relation between functions it is possible to partition the space of problems in equivalence classes in which the algorithm has the same behavior. We show that only the probabilistic model is able to generate different partitions of the set of possible problems and hence, it predetermines the number of different behaviors that the algorithm can exhibit. As a natural consequence of our definitions, all the objective functions are in the same equivalence class when the algorithm does not impose restrictions to the probabilistic model. The taxonomy of problems, which is also valid for finite populations, is studied in depth for a simple EDA that considers independence among the variables of the problem. We provide the sufficient and necessary condition to decide the equivalence between functions and then we develop the operators to describe and count the members of a class. In addition, we show the intrinsic relation between univariate EDAs and the neighborhood system induced by the Hamming distance by proving that all the functions in the same class have the same number of local optima and that they are in the same ranking positions. Finally, we carry out numerical simulations in order to analyze the different behaviors that the algorithm can exhibit for the functions defined over the search space [Formula: see text].

Analysis of Computational Time of Simple Estimation of Distribution Algorithms

Estimation of distribution algorithms (EDAs) are widely used in stochastic optimization. Impressive experimental results have been reported in the literature. However, little work has been done on analyzing the computation time of EDAs in relation to the problem size. It is still unclear how well EDAs (with a finite population size larger than two) will scale up when the dimension of the optimization problem (problem size) goes up. This paper studies the computational time complexity of a simple EDA, i.e., the univariate marginal distribution algorithm (UMDA), in order to gain more insight into EDAs complexity. First, we discuss how to measure the computational time complexity of EDAs. A classification of problem hardness based on our discussions is then given. Second, we prove a theorem related to problem hardness and the probability conditions of EDAs. Third, we propose a novel approach to analyzing the computational time complexity of UMDA using discrete dynamic systems and Chernoff bounds. Following this approach, we are able to derive a number of results on the first hitting time of UMDA on a well-known unimodal pseudo-boolean function, i.e., the LeadingOnes problem, and another problem derived from LeadingOnes, named BVLeadingOnes. Although both problems are unimodal, our analysis shows that LeadingOnes is easy for the UMDA, while BVLeadingOnes is hard for the UMDA. Finally, in order to address the key issue of what problem characteristics make a problem hard for UMDA, we discuss in depth the idea of ?margins? (or relaxation). We prove theoretically that the UMDA with margins can solve the BVLeadingOnes problem efficiently.

Effective Linkage Learning Using Low-Order Statistics and Clustering

The adoption of probabilistic models for selected individuals is a powerful approach for evolutionary computation. Probabilistic models based on high-order statistics have been used by estimation of distribution algorithms (EDAs), resulting better effectiveness when searching for global optima for hard optimization problems. This paper proposes a new framework for evolutionary algorithms, which combines a simple EDA based on order 1 statistics and a clustering technique in order to avoid the high computational cost required by higher order EDAs. The algorithm uses clustering to group genotypically similar solutions, relying that different clusters focus on different substructures and the combination of information from different clusters effectively combines substructures. The combination mechanism uses an information gain measure when deciding which cluster is more informative for any given gene position, during a pairwise cluster combination. Empirical evaluations effectively cover a comprehensive range of benchmark optimization problems.

A rigorous analysis of the compact genetic algorithm for linear functions

Estimation of distribution algorithms (EDAs) solve an optimization problem heuristically by finding a probability distribution focused around its optima. Starting with the uniform distribution, points are sampled with respect to this distribution and the distribution is changed according to the function values of the sampled points. Although there are many successful experiments suggesting the usefulness of EDAs, there are only few rigorous theoretical results apart from convergence results without time bounds. Here we present first rigorous runtime analyses of a simple EDA, the compact genetic algorithm (cGA), for linear pseudo-Boolean functions on n variables. We prove a general lower bound for all functions and a general upper bound for all linear functions. Simple test functions show that not all linear functions are optimized in the same runtime by the cGA.

A double-distribution statistical algorithm for composite laminate optimization

The paper proposes a new evolutionary algorithm termed Double-Distribution Optimization Algorithm (DDOA). DDOA belongs to the family of estimation of distribution algorithms (EDA) that build a statistical model of promising regions of the design space based on sets of good points and use it to guide the search. The efficiency of these algorithms is heavily dependent on the model accuracy. In this work, a generic framework for enhancing the model accuracy by incorporating statistical variable dependencies is presented. The proposed algorithm uses two distributions simultaneously: the marginal distributions of the design variables, complemented by the distribution of physically meaningful auxiliary variables. The combination of the two generates more accurate distributions of promising regions at a low computational cost. The paper demonstrates the efficiency of DDOA for three laminate optimization problems where the design variables are the fiber angles, and the auxiliary variables are integral quantities called lamination parameters. The results show that the reliability of DDOA in finding the optima is greater than that of simple EDA and a standard genetic algorithm, and that its advantage increases with the problem dimension.