A Step Forward in Studying the Compact Genetic Algorithm

Estimation of distribution algorithms (EDAs) are a successful branch of evolutionary algorithms (EAs) that evolve a probabilistic model instead of a population. Analogous to genetic drift in EAs, EDAs also encounter the phenomenon that the random sampling in the model update can move the sampling frequencies to boundary values not justified by the fitness. This can result in a considerable performance loss. This work gives the first tight quantification of this effect for three EDAs and one ant colony optimizer, namely for the univariate marginal distribution algorithm, the compact genetic algorithm, population-based incremental learning, and the max-min ant system with iteration-best update. Our results allow to choose the parameters of these algorithms in such a way that within a desired runtime, no sampling frequency approaches the boundary values without a clear indication from the objective function. This paper for the Hot-off-the-Press track at GECCO 2020 summarizes the work Sharp Bounds for Genetic Drift in Estimation of Distribution Algorithms by B. Doerr and W. Zheng, which has been accepted for publication in the IEEE Transactions on Evolutionary Computation [5].

Recently, there has been a growing interest in developing evolutionary algorithms based on probabilistic modeling. They are called probabilistic model-building genetic algorithms (PMBGAs) or estimation of distribution algorithms (EDAs). In this scheme, the offspring population is generated according to the estimated probability density model of the parent instead of using recombination and mutation operators. In this paper, we have proposed PMBGAs in permutation domains using edge histogram based sampling algorithms (EHBSAs). Two types of sampling algorithms, without template (EHBSA/WO) and with template (EHBSA/WT), are presented. The results were tested in the TSP and showed EHBSA/WT worked fairly well with a small population size in the test problems used. It also worked better than well-known traditional two-parent recombination operators.

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.

Estimation of distribution algorithms are a promising method in evolutionary computation. In the estimation of distribution algorithms, instead of using conventional crossover and mutation operations, probabilistic models are used to sample the genetic information in the next population. Although the use of probabilistic models enables EDAs to have several schema simultaneously, it sometimes causes worse performance due to converse schemata. In this paper, estimation of distribution algorithms with niche separation mechanism is proposed. Coexistence schemata are also newly introduced, where schemata at the same loci but converse information. The proposed method splits population into two subpopulations if such coexistence schemata are found. One of subpopulations is used to constitute the next generation while the probabilistic model of another subpopulation is enqueued. The queued probabilistic model is used if the current population is converged. The experimental results on max-sat problems and Ising spin glass problems show the effectiveness of the proposed method.

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.

The Estimation of Distribution Algorithms(EDAs) is a new paradigm for Evolutionary Computation. This new class of algorithms generalizes Genetic Algorithms(GAs) by replacing the crossover and mutation operators by learning and sampling the probability distribution of the best individuals of the population at each iteration of the algorithm. In this paper, we review the EDAs for the solution of combinatorial optimization problems and optimization in continuous domains. The paper gives a brief overview of the multiobjective problems(MOP) and estimation of distribution algorithms(EDAs). We introduce a representative algorithm called RMMEDA (Regularity Model Based Multi-objective Estimation of Distribution Algorithm). In order to improve the convergence performance of the algorithm, we improve the traditional RM-MEDA. The improvement we make is using part of the parent population with better performance instead of the entire parent population to establish a more accurate manifold model, and the RM-MEDA based on elitist strategy theory is proposed. Experimental results show that the improved RM-MEDA performs better on the convergence metric and the algorithm runtime than the original one.KeywordsEDARMMEDAElitist Strategy

Estimation of distribution algorithm (EDA) is a new class of evolutionary algorithms with a wide range of real-world applications. However, it has been well known that the performance of EDA is not satisfactory enough if its population size is small. But to simply increase its population size may result in slow convergence. To the best knowledge of the authors', very few work has been done on improving the performance of EDA under small population size. This paper illustrates why EDA does not work well under small population size and proposes a novel approach termed as Over-Selection to boost EDA under small population size. Experimental results on several benchmark problems demonstrate that Over-Selection based EDA is often able to achieve a better solution without significantly increasing its time consumption when compared with the original version of EDA.

