Universities are encouraging the implementation of innovative methodologies and teaching strategies to develop an interactive and appealing educational environment where students are the focus of the learning process. In such a personalised learning environment, an increase of the students’ engagement and the improvement of the outcomes arise. MathE has been developed to help achieve this goal. Based on collaborative procedures, internet resources – both pre-existing and freely available as well as resources specifically conceived by the project team – and communities of practices, MathE intends to be a tool to nurture and stimulate the learning of Mathematics in higher education. This study introduces and describes the MathE platform, which is divided into three sections: Student’s Assessment, Library and Community of Practice. An in-depth description of the Student’s Assessment section is presented and an analysis of the results obtained from students, when using this feature of the platform, is also provided. After this, and based on the answers to an online survey, the impact of the MathE platform among students and teachers of eight countries is shown. Although the number of collected results is still scarce, it allows the recognition of a trend regarding the use of the material of the Student’s Assessment section for autonomous study. The results indicate the platform is well organized, with a satisfactory amount and diversity of questions and good interconnection between the various parts. Nevertheless, both teachers and students indicate that more questions should be introduced. The overall opinion about the MathE platform is very favourable.
In this study, we propose a multistart method based on an extended version of the Hooke and Jeeves (HJ) algorithm for computing multiple solutions of mixed variable optimization problems. The inequality and equality constraints of the problem are handled by a filter set methodology. The basic ideas present in the HJ algorithm, namely the exploratory and pattern moves, are extended to consider two objective functions and to handle continuous and integer variables simultaneously. This proposal is integrated into a multistart method as a local search procedure that is repeatedly invoked to converge to different global and non-global optimal solutions starting from randomly generated points. To avoid repeated convergence to previously computed solutions, the concept of region of attraction of an optimizer is implemented. The performance of the new method is tested on benchmark problems. Its effectiveness is emphasized by a comparison with a well-known solver.
Abstract. Multilocal programming aims to locate all the local solutions of an optimization problem. A stochastic method based on a multistart strategy and a derivative-free filter local search for solving general constrained optimization problems is presented. The filter methodology is integrated into a coordinate search paradigm in order to generate a set of trial approximations that might be acceptable if they improve the constraint violation or the objective function value relative to the current one. Preliminary numerical experiments with a benchmark set of problems show the effectiveness of the proposed method.
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