Teaching Mathematics to Computer Scientists: Reflections and a Case Study

Mathematics, despite being the foundation of computer science, is nowadays often considered a totally separate subject. The fact that many jobs in computer science do not explicitly require any specific mathematical knowledge posed questions about the importance of mathematics within computer science undergraduate curricula. In many educational systems a prior high school knowledge of mathematics is often not a mandatory requirement to be enrolled into a degree of computer science. On the other hand, several studies report that mathematics is important to computer scientists since it provides essential analytical and critical skills and since many professional and research tasks in computer science require an in-depth understanding of mathematical concepts. From this assumption, this article proposes an analysis of the cohort of computer science' students, with a specific reference to British Universities, and identifies some challenges that lecturers of mathematical subjects normally face. On the basis of this analysis this article proposes two teaching techniques to promote effective learning. The proposed techniques aim at addressing the diversity of cohorts in terms of mathematical background and skepticism from part of the cohort of students to consider mathematics as an essential element of their education. Numerical results indicate the validity and effectiveness of the proposed teaching techniques

Swarm Robotics

This study analyzes and designs the Swarm intelligence (SI) that Self-organizing migrating algorithm (SOMA) represents to solve industrial practice as well as academic optimization problems, and applies them to swarm robotics. Specifically, the characteristics of SOMA are clarified, shaping the basis for the analysis of SOMA's strengths and weaknesses for the release of SOMA T3A, SOMA Pareto, and iSOMA, with outstanding performance, confirmed by well-known test suites from IEEE CEC 2013, 2015, 2017, and 2019. Besides, the dynamic path planning problem for swarm robotics is handled by the proposed algorithms considered as a prime instance. The computational and simulation results on Matlab have proven the performance of the novel algorithms as well as the correctness of the obstacle avoidance method for mobile robots and drones. Furthermore, two out of the three proposed versions achieved the tie for 3rd (the same ranking with HyDE-DF) and 5th place in the 100-Digit Challenge at CEC 2019, GECCO 2019, and SEMCCO 2019 competition, something that any other version of SOMA has yet to do. They show promising possibilities that SOMA and SI algorithms offer.Tato práce se zabývá analýzou a vylepšením hejnové inteligence, kterou představuje samoorganizující se migrační algoritmus s možností využití v průmyslové praxi a se zaměřením na hejnovou robotiku. Je analyzován algoritmus SOMA, identifikovány silné a slabé stránky a navrženy nové verze SOMA jako SOMA T3A, SOMA Pareto, iSOMA s vynikajícím výkonem, potvrzeným známými testovacími sadami IEEE CEC 2013, 2015, 2017 a 2019. Tyto verze jsou pak aplikovány na problém s dynamickým plánováním dráhy pro hejnovou robotiku. Výsledky výpočtů a simulace v Matlabu prokázaly výkonnost nových algoritmů a správnost metody umožňující vyhýbání se překážkám u mobilních robotů a dronů. Kromě toho dvě ze tří navržených verzí dosáhly na 3. a 5. místo v soutěži 100-Digit Challenge na CEC 2019, GECCO 2019 a SEMCCO 2019, což je potvrzení navržených inovací. Práce tak demonstruje nejen vylepšení SOMA, ale i slibné možnosti hejnové inteligence.460 - Katedra informatikyvyhově

Evolutionary framework with reinforcement learning-based mutation adaptation

Although several multi-operator and multi-method approaches for solving optimization problems have been proposed, their performances are not consistent for a wide range of optimization problems. Also, the task of ensuring the appropriate selection of algorithms and operators may be inefficient since their designs are undertaken mainly through trial and error. This research proposes an improved optimization framework that uses the benefits of multiple algorithms, namely, a multi-operator differential evolution algorithm and a co-variance matrix adaptation evolution strategy. In the former, reinforcement learning is used to automatically choose the best differential evolution operator. To judge the performance of the proposed framework, three benchmark sets of bound-constrained optimization problems (73 problems) with 10, 30 and 50 dimensions are solved. Further, the proposed algorithm has been tested by solving optimization problems with 100 dimensions taken from CEC2014 and CEC2017 benchmark problems. A real-world application data set has also been solved. Several experiments are designed to analyze the effects of different components of the proposed framework, with the best variant compared with a number of state-of-the-art algorithms. The experimental results show that the proposed algorithm is able to outperform all the others considered.</p

