Stability of nonlinear impulsive higher order differential – fractional integral delay equations with nonlocal initial conditions

The aim of this paper is to investigate some types of stability such as generalized Hyers-Ulam- Rassias stability(G-H-U-R-stabile) and the relation with Hyers-Ulam(H-U-stabile) stable and Hyers-Ulam-Rassias stable (H-U-R-stabile) and generalized Hyers-Ulam stable (G-H-U- stable) to obtain which one guarantee to satisfy stability of equations included a nonlinear function some of them contains a delay time of solution and the other contain a vector of different order of  derivatives for the  solution to n-time  and vector of fractional order of integrals with different fractional orders and that was the for using a claculse of fractional calculus to satisfies the issue of this techniques. Moreover, the nonlocal initial   values for the proposal equation of nonlinear impulsive higher order differential – fractional integral delay time equations which are adding more interesting for nonlinear analytic object of nonlinear higher order integro – fractional order impulsive classes, and the impulsive difference of the equation has some necessary conditions to prove the results of solution to be stable with certain type has related with other types. The necessary and sufficient conditions which assumed on this nonlinear higher order integro-differential impulsive equation have been achieved the stability with interesting certain estimates obtain through the proving technique. Also the uniqueness of solution has been studied with same conditions was presented for stability and used for that issue a contraction fixed point theorem

Rulet Elektromanyetik Alan Optimizasyon (R-EFO) Algoritması

Meta-sezgisel optimizasyon algoritmalarının yerel arama performansları üzerinde etkili olan iki temel öğe seçim yöntemleri ve arama operatörleridir. Bu makale çalışmasında olasılıksal bir seçim yöntemi olan rulet tekerleğinin güncel bir meta-sezgisel arama tekniği olan elektromanyetik alan optimizasyon (electromagnetic field optimization, EFO) algoritmasının yerel arama performansı üzerindeki etkisi araştırılmaktadır. Elektromanyetik optimizasyon algoritmasında çözüm adayları topluluğu uygunluk değerlerine bağlı olarak pozitif, nötr ve negatif alanlara ayrılmaktadır. Bu üç alandan seçilen çözüm adayları ise arama sürecine rehberlik etmektedirler. Bu süreçte çözüm adayları açgözlü ve rastgele seçim yöntemleri ile belirlenmektedir. Bu makale çalışmasında ise negatif alandan çözüm adaylarının seçimi için rulet tekniği kullanılmaktadır. Deneysel çalışmalarda literatürdeki en güncel sürekli değer problemleri olan CEC17 test seti kullanılmıştır. Deneysel çalışma sonuçları istatistiksel olarak ikili karşılaştırmalarda kullanılan wilcoxon runk sum test ile analiz edilmiştir. Analiz sonuçlarına göre rulet seçim yöntemi EFO algoritmasının arama performansını kayda değer şekilde artırmaktadır

Predominant Cognitive Learning Particle Swarm Optimization for Global Numerical Optimization

Particle swarm optimization (PSO) has witnessed giant success in problem optimization. Nevertheless, its optimization performance seriously degrades when coping with optimization problems with a lot of local optima. To alleviate this issue, this paper designs a predominant cognitive learning particle swarm optimization (PCLPSO) method to effectively tackle complicated optimization problems. Specifically, for each particle, a new promising exemplar is constructed by letting its personal best position cognitively learn from a better personal experience randomly selected from those of others based on a novel predominant cognitive learning strategy. As a result, different particles preserve different guiding exemplars. In this way, the learning effectiveness and the learning diversity of particles are expectedly improved. To eliminate the dilemma that PCLPSO is sensitive to the involved parameters, we propose dynamic adjustment strategies, so that different particles preserve different parameter settings, which is further beneficial to promote the learning diversity of particles. With the above techniques, the proposed PCLPSO could expectedly compromise the search intensification and diversification in a good way to search the complex solution space properly to achieve satisfactory performance. Comprehensive experiments are conducted on the commonly adopted CEC 2017 benchmark function set to testify the effectiveness of the devised PCLPSO. Experimental results show that PCLPSO obtains considerably competitive or even much more promising performance than several representative and state-of-the-art peer methods

Machine learning assisted optimization with applications to diesel engine optimization with the particle swarm optimization algorithm

A novel approach to incorporating Machine Learning into optimization routines is presented. An approach which combines the benefits of ML, optimization, and meta-model searching is developed and tested on a multi-modal test problem; a modified Rastragin\u27s function. An enhanced Particle Swarm Optimization method was derived from the initial testing. Optimization of a diesel engine was carried out using the modified algorithm demonstrating an improvement of 83% compared with the unmodified PSO algorithm. Additionally, an approach to enhancing the training of ML models by leveraging Virtual Sensing as an alternative to standard multi-layer neural networks is presented. Substantial gains were made in the prediction of Particulate matter, reducing the MMSE by 50% and improving the correlation R^2 from 0.84 to 0.98. Improvements were made in models of PM, NOx, HC, CO, and Fuel Consumption using the method, while training times and convergence reliability were simultaneously improved over the traditional approach