Multiple Offspring Sampling Research Articles

SoftFEM: The Soft Finite Element Method

SummaryWhile the finite element method (FEM) has now reached full maturity both in academy and industry, its use in optimization pipelines remains either computationally intensive or cumbersome. In particular, currently used optimization schemes leveraging FEM still require the choice of dedicated optimization algorithms for a specific design problem, and a “black box” approach to FEM‐based optimization remains elusive. To this end, we propose here an integrated finite element‐soft computing method, ie, the soft FEM (SoftFEM), which integrates a finite element solver within a metaheuristic search wrapper. To illustrate this general method, we focus here on solid mechanics problems. For these problems, SoftFEM is able to optimize geometry changes and mechanistic measures based on geometry constraints and material properties inputs. From the optimization perspective, the use of a fitness function based on finite element calculation imposes a series of challenges. To bypass the limitations in search capabilities of the usual optimization techniques (local search and gradient‐based methods), we propose, instead a hybrid self adaptive search technique, the multiple offspring sampling (MOS), combining two metaheuristics methods: one population‐based differential evolution method and a local search optimizer. The formulation coupling FEM to the optimization wrapper is presented in detail and its flexibility is illustrated with three representative solid mechanics problems. More particularly, we propose here the MOS as the most versatile search algorithm for SoftFEM. A new method for the identification of nonfully determined parameters is also proposed.

An Insight into Bio-inspired and Evolutionary Algorithms for Global Optimization: Review, Analysis, and Lessons Learnt over a Decade of Competitions

Over the recent years, continuous optimization has significantly evolved to become the mature research field it is nowadays. Through this process, evolutionary algorithms had an important role, as they are able to obtain good results with limited resources. Among them, bio-inspired algorithms, which mimic cooperative and competitive behaviors observed in animals, are a very active field, with more proposals every year. This increment in the number of optimization algorithms is apparent in the many competitions held at corresponding special sessions in the last 10 years. In these competitions, several algorithms or ideas have become points of reference, and used as starting points for more advanced algorithms in following competitions. In this paper, we have obtained, for different real-parameter competitions, their benchmarks, participants, and winners (from the competitions’ website) and we review the most relevant algorithms and techniques, presenting the trajectory they have followed over the last years and how some of these works have deeply influenced the top performing algorithms of today. The aim is to be both a useful reference for researchers new to this interesting research topic and a useful guide for current researchers in the field. We have observed that there are several algorithms, like the Covariance Matrix Adaptation Evolution Strategy (CMA-ES), the Success-History based Adaptive Differential Evolution with Linear Population Size Reduction (L-SHADE), Mean-Variance Mapping Optimization (MVMO), and Multiple Offspring Sampling (MOS), which have obtained a strong influence over other algorithms. We have also suggested several techniques that are being widely adopted among the winning proposals, and that could be used for more competitive algorithms. Global optimization is a mature research field in continuous improvement, and the history of competitions provides useful information about the past that can help us to learn how to go forward in the future.

Bayesian Classifiers Applied to the Tennessee Eastman Process

Fault diagnosis includes the main task of classification. Bayesian networks (BNs) present several advantages in the classification task, and previous works have suggested their use as classifiers. Because a classifier is often only one part of a larger decision process, this article proposes, for industrial process diagnosis, the use of a Bayesian method called dynamic Markov blanket classifier that has as its main goal the induction of accurate Bayesian classifiers having dependable probability estimates and revealing actual relationships among the most relevant variables. In addition, a new method, named variable ordering multiple offspring sampling capable of inducing a BN to be used as a classifier, is presented. The performance of these methods is assessed on the data of a benchmark problem known as the Tennessee Eastman process. The obtained results are compared with naive Bayes and tree augmented network classifiers, and confirm that both proposed algorithms can provide good classification accuracies as well as knowledge about relevant variables.

Evaluating the Multiple Offspring Sampling framework on complex continuous optimization functions

In this contribution we present a study on the combination of Differential Evolution and the IPOP-CMA-ES algorithms. The hybrid algorithm has been constructed by using the Multiple Offspring Sampling framework, which allows the seamless combination of multiple metaheuristics in a dynamic algorithm capable of adjusting the participation of each of the composing algorithms according to their current performance. In this study we analyze the existing synergies, if any, emerging from the combination of the two algorithms. For this purpose, the COCO suite used in BBOB 2009 and 2010 Workshops has been used. The experimental results on the noiseless testbed show a robust behavior of the algorithm and a good scalability as the dimensionality increases. In the noisy testbed, the algorithm shows a good performance on functions with moderate to severe noise.