As faults are unavoidable in large scale multiprocessor systems, it is important to be able to determine which units of the system are working and which are faulty. System-level diagnosis is a long-standing realistic approach to detect faults in multiprocessor systems. Diagnosis is based on the results of tests executed on the system units. In this work we evaluate the performance of evolutionary algorithms applied to the diagnosis problem. Experimental results are presented for both the traditional genetic algorithm (GA) and specialized versions of the GA. We then propose and evaluate specialized versions of Estimation of Distribution Algorithms (EDA) for system-level diagnosis: the compact GA and Population-Based Incremental Learning both with and without negative examples. The evaluation was performed using four metrics: the average number of generations needed to find the solution, the average fitness after up to 500 generations, the percentage of tests that got to the optimal solution and the average time until the solution was found. An analysis of experimental results shows that more sophisticated algorithms converge faster to the optimal solution.

Evolutionary algorithms and elliptical copulas applied to continuous optimization problems

Communities are basic units of complex networks and understanding of their structure help us to understand the structure of a network. Communities are groups of nodes that have many links inside and few links outside them. Community detection in a network can be modeled as an optimization problem. We can use some measures such as Modularity and Community Score for evaluating the quality of a partition of nodes. In this paper, we present a new algorithm for detecting communities in networks based on an Estimation of Distribution Algorithm (EDA) with the assumption that the problem variables are independent. EDAs are those evolutionary algorithms that build and sample the probabilistic models of selected solutions instead of using crossover and mutation operators. In this paper, we assess our algorithm by synthetic and real data sets and compare it with other community detection algorithms.

The Pareto front (Pareto set) of a continuous optimization problem with m objectives is a (m-1) dimensional piecewise continuous manifold in the objective space (the decision space) under some mild conditions. Based on this regularity property in the objective space, we have recently developed several multiobjective estimation of distribution algorithms (EDAs). However, this property has not been utilized in the decision space. Using the regularity property in both the objective and decision space, this paper proposes a simple EDA for multiobjective optimization. Since the location information has not efficiently used in EDAs, a combination of EDA and differential evolution (DE) is suggested for improving the algorithmic performance. The hybrid method and the pure EDA method proposed in this paper, and a DE based method are compared on several test instances. Experimental results have shown that the algorithm with the proposed strategy is very promising.

Estimation of Distribution Algorithms (EDAs) are a set of algorithms that belong to the field of Evolutionary Computation. In EDAs there are neither crossover nor mutation operators. Instead, the new population of individuals is sampled from a probability distribution, which is estimated from a database that contains the selected individuals from the previous generation. Thus, the interrelations between the different variables that represent the individuals may be explicitly expressed through the joint probability distribution associated with the individuals selected at each generation.

DE/EDA: A new evolutionary algorithm for global optimization

Finding a good model and efficiently estimating the distribution is still an open challenge in estimation of distribution algorithms (EDAs). Factorization encoded by models in most of the EDAs are constrained. However for optimization of many real-world problems, finding the model capable of representing complex interactions without much computational complexity overhead is the key challenge. On the other hand factor graph which is the most natural graphical model for representing additively decomposable functions is rarely employed in EDAs. In this paper we introduce Factor Graph based EDA (FGEDA) which learns factor graph as the model and estimate the probability distribution represented by the learned factor graph using Markov blanket canonical factorization. The class of factorization that is employed for approximation of distribution in FGEDA is expanded relative to famous EDAs. We have used matrix factorization for learning the factor graph of the problem based on the pairwise mutual information between pair of variables. Gibbs sampling and BB-wise crossover are used to generate new samples. Empirical evaluation as well as theoretical analysis of the approach show the efficiency and power of FGEDA in the optimization of functions with complex interactions. It is showed experimentally that FGEDA outperform other well-known EDAs.

Decomposition to smaller sub-problems is a general approach in problem solving. Many of the real-world problems can be decomposed into a number of sub-problems which may be solved easier. Appropriate decomposition is a significant issue specially for optimization problems where the optimal solution is usually obtained by combining the solutions of sub-problems. Estimation of distribution algorithms (EDAs) are a type of evolutionary algorithms that learn a model of problem from the population of candidate solutions. This model is intended to capture the interactions between problem variables, thus facilitating problem decomposition and is used to generate new solutions. In this paper, a novel type of problems is presented that is designed to challenge the model building process in discrete EDAs. The main idea is to propose a set of problems that their candidate solutions can be simultaneously decomposed into different sub-problems. This means that the candidate solution of a problem may be interpreted by two or more different structure where only one is true, resulting in the optimal solution to that problem. Some of these decompositions or structures may be more likely according to the low-order statistics collected from the population of candidate solutions, but may not necessarily lead to the optimal solution. Learning the correct structure/decomposition is a challenge for the model building process in EDA. The experimental results show that the proposed problems are indeed difficult for EDAs even when expressive models such as Bayesian networks are used to capture the interactions in the problem.