SQG-Differential Evolution for difficult optimization problems under a tight function evaluation budget

In the context of industrial engineering, it is important to integrate efficient computational optimization methods in the product development process. Some of the most challenging simulation-based engineering design optimization problems are characterized by: a large number of design variables, the absence of analytical gradients, highly non-linear objectives and a limited function evaluation budget. Although a huge variety of different optimization algorithms is available, the development and selection of efficient algorithms for problems with these industrial relevant characteristics, remains a challenge. In this communication, a hybrid variant of Differential Evolution (DE) is introduced which combines aspects of Stochastic Quasi-Gradient (SQG) methods within the framework of DE, in order to improve optimization efficiency on problems with the previously mentioned characteristics. The performance of the resulting derivative-free algorithm is compared with other state-of-the-art DE variants on 25 commonly used benchmark functions, under tight function evaluation budget constraints of 1000 evaluations. The experimental results indicate that the new algorithm performs excellent on the 'difficult' (high dimensional, multi-modal, inseparable) test functions. The operations used in the proposed mutation scheme, are computationally inexpensive, and can be easily implemented in existing differential evolution variants or other population-based optimization algorithms by a few lines of program code as an non-invasive optional setting. Besides the applicability of the presented algorithm by itself, the described concepts can serve as a useful and interesting addition to the algorithmic operators in the frameworks of heuristics and evolutionary optimization and computing

Stochastic Optimization in Econometric Models – A Comparison of GA, SA and RSG

This paper shows that, in case of an econometric model with a high sensitivity to data, using stochastic optimization algorithms is better than using classical gradient techniques. In addition, we showed that the Repetitive Stochastic Guesstimation (RSG) algorithm –invented by Charemza-is closer to Simulated Annealing (SA) than to Genetic Algorithms (GAs), so we produced hybrids between RSG and SA to study their joint behavior. The evaluation of all algorithms involved was performed on a short form of the Romanian macro model, derived from Dobrescu (1996). The subject of optimization was the model’s solution, as function of the initial values (in the first stage) and of the objective functions (in the second stage). We proved that a priori information help “elitist “ algorithms (like RSG and SA) to obtain best results; on the other hand, when one has equal believe concerning the choice among different objective functions, GA gives a straight answer. Analyzing the average related bias of the model’s solution proved the efficiency of the stochastic optimization methods presented.underground economy, Laffer curve, informal activity, fiscal policy, transitionmacroeconomic model, stochastic optimization, evolutionary algorithms, Repetitive Stochastic Guesstimation

Metaheuristic design of feedforward neural networks: a review of two decades of research

Over the past two decades, the feedforward neural network (FNN) optimization has been a key interest among the researchers and practitioners of multiple disciplines. The FNN optimization is often viewed from the various perspectives: the optimization of weights, network architecture, activation nodes, learning parameters, learning environment, etc. Researchers adopted such different viewpoints mainly to improve the FNN's generalization ability. The gradient-descent algorithm such as backpropagation has been widely applied to optimize the FNNs. Its success is evident from the FNN's application to numerous real-world problems. However, due to the limitations of the gradient-based optimization methods, the metaheuristic algorithms including the evolutionary algorithms, swarm intelligence, etc., are still being widely explored by the researchers aiming to obtain generalized FNN for a given problem. This article attempts to summarize a broad spectrum of FNN optimization methodologies including conventional and metaheuristic approaches. This article also tries to connect various research directions emerged out of the FNN optimization practices, such as evolving neural network (NN), cooperative coevolution NN, complex-valued NN, deep learning, extreme learning machine, quantum NN, etc. Additionally, it provides interesting research challenges for future research to cope-up with the present information processing era

State-of-the-art in aerodynamic shape optimisation methods

Aerodynamic optimisation has become an indispensable component for any aerodynamic design over the past 60 years, with applications to aircraft, cars, trains, bridges, wind turbines, internal pipe flows, and cavities, among others, and is thus relevant in many facets of technology. With advancements in computational power, automated design optimisation procedures have become more competent, however, there is an ambiguity and bias throughout the literature with regards to relative performance of optimisation architectures and employed algorithms. This paper provides a well-balanced critical review of the dominant optimisation approaches that have been integrated with aerodynamic theory for the purpose of shape optimisation. A total of 229 papers, published in more than 120 journals and conference proceedings, have been classified into 6 different optimisation algorithm approaches. The material cited includes some of the most well-established authors and publications in the field of aerodynamic optimisation. This paper aims to eliminate bias toward certain algorithms by analysing the limitations, drawbacks, and the benefits of the most utilised optimisation approaches. This review provides comprehensive but straightforward insight for non-specialists and reference detailing the current state for specialist practitioners

A genetic-algorithms based evolutionary computational neural network for modelling spatial interaction data

Building a feedforward computational neural network model (CNN) involves two distinct tasks: determination of the network topology and weight estimation. The specification of a problem adequate network topology is a key issue and the primary focus of this contribution. Up to now, this issue has been either completely neglected in spatial application domains, or tackled by search heuristics (see Fischer and Gopal 1994). With the view of modelling interactions over geographic space, this paper considers this problem as a global optimization problem and proposes a novel approach that embeds backpropagation learning into the evolutionary paradigm of genetic algorithms. This is accomplished by interweaving a genetic search for finding an optimal CNN topology with gradient-based backpropagation learning for determining the network parameters. Thus, the model builder will be relieved of the burden of identifying appropriate CNN-topologies that will allow a problem to be solved with simple, but powerful learning mechanisms, such as backpropagation of gradient descent errors. The approach has been applied to the family of three inputs, single hidden layer, single output feedforward CNN models using interregional telecommunication traffic data for Austria, to illustrate its performance and to evaluate its robustness.