This diploma thesis deals with application optimization method in circular economy branch. The introduction is focused on explaining main features of the issue and its benefits for economy and environment. Afterwards are mentioned some obstacles, which are preventing transition from current waste management. Mathematical apparatus, which is used in practical section, is described in the thesis. Core of the thesis is mathematical optimization model, which is implemented in the GAMS software, and generator of input data is made in VBA. The model includes all of significant waste management options with respect to economic and enviromental aspect, including transport. Functionality is then demostrated on a small task. Key thesis result is application of the model on real data concerning Czech Republic. In conclusion an analysis of computation difficulty, given the scale of the task, is accomplished.

Táto diplomová práca sa zaoberá návrhom a konštrukciou elektromagnetickej, polohovacej platformy, pre testovanie nelineárnych riadiacich a identifikačných algoritmov. Platforma je založená na tvarovaní magnetického poľa v každom bode pomocou troch elektromagnetov a polohuje oceľovú guličku po dotykovom paneli ktorý sníma polohu tejto guličky. Platforma má slúžiť hlavne pre demonštráciu rôznych nelineárnych riadiacich algoritmov vo výukovom prostredí. Tri príklady takýchto algoritmov sú ukázané a overené v rámci tejto diplomovej práce.

This diploma thesis is focused on designing and specifying a linear quadratic regulator for longitudinal and lateral motion of the aircraft. The regulator is designed for a linear system obtained from a linearization of our nonlinear dynamic dynamic model of aircraft around the basic reference state (trimmed state-and-level ight). To nd a complete description of this reference state, some optimality problem has to be solved and the solution of this problem is called a trimmed state.

The thesis focuses on implementation of a hot runner controller for injection molds for plastic materials with a maximum number of 56 regulated zones. The first part of the thesis deals with already existing and used solutions of the given subject. The following part of the thesis describes the principles of temperature measurement by means of thermoelectric sensors, including their linearization as well as communication protocols MODBUS, EUROMAP 17. The identification of a regulated system ( heating zone) has been carried out before the hardware design. The development process is divided into some parts : system conception, hardware design, software development. The controller consists of measuring modules designed to collect data and handle power controllers for management of performance of heating elements. The necessary calculation power is integrated into the controllling computer. All parts of a hot runner controller are implemented taking into account the costs.

This research is concerned with the development of algorithmic approaches for solving problems that arise in the design and analysis of telecommunication networks, location-allocation distribution contexts, and intelligent transportation networks. Specifically, the corresponding problems addressed in these areas are a local access and transport area (LATA) network design problem, the discrete equal-capacity p-median problem (PMED), and the estimation of dynamic origin-destination path ows or trip tables in a general network. For the LATA network problem, we develop a model and apply the Reformulation-Linearization Technique (RLT) to construct various enhanced tightened versions of the proposed model. We also design efficient Lagrangian dual schemes for solving the linear programming relaxation of the various enhanced models, and construct an effective heuristic procedure for deriving good quality solutions in this process. Extensive computational results are provided to demonstrate the progressive tightness resulting from the enhanced formulations and their effect on providing good quality feasible solutions. The results indicate that the proposed procedures typically yield solutions having an optimality gap of less than 2% with respect to the derived lower bound, within a reasonable effort that involves the solution of a single linear program. For the discrete equal-capacity p-median problem, we develop various valid inequalities, a separation routine for generating cutting planes via specific members of such inequalities, as well as an enhanced reformulation that constructs a partial convex hull representation that subsumes an entire class of valid inequalities via its linear programming relaxation. We also propose suitable heuristic schemes for solving this problem, based on sequentially rounding the continuous relaxation solutions obtained for the various equivalent formulations of the problem. Extensive computational results are provided to demonstrate the effectiveness of the proposed valid inequalities, enhanced formulations, and heuristic schemes. The results indicate that the proposed schemes for tightening the underlying relaxations play a significant role in enhancing the performance of both exact and heuristic solution methods for solving this class of problems. For the estimation of dynamic path ows in a general network, we propose a parametric optimization approach to estimate time-dependent path ows, or origin-destination trip tables, using available data on link traffic volumes for a general road network. Our model assumes knowledge of certain time-dependent link ow contribution factors that are a dynamic generalization of the path-link incidence matrix for the static case. We propose a column generation approach that uses a sequence of dynamic shortest path subproblems in order to solve this problem. Computational results are presented on several variants of two sample test networks from the literature. These results indicate the viability of the proposed approach for use in an on-line mode in practice. Finally, we present a summary of our developments and results, and offer several related recommendations for future research. / Ph. D.

