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This paper introduces MADEB, a Memetic Algebraic Differential Evolution algorithm for the Binary search space. MADEB has been applied to the Multidimensional Two-Way Number Partitioning Problem (MDTWNPP) and its main components are the binary differential mutation operator and a variable neighborhood descent procedure. The binary differential mutation is a concrete application of the abstract algebraic framework for the binary search space. The variable neighborhood descent is a local search procedure specifically designed for MDTWNPP. Experiments have been held on a widely accepted benchmark suite and MADEB is experimentally compared with respect to the current state-of-the-art algorithms for MDTWNPP. The experimental results clearly show that MADEB is the new state-of-the-art algorithm in the problem here investigated.

Motivated from the previously proposed algebraic framework for combinatorial optimization, here we introduce a novel formal languages-based perspective on discrete search spaces that allows to automatically derive algebraic evolutionary algorithms. The practical effect of the proposed approach is that the algorithm designer does not need to choose a solutions encoding and implement algorithmic procedures. Indeed, he/she only has to provide the group presentation of the discrete solutions of the problem at hand. Then, the proposed mechanism allows to automatically derive concrete implementations of a chosen evolutionary algorithms. Theoretical guarantees about the feasibility of the proposed approach are provided.

In this work we introduce a novel graph-based approach to elicit students’ communities. Teaching, in the blended learning environment, is delivered as a mixture of online and offline activities. While the online activities can be tracked and analysed in the Virtual Learning Environment, the offline activities fall out of the educators’ control scope. In this educational setting, communications take place using side channels, such as the instant messaging applications and social network platform. Using our approach, the students’ groupings and social interactions can be elicited by analysing the student-system interactions. The co-occurrence of interactions among the students give information about their social connections. This conveys information useful to elicit the students’ interaction graph and the student communities contained in it. Students’ leader-follower community structure can be elicited starting from the interaction network. This can empower teachers to plan and revise their Learning Designs as well as to identify situations that need teacher’s intervention, e.g. students at risk of failing the exam and/or dropping the studies.

In this work we introduce a novel Learning Analytics approach to identify students’ communities. The introduction of Learning Management Systems in higher education requires the educators to plan their Learning Design (LD) process with the online scenario in mind. We examined the blended learning environment where this process takes place in the Virtual Learning Environment. This allows the educators to track most of the students’ individual activities, but the communications may be excluded from tracking since the students can use side communications channels, such as face-to-face communication, instant messaging and social network platforms. Our approach, using the student-system interactions histories, helps to discover hidden relationships among the students. The elicited information about students’ groupings and social interactions’ evolution over time can be used by educators to adapt and improve their LD process, to find associations between students’ social interactions and their academic performance, as well as to promote team-based learning.

In this paper we propose an extension to the algebraic differential evolution approach for permutation based problems (DEP). Conversely from classical differential evolution, DEP is fully combinatorial and it is extended in two directions: new generating sets based on exchange and insertion moves are considered, and the case \(F>1\) is now allowed for the differential mutation operator. Moreover, also the crossover and selection operators of the original DEP have been modified in order to address the linear ordering problem with cumulative costs (LOPCC). The new DEP schemes are compared with the state-of-the-art LOPCC algorithms using a widely adopted benchmark suite. The experimental results show that DEP reaches competitive performances and, most remarkably, found 21 new best known solutions on the 50 largest LOPCC instances.

Particle Swarm Optimization (PSO) is a popular optimization technique based on swarm intelligence concepts. Estimation of Distribution Algorithms (EDAs) are a relatively new class of evolutionary algorithms which build a probabilistic model of the population dynamics and use this model to sample new individuals. Recently, the hybridization of PSO and EDAs is emerged as a new research trend. In this paper, we introduce a new hybrid approach that uses a mixture of Gaussian distributions. The obtained algorithm, called PSEDA, can be seen as an implementation of the PSO behaviour in the EDAs framework. Experiments on well known benchmark functions have been held and the performances of PSEDA are compared with those of classical PSO.