Generalised Pattern Search with Restarting Fitness Landscape Analysis

Fitness landscape analysis for optimisation is a technique that involves analysing black-box optimisation problems to extract pieces of information about the problem, which can beneficially inform the design of the optimiser. Thus, the design of the algorithm aims to address the specific features detected during the analysis of the problem. Similarly, the designer aims to understand the behaviour of the algorithm, even though the problem is unknown and the optimisation is performed via a metaheuristic method. Thus, the algorithmic design made using fitness landscape analysis can be seen as an example of explainable AI in the optimisation domain. The present paper proposes a framework that performs fitness landscape analysis and designs a Pattern Search (PS) algorithm on the basis of the results of the analysis. The algorithm is implemented in a restarting fashion: at each restart, the fitness landscape analysis refines the analysis of the problem and updates the pattern matrix used by PS. A computationally efficient implementation is also presented in this study. Numerical results show that the proposed framework clearly outperforms standard PS and another PS implementation based on fitness landscape analysis. Furthermore, the two instances of the proposed framework considered in this study are competitive with popular algorithms present in the literature

Differential evolution with an individual-dependent mechanism

Differential evolution (DE) is a well-known optimization algorithm that utilizes the difference of positions between individuals to perturb base vectors and thus generate new mutant individuals. However, the difference between the fitness values of individuals, which may be helpful to improve the performance of the algorithm, has not been used to tune parameters and choose mutation strategies. In this paper, we propose a novel variant of DE with an individual-dependent mechanism that includes an individual-dependent parameter (IDP) setting and an individual-dependent mutation (IDM) strategy. In the IDP setting, control parameters are set for individuals according to the differences in their fitness values. In the IDM strategy, four mutation operators with different searching characteristics are assigned to the superior and inferior individuals, respectively, at different stages of the evolution process. The performance of the proposed algorithm is then extensively evaluated on a suite of the 28 latest benchmark functions developed for the 2013 Congress on Evolutionary Computation special session. Experimental results demonstrate the algorithm's outstanding performance

DIFFERENTIAL EVOLUTION-BASED METHODS FOR NUMERICAL OPTIMIZATION

Ph.DDOCTOR OF PHILOSOPH

Novel Memetic Computing Structures for Continuous Optimisation

This thesis studies a class of optimisation algorithms, namely Memetic Computing Structures, and proposes a novel set of promising algorithms that move the first step towards an implementation for the automatic generation of optimisation algorithms for continuous domains. This thesis after a thorough review of local search algorithms and popular meta-heuristics, focuses on Memetic Computing in terms of algorithm structures and design philosophy. In particular, most of the design carried out during my doctoral studies is inspired by the lex parsimoniae, aka Ockham’s Razor. It has been shown how simple algorithms, when well implemented can outperform complex implementations. In order to achieve this aim, the design is always carried out by attempting to identify the role of each algorithmic component/operator. In this thesis, on the basis of this logic, a set of variants of a recently proposed algorithms are presented. Subsequently a novel memetic structure, namely Parallel Memetic Structure is proposed and tested against modern algorithms representing the state of the art in optimisation. Furthermore, an initial prototype of an automatic design platform is also included. This prototype performs an analysis on separability of the optimisation problem and, on the basis of the analysis results, designs some parts of the parallel structure. Promising results are included. Finally, an investigation of the correlation among the variables and problem dimensionality has been performed. An extremely interesting finding of this thesis work is that the degree of correlation among the variables decreases when the dimensionality increases. As a direct consequence of this fact, large scale problems are to some extent easier to handle than problems in low dimensionality since, due to the lack of correlation among the variables, they can effectively be tackled by an algorithm that performs moves along the axes

Predição da estrutura de proteínas off-lattice usando evolução diferencial multiobjetivo adaptativa

