The need for solving nonlinear optimization problems is pervasive in many fields. Particle swarm optimization, advantageous with the simple underlying implementation logic, and simultaneous perturbation stochastic approximation, which is famous for its saving in the computational power with the gradient-free attribute, are two solutions that deserve attention. Many researchers have exploited their merits in widely challenging applications. However, there is a known fact that both of them suffer from a severe drawback, non- effectively converging to the global best solution, because of the local “traps” spreading on the searching space. In this article, we propose two approaches to remedy this issue by combined their advantages. In the first algorithm, the gradient information helps optimize half of the particles at the initialization stage and then further updates the global best position. If the global best position is located in one of the local optima, the searching surface’s additional gradient estimation can help it jump out. The second algorithm expands the implementation of the gradient information to all the particles in the swarm to obtain the optimized personal best position. Both have to obey the rule created for updating the particle(s); that is, the solution found after employing the gradient information to the particle(s) has to perform more optimally. In this work, the experiments include five cases. The three previous methods with a similar theoretical basis and the two basic algorithms take participants in all five. The experimental results prove that the proposed two algorithms effectively improved the basic algorithms and even outperformed the previously designed three algorithms in some scenarios.

This paper studies the inverse source problem for the Helmholtz equation with a point source in a two dimensional domain. Given complete boundary data and appropriate discretization Tikhonov regularization is established to be an effective method at finding the point source. Furthermore, it was found that Tikhonov regularization can locate point sources even given significant noise, as well as incomplete boundary data in complicated domains.

Proven i dagens skola är ofta av klassisk karaktär, skrivna så att de endast syftar till naturvetenskapen som en produkt. Hur skall vi få proven mer motiverande för eleverna? Ett sätt kan vara att införa mer vardagsanknutna problem i proven. Arbetet syftar till att göra en jämförande studie bland ett antal naturvetenskapsstuderande gymnasieelever, där vi jämför elevers prestation och motivation vid klassiska faktabetonade fysikproblem kontra vardagsanknutna frågor. Detta följs upp av elevintervjuer. Avslutningsvis diskuteras elevernas resultat, redovisningar och intervjusvar, samt undersökningens tillförlitlighet.

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Keeping students engaged in the learning process is a challenge faced by most teachers. Instituting a bell schedule that requires them to make changes in their traditional instructional delivery may increase that challenge exponentially. The benefit of an extended period, also known as the block schedule, is that it permits the opportunity for teachers to alter their instruction with learning experiences that require more than 55 minutes by using engaging student-centered instruction. One reality of teaching on a block schedule is that many teachers lack the knowledge of effective strategies and rely on instructional devices they employed on a shorter time period. The purpose behind this work is to create a manual that demonstrates engaging student centered strategies and becomes a resource for teachers who are searching for instructional models to utilize in the block schedule. It does this in part by featuring actual hands-on strategies from three instructional models that can be readily used by classroom teachers. With the generative information about the models and activities that is provided in the manual, teachers are encouraged to create their own activities. Finally, the work provides solicited teacher feedback on the utility of the manual. / Ed. D.

In this thesis we consider the maximum number of points in $mathbb{R}^d$ which form exactly $t$ distinct triangles, which we denote by $F_d(t)$. We determine the values of $F_d(1)$ for all $dgeq3$, as well as determining $F_3(2)$. It was known from the work of Epstein et al. cite{Epstein} that $F_2(1) = 4$. Here we show somewhat surprisingly that $F_3(1) = 4$ and $F_d(1) = d + 1$, whenever $d geq 3$, and characterize the optimal point configurations. We also show that $F_3(2) = 6$ and give one such optimal point configuration. This is a higher dimensional extension of a variant of the distinct distance problem put forward by ErdH{o}s and Fishburn cite{ErdosFishburn}. / Master of Science / In this thesis we consider the following question: Given a number of triangles, t, where each of these triangles are different, we ask what is the maximum number of points that can be placed in d-dimensional space, such that every triplets of these points form the vertices of only the t allowable triangles. We answer this for every dimension, d when the number of triangles is t = 1, as well as show that when t = 2 triangle are in d = 3-dimensional space. This set of questions rises from considering the work of Erd˝os and Fishburn in higher dimensional space [EF].

The k–server problem is of significant importance to the theoretical computer science and the operations research community. In this problem, we are given k servers, their initial locations and a sequence of n requests that arrive one at a time. All these locations are points from some metric space and the cost of serving a request is given by the distance between the location of the request and the current location of the server selected to process the request. We must immediately process the request by moving a server to the request location. The objective in this problem is to minimize the total distance traveled by the servers to process all the requests. In this thesis, we present an empirical analysis of a new online algorithm for k-server problem. This algorithm maintains two solutions, online solution, and an approximately optimal offline solution. When a request arrives we update the offline solution and use this update to inform the online assignment. This algorithm is motivated by the Robust-Matching Algorithm [RMAlgorithm, Raghvendra, APPROX 2016] for the closely related online bipartite matching problem. We then give a comprehensive experimental analysis of this algorithm and also provide a graphical user interface which can be used to visualize execution instances of the algorithm. We also consider these problems under stochastic setting and implement a lookahead strategy on top of the new online algorithm. / MS / Motivated by real-time logistics, we study the online versions of the well-known bipartite matching and the k-server problems. In this problem, there are servers (delivery vehicles) located in different parts of the city. When a request for delivery is made, we have to immediately assign a delivery vehicle to this request without any knowledge of the future. Making cost-effective assignments, therefore, becomes incredibly challenging. In this thesis, we implement and empirically evaluate a new algorithm for the k-server and online matching problems.

Increasing the usability of software by integrating usability engineering into the development cycle has become common practice. Although usability engineering is effective, it can be expensive, and organizations want to receive the best possible returns on their investments. Oftentimes, however, organizations spend large sums of money collecting usability problem data through activities such as usability testing, but do not receive acceptable returns on those investments during redesign. The primary reason is that there is an almost complete lack of methods and tools for usability problem data analysis to transform raw usability data into effective inputs for developers. In this thesis, we develop an infrastructure for usability problem data analysis to address the need for better returns on usability engineering investments. The infrastructure consists of four main components: a framework, a process, tools, and semantic analysis technology. Embedded within the infrastructure is the User Action Framework, a conceptual framework of usability concepts, which is used to organize usability data. The process addresses extraction of usability problems from raw usability data, diagnosis of problems according to usability concepts, and reporting of problems in a form that is usable by developers. The tools leverage the framework and guide practitioners through the process, while the semantic analysis technology supplements the capabilities of the tools to automate parts of the process. / Master of Science

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