A comparative analysis of formulations for the Hamiltonian p-Median Problem

Tese de Mestrado, Estatística e Investigação Operacional , 2022, Universidade de Lisboa, Faculdade de CiênciasIn this dissertation we study the Hamiltonian p-Median Problem, a combinatorial optimization problem in which, given an undirected graph G = (V, E) and a cost for each edge, the objective is to find the cheapest way to partition the set of nodes into p subsets with each subset being connected by a single cycle. This is a problem which may therefore be seen as a generalization of the Travelling Salesman Problem (TSP). When working with MILP models for the TSP, sets of constraints to prevent feasible solutions with more than one cycle are added to an assignment formulation. Similarly, when working with such models for the HpMP, sets of constraints to prevent feasible solutions with more than p cycles can also be added to an assignment formulation, and these are often very similar to sets of constraints already used in models for the TSP, albeit with some modifications. However, these sets are not sufficient to guarantee every feasible solution has exactly p cycles, since it may have fewer than p cycles. To this end, additional sets of constraints for preventing solutions with less than p cycles may be introduced, and these will be the focal point of this work. The work begins with a brief introduction to the problem and some literature review. After that, several compact formulations for this problem are presented. The presentation of these models will be split into three parts. In the first part, a model upon which all other models are built is presented. The second part focuses on a model used to prevent solutions with more than p cycles, while the third part focuses on two models used to prevent solutions with less than p cycles (in which nodes are assigned to depots or cycles), accompanied by some valid inequalities. Finally, some of the models presented in this work are tested and the results and possibilities for future work are discussed

Activities for Mech E\u27s

This document will describe the development of a solution for enforcing the topics covered in the ME 329 - Mechanical System Design curriculum by bringing quality equipment to a classroom setting. The project Sponsor, Professor Lauren Cooper, has also noticed a lack of hands-on experience for many students entering this class. Our team is attempting to develop a solution for this problem. To better understand what students would want to learn, or would have liked to learn more about, we conducted surveys of past, present, and future students as well as conducted interviews with professors that have taught the course. We also researched past projects from different schools as well as articles of similar products that are and were on the market. All of this information led to the conclusion that students will most benefit from (and enjoy) a lab project where they first learn fundamental gear train concepts with an exploratory approach, then work on a project that combines the theoretical concepts learned in the course with the experimental results obtained from a physical apparatus. Through ideation, concept prototyping, functional decomposition, and morphological decision-making, we came up with a two-part solution. The solution will be a pair of activities that students will complete over a multi-week period. The first activity will be a modular, hands-on apparatus that students can configure with different parameters to see how these changes affect the system\u27s performance. In the second, students will apply their knowledge from the exploratory lab into a design activity that models a real-world scenario, in this case a wind turbine. To prototype the activities, we purchased a number of components, screws, and measuring devices. Many of the components came from a single online supplier, ServoCity. These components were picked for their configuration capability, being able to be arranged into many configurations. The rest of the components require only a small amount of modification or are 3D printed. Both designs were tested against technical engineering specifications, as well as at least some amount of user testing from current or former students and faculty. Both designs met the specifications, and we are confident they will serve well as solutions to the problem posed. In addition to creating prototypes, we also developed lesson plans and lab manuals for both activities. The former provides suggestions to professors for how to implement the activity including optimal group sizes, time to spend on each activity, and work to require of students. The latter prepares students to interact with the activities and walks them through guided activities to facilitate discovery of important concepts. The following report describes the background, objectives, design process, prototyping process, and verification process for this project as well as the recommendations and next steps for our Sponsor after receiving the results

The PHMC algorithm for simulations of dynamical fermions: II - Performance analysis

We compare the performance of the PHMC algorithm with the one of the HMC algorithm in practical simulations of lattice QCD. We show that the PHMC algorithm can lead to an acceleration of numerical simulations. It is demonstrated that the PHMC algorithm generates configurations carrying small isolated eigenvalues of the lattice Dirac operator and hence leads to a sampling of configuration space that is different from that of the HMC algorithm.Comment: Latex2e file, 6 figures, 31 page

Disorder induced critical phenomena in magnetically glassy Cu-Al-Mn alloys

Measurements of magnetic hysteresis loops in Cu-Al-Mn alloys of different Mn content at low temperatures are presented. The loops are smooth and continuous above a certain temperature, but exhibit a magnetization discontinuity below that temperature. Scaling analysis suggest that this system displays a disorder induced phase transition line. Measurements allow to determine the critical exponents $\beta=0.03\pm 0.01$ and $\beta \delta = 0.4 \pm 0.1$ in agreement with those reported recently [Berger et al., Phys. Rev. Lett. {\bf 85}, 4176 (2000)]Comment: 4 pages, 5 figure

Origin and Detectability of coorbital planets from radial velocity data

We analyze the possibilities of detection of hypothetical exoplanets in coorbital motion from synthetic radial velocity (RV) signals, taking into account different types of stable planar configurations, orbital eccentricities and mass ratios. For each nominal solution corresponding to small-amplitude oscillations around the periodic solution, we generate a series of synthetic RV curves mimicking the stellar motion around the barycenter of the system. We then fit the data sets obtained assuming three possible different orbital architectures: (a) two planets in coorbital motion, (b) two planets in a 2/1 mean-motion resonance, and (c) a single planet. We compare the resulting residuals and the estimated orbital parameters. For synthetic data sets covering only a few orbital periods, we find that the discrete radial velocity signal generated by a coorbital configuration could be easily confused with other configurations/systems, and in many cases the best orbital fit corresponds to either a single planet or two bodies in a 2/1 resonance. However, most of the incorrect identifications are associated to dynamically unstable solutions. We also compare the orbital parameters obtained with two different fitting strategies: a simultaneous fit of two planets and a nested multi-Keplerian model. We find that the nested models can yield incorrect orbital configurations (sometimes close to fictitious mean-motion resonances) that are nevertheless dynamically stable and with orbital eccentricities lower than the correct nominal solutions. Finally, we discuss plausible mechanisms for the formation of coorbital configurations, by the interaction between two giant planets and an inner cavity in the gas disk. For equal mass planets, both Lagrangian and anti-Lagrangian configurations can be obtained from same initial condition depending on final time of integration.Comment: 14 pages, 16 figures.2012. MNRAS, 421, 35

Development Of Decision Support System For Scheduling LPG Supply-Distribution At Teluk Semangka Port (Case Study: PT. Pertamina Persero)

PT Pertamina (Persero) as the main contributor for LPG supply and distribution in Indonesia relies on the VLGC (Very Large Gas Capacity) for upstream transportation mode. All upstream activities are happened at Teluk Semangka Port, which is the main terminal for import supply and regional distribution throughout Java and Sumatra. The complexity in scheduling VLGC caused time consuming and high cost (demurrage cost and charter cost). Current report stated that through 2007 until 2013, there is a significant demurrage cost increased. This condition can jeopardized the supply and distribution process because of large budget allocation for covering the demurrage cost along with VLGC charter cost. A Decision Support System (DSS) is developed to generate schedule for each operated VLGC that both save time and gives the user recommendation in reducing cost. Several factors are considered in designing the DSS, such as lifting prioritization, demurrage cost, charter cost, and VLGC utilization. Besides its ability to generate complex schedule, an easy to use interface is designed for user to interact with the DSS. From several trials using real data taken from company database, it resulted five operated VLGCs as the best number of VLGCs to be operated. Therefore, it can be a recommendation for deciding the number of operated VLGCs in the following year