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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.

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. In this study, we propose an extended version of the Hooke and Jeeves algorithm that uses a simple heuristic to handle integer and/or binary variables and a filter set methodology to handle constraints. This proposal is integrated into a multistart method as a local solver and it is repeatedly called in order to compute different optimal solutions. Then, the best of all stored optimal solutions is selected as the global optimum. The performance of the new method is tested on benchmark problems. Its effectiveness is emphasized by a comparison with other well-known stochastic solvers.

Abstract. A mixed-integer nonlinear programming problem (MINLP) is a problem with continuous and integer variables and at least, one nonlinear function. This kind of problem appears in a wide range of real applications and is very difficult to solve. The difficulties are due to the nonlinearities of the functions in the problem and the integrality restrictions on some variables. When they are nonconvex then they are the most difficult to solve above all. We present a methodology to solve nonsmooth nonconvex MINLP problems based on a branch and bound paradigm and a stochastic strategy. To solve the relaxed subproblems at each node of the branch and bound tree search, an algorithm based on a multistart strategy with a coordinate search filter methodology is implemented. The produced numerical results show the robustness of the proposed methodology.

The digital transformation that the world is facing has a strong impact in the professional occupations and job profiles in the factories of the future context, requiring the need of upskilling and re-qualification of the workforce. Taking this into account, an Industrial Collaborative Educational Design (ICoED) is presented comprising three stages and eight steps, and considering a democratic and collaborative participation of the different stakeholders, namely the managers, educators and learners, each one providing its own perspective on the design of the training programme. In this co-design process, the analysis of the skills' gap is a crucial task to prepare the initial stage of the process, particularly identifying the needs in terms of soft and hard skills. The proposed ICoED process was applied to solve an upskilling problem of an industrial metal stamping company, with the participants performing three workshops to execute the eight steps, reaching a training programme with five modules, each one settled with proper activities, resources and infrastructures.

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