Nonlinear continuous global optimization by modified differential evolution

The task of global optimization is to find a point where the objective function obtains its most extreme value. Differential evolution (DE) is a population-based heuristic approach that creates new candidate solutions by combining several points of the same population. The algorithm has three parameters: amplification factor of the differential variation, crossover control parameter and population size. It is reported that DE is sensitive to the choice of these parameters. To improve the quality of the solution, in this paper, we propose a modified differential evolution introducing self-adaptive parameters, modified mutation and the inversion operator. We test our method with a set of nonlinear continuous optimization problems with simple bounds.Fundação para a Ciência e a Tecnologia (FCT

Adaptive multi-population inflationary differential evolution

This paper proposes a multi-population adaptive version of inflationary differential evolution algorithm. Inflationary differential evolution algorithm (IDEA) combines basic differential evolution (DE) with some of the restart and local search mechanisms of Monotonic Basin Hopping (MBH). In the adaptive version presented in this paper, the DE parameters CR and F are automatically adapted together with the size of the local restart bubble and the number of local restarts of MBH. The proposed algorithm implements a simple but effective mechanism to avoid multiple detections of the same local minima. The novel mechanism allows the algorithm to decide whether to start or not a local search. The algorithm has been extensively tested over more than fifty test functions from the competitions of the Congress on Evolutionary Computation (CEC), CEC 2005, CEC 2011 and CEC 2014, and compared against all the algorithms participating in those competitions. For each test function, the paper reports best, worst, median, mean and standard deviation values of the best minimum found by the algorithm. Comparisons with other algorithms participating in the CEC competitions are presented in terms of relative ranking, Wilcoxon tests and success rates. For completeness, the paper presents also the single population adaptive IDEA, that can adapt only CR and F, and shows that this simpler version can outperform the multi-population one if the radius of the restart bubble and the number of restarts are properly chosen

Advances in global optimization of high brightness beams

High brightness electron beams play an important role in accelerator-based applications such as driving X-ray free electron laser (FEL) radiation. In this paper, we report on advances in global beam dynamics optimization of an accelerator design using start-to-end simulations and a new parallel multi-objective differential evolution optimization method. The global optimization results in significant improvement of the final electron beam brightness

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

Adaptive distributed differential evolution

Due to the increasing complexity of optimization problems, distributed differential evolution (DDE) has become a promising approach for global optimization. However, similar to the centralized algorithms, DDE also faces the difficulty of strategies' selection and parameters' setting. To deal with such problems effectively, this article proposes an adaptive DDE (ADDE) to relieve the sensitivity of strategies and parameters. In ADDE, three populations called exploration population, exploitation population, and balance population are co-evolved concurrently by using the master-slave multipopulation distributed framework. Different populations will adaptively choose their suitable mutation strategies based on the evolutionary state estimation to make full use of the feedback information from both individuals and the whole corresponding population. Besides, the historical successful experience and best solution improvement are collected and used to adaptively update the individual parameters (amplification factor F and crossover rate CR) and population parameter (population size N), respectively. The performance of ADDE is evaluated on all 30 widely used benchmark functions from the CEC 2014 test suite and all 22 widely used real-world application problems from the CEC 2011 test suite. The experimental results show that ADDE has great superiority compared with the other state-of-the-art DDE and adaptive differential evolution variants