Protein Structure Prediction (PSP) can be considered one of the most challenging problems in Bioinformatics nowadays. When a protein is in its conformation state, the free energy is minimized. Evaluation of protein conformation is generally performed based on two values of the estimated free energy, i.e., those provided by intra and intermolecular interactions among atoms. Some recent experimental studies show that these interactions are in conflit, justifying the use of multiobjective optimization approaches to solve PSP. In this case, the energy optimization is performed separately, different from the mono-objective optimization which considers the sum of free energy. Differential Evolution (DE) is a technique based on Evolutionary Computation and represents an interesting alternative to solve multiobjective PSP. In this work, an optimizer based on DE is proposed to solve the PSP problem. Due to the great number of parameters, typical for evolutionary algorithms, this work also investigates adaptive parameters strategies. In experiments, a simple approach based on ED is evaluated for PSP. An evolution for this method, which incorporates concepts of the MOEA/D algorithm and parameter adaptation techniques is tested for a set of benchmarks in the multiobjective optimization context. The preliminary results for PSP (for six real proteins) are promising and those obtained for the benchmark set stands the proposed approach as a candidate to the state-of-art for multiobjective optimization.Fundação AraucáriaA Predição da Estrutura das Proteínas, conhecida como PSP (Protein Structure Prediction) pode ser considerada um dos problemas mais desafiadores da Bioinformática atualmente. Quando uma proteína está em seu estado de conformação nativa, a energia livre tende para um valor mínimo. Em geral, a predição da conformação de uma proteína por métodos computacionais é feita pela estimativa de dois valores de energia livre que são provenientes das interações intra e intermoleculares entre os átomos. Alguns estudos recentes indicam que estas interações estão em conflito, justificando o uso de abordagens baseadas em otimização multiobjetivo para a solução do PSP. Neste caso, a otimização destas energias é realizada separadamente, diferente da formulação mono-objetivo que considera a soma das energias. A Evolução Diferencial (ED) é uma técnica baseada em Computação Evolucionária e representa uma alternativa interessante para abordar o PSP. Este trabalho busca desenvolver um otimizador baseado no algoritmo de ED para o problema da Predição da Estrutura de Proteínas multiobjetivo. Este trabalho investiga ainda estratégias baseadas em parâmetros adaptativos para a evolução diferencial. Nicialmente avalia-se uma abordagem simples baseada em ED proposta para a solução do PSP. Uma evolução deste método que incorpora conceitos do algoritmo MOEA/D e adaptação de parâmetros é testada em um conjunto de problemas benchmark de otimização multiobjetivo. Os resultados preliminares obtidos para o PSP (para seis proteínas reais) são promissores e aqueles obtidos para o conjunto benchmark colocam a abordagem proposta como candidata para otimização multiobjetivo

Predição da estrutura de proteínas off-lattice usando evolução diferencial multiobjetivo adaptativa

Protein Structure Prediction (PSP) can be considered one of the most challenging problems in Bioinformatics nowadays. When a protein is in its conformation state, the free energy is minimized. Evaluation of protein conformation is generally performed based on two values of the estimated free energy, i.e., those provided by intra and intermolecular interactions among atoms. Some recent experimental studies show that these interactions are in conflit, justifying the use of multiobjective optimization approaches to solve PSP. In this case, the energy optimization is performed separately, different from the mono-objective optimization which considers the sum of free energy. Differential Evolution (DE) is a technique based on Evolutionary Computation and represents an interesting alternative to solve multiobjective PSP. In this work, an optimizer based on DE is proposed to solve the PSP problem. Due to the great number of parameters, typical for evolutionary algorithms, this work also investigates adaptive parameters strategies. In experiments, a simple approach based on ED is evaluated for PSP. An evolution for this method, which incorporates concepts of the MOEA/D algorithm and parameter adaptation techniques is tested for a set of benchmarks in the multiobjective optimization context. The preliminary results for PSP (for six real proteins) are promising and those obtained for the benchmark set stands the proposed approach as a candidate to the state-of-art for multiobjective optimization.Fundação AraucáriaA Predição da Estrutura das Proteínas, conhecida como PSP (Protein Structure Prediction) pode ser considerada um dos problemas mais desafiadores da Bioinformática atualmente. Quando uma proteína está em seu estado de conformação nativa, a energia livre tende para um valor mínimo. Em geral, a predição da conformação de uma proteína por métodos computacionais é feita pela estimativa de dois valores de energia livre que são provenientes das interações intra e intermoleculares entre os átomos. Alguns estudos recentes indicam que estas interações estão em conflito, justificando o uso de abordagens baseadas em otimização multiobjetivo para a solução do PSP. Neste caso, a otimização destas energias é realizada separadamente, diferente da formulação mono-objetivo que considera a soma das energias. A Evolução Diferencial (ED) é uma técnica baseada em Computação Evolucionária e representa uma alternativa interessante para abordar o PSP. Este trabalho busca desenvolver um otimizador baseado no algoritmo de ED para o problema da Predição da Estrutura de Proteínas multiobjetivo. Este trabalho investiga ainda estratégias baseadas em parâmetros adaptativos para a evolução diferencial. Nicialmente avalia-se uma abordagem simples baseada em ED proposta para a solução do PSP. Uma evolução deste método que incorpora conceitos do algoritmo MOEA/D e adaptação de parâmetros é testada em um conjunto de problemas benchmark de otimização multiobjetivo. Os resultados preliminares obtidos para o PSP (para seis proteínas reais) são promissores e aqueles obtidos para o conjunto benchmark colocam a abordagem proposta como candidata para otimização multiobjetivo