A new model of Hopfield network with fractional-order neurons for parameter estimation

In this work, we study an application of fractional-order Hopfield neural networks for optimization problem solving. The proposed network was simulated using a semi-analytical method based on Adomian decomposition,, and it was applied to the on-line estimation of time-varying parameters of nonlinear dynamical systems. Through simulations, it was demonstrated how fractional-order neurons influence the convergence of the Hopfield network, improving the performance of the parameter identification process if compared with integer-order implementations. Two different approaches for computing fractional derivatives were considered and compared as a function of the fractional-order of the derivatives: the Caputo and the Caputo–Fabrizio definitions. Simulation results related to different benchmarks commonly adopted in the literature are reported to demonstrate the suitability of the proposed architecture in the field of on-line parameter estimation.

A Road Map of Optimization Problem Solving Techniques, Nomenclature and Algorithms

Optimization problems are different from other mathematical problems in that they are able to discover solutions which are ideal or near ideal in accordance to the goals. Problems are not solved in one step, but we follow different sequence of steps to reach the solution. The steps could be to define problems, construct and solve models and evaluate and implement solutions. This paper presents an overall outlook of how a problem of optimization type can be solved

Boosting Combinatorial Problem Modeling with Machine Learning

In the past few years, the area of Machine Learning (ML) has witnessed tremendous advancements, becoming a pervasive technology in a wide range of applications. One area that can significantly benefit from the use of ML is Combinatorial Optimization. The three pillars of constraint satisfaction and optimization problem solving, i.e., modeling, search, and optimization, can exploit ML techniques to boost their accuracy, efficiency and effectiveness. In this survey we focus on the modeling component, whose effectiveness is crucial for solving the problem. The modeling activity has been traditionally shaped by optimization and domain experts, interacting to provide realistic results. Machine Learning techniques can tremendously ease the process, and exploit the available data to either create models or refine expert-designed ones. In this survey we cover approaches that have been recently proposed to enhance the modeling process by learning either single constraints, objective functions, or the whole model. We highlight common themes to multiple approaches and draw connections with related fields of research.

MULTI-CRITERIA PROGRAMMING METHODS AND PRODUCTION PLAN OPTIMIZATION PROBLEM SOLVING IN METAL INDUSTRY

This paper presents the production plan optimization in the metal industry considered as a multi-criteria programming problem. We first provided the definition of the multi-criteria programming problem and classification of the multicriteria programming methods. Then we applied two multi-criteria programming methods (the STEM method and the PROMETHEE method) in solving a problem of multi-criteria optimization production plan in a company from the metal industry. The obtained results indicate a high efficiency of the applied methods in solving the problem.

Peningkatan Kemampuan Pemecahan Masalah Prediksi Soal-Soal Ujian Nasional Mata Pelajaran Matematika Melalui Pendekatan Jigsaw Pada Peserta Didik Kelas IX A SMP Negeri 4 Boyolali Semester Genap Tahun Pelajaran 2012/2013

The purpose of this study was to describe the optimization problem solving skills predictions about national exam mathematics courses through Jigsaw approach at a ninth grade students of State Junior High School 4 Boyolali. Subject and source of research data were do students of class IX A. The methods of collecting data were questionnaires, documentation, and test. Data were analyzed using a critical and comparative analysis. Indicators of success or graduation used criteria 5.5 (scale 4) or 55 (scale 100) and a target of 100% completion. The procedure used a classroom action research study conducted in three cycles, the first cycle was as initial condition, while the second and third cycles were as action. The results of research suggest that: (1) the motivation of participants students in learning mathematics courses before cycle can be described increase in the result, namely from before cycle to the first cycle, an increase of before cycle is average of 56 to the first cycle of an average of 58 (4%), of the first cycle an average of 58 the second cycle to an average of 79 of 21 (36%). Thus, the higher motivation of learners shows an impact on learning outcomes. While the mathematics learning outcomes can be described increase in the result, namely from before cycle to the first cycle, an increase of before cycle average of 45 to the first cycle an average of 59 of 14 (31%), from the first cycle an average of 59 to the second cycle mean average 69 of 10 (17%). Finally it can be said that using jigsaw for optimization problem solving skills predictions about national exam mathematics courses is recommended.