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

Limited Evaluation Cooperative Co-evolutionary Differential Evolution for Large-scale Neuroevolution

Many real-world control and classification tasks involve a large number of features. When artificial neural networks (ANNs) are used for modeling these tasks, the network architectures tend to be large. Neuroevolution is an effective approach for optimizing ANNs; however, there are two bottlenecks that make their application challenging in case of high-dimensional networks using direct encoding. First, classic evolutionary algorithms tend not to scale well for searching large parameter spaces; second, the network evaluation over a large number of training instances is in general time-consuming. In this work, we propose an approach called the Limited Evaluation Cooperative Co-evolutionary Differential Evolution algorithm (LECCDE) to optimize high-dimensional ANNs. The proposed method aims to optimize the pre-synaptic weights of each post-synaptic neuron in different subpopulations using a Cooperative Co-evolutionary Differential Evolution algorithm, and employs a limited evaluation scheme where fitness evaluation is performed on a relatively small number of training instances based on fitness inheritance. We test LECCDE on three datasets with various sizes, and our results show that cooperative co-evolution significantly improves the test error comparing to standard Differential Evolution, while the limited evaluation scheme facilitates a significant reduction in computing time

Comparing Evolutionary Operators, Search Spaces, and Evolutionary Algorithms in the Construction of Facial Composites

Facial composite construction is one of the most successful applications of interactive evolutionary computation. In spite of this, previous work in the area of composite construction has not investigated the algorithm design options in detail. We address this issue with four experiments. In the first experiment a sorting task is used to identify the 12 most salient dimensions of a 30-dimensional search space. In the second experiment the performances of two mutation and two recombination operators for interactive genetic algorithms are compared. In the third experiment three search spaces are compared: a 30-dimensional search space, a mathematically reduced 12-dimensional search space, and a 12-dimensional search space formed from the 12 most salient dimensions. Finally, we compare the performances of an interactive genetic algorithm to interactive differential evolution. Our results show that the facial composite construction process is remarkably robust to the choice of evolutionary operator(s), the dimensionality of the search space, and the choice of interactive evolutionary algorithm. We attribute this to the imprecise nature of human face perception and differences between the participants in how they interact with the algorithms. Povzetek: Kompozitna gradnja obrazov je ena izmed najbolj uspešnih aplikacij interaktivnega evolucijskega ra?cunanja. Kljub temu pa do zdaj na podro?cju kompozitne gradnje niso bile podrobno raziskane možnosti snovanja algoritma. To vprašanje smo obravnavali s štirimi poskusi. V prvem je uporabljeno sortiranje za identifikacijo 12 najbolj izstopajo?cih dimenzij 30-dimenzionalnega preiskovalnega prostora. V drugem primerjamo u?cinkovitost dveh mutacij in dveh rekombinacijskih operaterjev za interaktivni genetski algoritem. V tretjem primerjamo tri preiskovalne prostore: 30-dimenzionalni, matemati?cno reducirani 12-dimenzionalni in 12-dimenzionalni prostor sestavljen iz 12 najpomembnejših dimenzij. Na koncu smo primerjali uspešnost interaktivnega genetskega algoritma z interaktivno diferencialno evolucijo. Rezultati kažejo, da je proces kompozitne gradnje obrazov izredno robusten glede na izbiro evolucijskega operatorja(-ev), dimenzionalnost preiskovalnega prostora in izbiro interaktivnega evolucijskega algoritma. To pripisujemo nenatan?cni naravi percepcije in razlikam med interakcijami uporabnikov z algoritmom

Differential evolution with an evolution path: a DEEP evolutionary algorithm

Utilizing cumulative correlation information already existing in an evolutionary process, this paper proposes a predictive approach to the reproduction mechanism of new individuals for differential evolution (DE) algorithms. DE uses a distributed model (DM) to generate new individuals, which is relatively explorative, whilst evolution strategy (ES) uses a centralized model (CM) to generate offspring, which through adaptation retains a convergence momentum. This paper adopts a key feature in the CM of a covariance matrix adaptation ES, the cumulatively learned evolution path (EP), to formulate a new evolutionary algorithm (EA) framework, termed DEEP, standing for DE with an EP. Without mechanistically combining two CM and DM based algorithms together, the DEEP framework offers advantages of both a DM and a CM and hence substantially enhances performance. Under this architecture, a self-adaptation mechanism can be built inherently in a DEEP algorithm, easing the task of predetermining algorithm control parameters. Two DEEP variants are developed and illustrated in the paper. Experiments on the CEC'13 test suites and two practical problems demonstrate that the DEEP algorithms offer promising results, compared with the original DEs and other relevant state-of-the-art EAs

Differential Evolution-based 3D Directional Wireless Sensor Network Deployment Optimization

Wireless sensor networks (WSNs) are applied more and more widely in real life. In actual scenarios, 3D directional wireless sensors (DWSs) are constantly employed, thus, research on the real-time deployment optimization problem of 3D directional wireless sensor networks (DWSNs) based on terrain big data has more practical significance. Based on this, we study the deployment optimization problem of DWSNs in the 3D terrain through comprehensive consideration of coverage, lifetime, connectivity of sensor nodes, connectivity of cluster headers and reliability of DWSNs. We propose a modified differential evolution (DE) algorithm by adopting CR-sort and polynomial-based mutation on the basis of the cooperative coevolutionary (CC) framework, and apply it to address deployment problem of 3D DWSNs. In addition, to reduce computation time, we realize implementation of message passing interface (MPI) parallelism. As is revealed by the experimentation results, the modified algorithm proposed in this paper achieves satisfying performance with respect to either optimization results or operation time