京都大学 / 新制・課程博士 / 博士(情報学) / 甲第24040号 / 情博第796号 / 新制||情||135(附属図書館) / 京都大学大学院情報学研究科システム科学専攻 / (主査)教授 加納 学, 教授 大塚 敏之, 教授 下平 英寿 / 学位規則第4条第1項該当 / Doctor of Informatics / Kyoto University / DGAM

This thesis considers two kinds of problems, motivated by practical applications in data center operations and maintenance. Data centers are the brain of the internet, each hosting as many as tens of thousands of IT devices, making them a considerable global energy consumption contributor (more than 1 percent of global power consumption). There is a large body of work at different layers aimed at reducing the total power consumption for data centers. One of the key places to save power is addressing the thermal heterogeneity in data centers by thermal-aware workload distribution. The corresponding optimization problem is challenging due to its combinatorial nature and the computational complexity of thermal models. In this thesis, a holistic theoretical approach is proposed for thermal-aware workload distribution which uses linearization to make the problem model-independent and easier to study. Two general optimization problems are defined. In the first problem, several cooling parameters and heat recirculation effects are considered, where two red-line temperatures are defined for idle and fully utilized servers to allow the cooling effort to be reduced. The resulting problem is a mixed integer linear programming problem which is solved approximately using a proposed heuristic. Numerical results confirm that the proposed approach outperforms commonly considered baseline algorithms and commercial solvers (MATLAB) and can reduce the power consumption by more than 10 percent. In the next problem, additional operational costs related to reliability of the servers are considered. The resulting problem is solved by a generalization of the proposed heuristics integrated with a Model Predictive Control (MPC) approach, where demand predictions are available. Finally, in the second type of problems, we address a problem in inventory management related to data center maintenance, where we develop an efficient dynamic programming algorithm to solve a lot-sizing problem. The algorithm is based on a key structural property that may be of more general interest, that of a just-in-time ordering policy. / Thesis / Doctor of Philosophy (PhD) / Data centers, each hosting as many as tens of thousands of IT devices, contribute to a considerable portion of energy usage worldwide (more than 1 percent of global power consumption). They also encounter other operational costs mostly related to reliability of devices and maintenance. One of the key places to reduce energy consumption is through addressing the thermal heterogeneity in data centers by thermal-aware work load distribution for the servers. This prevents hot spot generation and addresses the trade-off between IT and cooling power consumption, the two main power consump tion contributors. The corresponding optimization problem is challenging due to its combinatorial nature and the complexity of thermal models. In this thesis, we present a holistic approach for thermal-aware workload distribution in data centers, using lin earization to make the problem model-independent and simpler to study. Two quite general nonlinear optimization problems are defined. The results confirm that the proposed approach completed by a proposed heuristic solves the problems efficiently and with high precision. Finally, we address a problem in inventory management related to data center maintenance, where we develop an efficient algorithm to solve a lot-sizing problem that has a goal of reducing data center operational costs.

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This dissertation is devoted to the development of new flow-based formulations for the asymmetric traveling salesman problem (ATSP) and to the demonstration of their applicability in effectively solving some scheduling problems. The ATSP is commonly encountered in the areas of manufacturing planning and scheduling, and transportation logistics. The integration of decisions pertaining to production and shipping, in the supply chain context, has given rise to an additional and practical relevance to this problem especially in situations involving sequence-dependent setups and routing of vehicles. Our objective is to develop new ATSP formulations so that algorithms can be built by taking advantage of their relaxations (of integer variables, thereby, resulting in linear programs) to effectively solve large-size problems. In view of our objective, it is essential to have a formulation that is amenable to the development of an effective solution procedure for the underlying problem. One characteristic of a formulation that is helpful in this regard is its tightness. The tightness of a formulation usually refers to the quality of its approximation to the convex hull of integer feasible solutions. Another characteristic is its compactness. The compactness of a formulation is measured by the number of variables and constraints that are used to formulate a given problem. Our formulations for the ATSP and the scheduling problems that we address are both tight and compact. We present a new class of polynomial length formulations for the asymmetric traveling salesman problem (ATSP) by lifting an ordered path-based model using logical restrictions in concert with the Reformulation-Linearization Technique (RLT). We show that a relaxed version of this formulation is equivalent to a flow-based ATSP model, which, in turn, is tighter than the formulation based on the exponential number of Dantzig-Fulkerson-Johnson (DFJ) subtour elimination constraints. The proposed lifting idea is applied to derive a variety of new formulations for the ATSP, and a detailed analysis of these formulations is carried out to show that some of these formulations are the tightest among those presented in the literature. Computational results are presented to exhibit the relative tightness of our formulations and the efficacy of the proposed lifting process.> While the computational results demonstrate the efficacy of employing the proposed theoretical RLT and logical lifting ideas, yet it remains of practical interest to take due advantage of the tightest formulations. The key requirement to accomplish this is the ability to solve the underlying LP relaxations more effectively. One approach, to that end, is to solve these LP relaxations to (near-) optimality by using deflected subgradient methods on Lagrangian dual formulations. We solve the LP relaxation of our tightest formulation, ATSP6, to (near-) optimality by using a deflected subgradient algorithm with average direction strategy (SA_ADS) (see Sherali and Ulular [69]). We also use two nondifferentiable optimization (NDO) methods, namely, the variable target value method (VTVM) presented by Sherali et al. [66] and the trust region target value method (TRTV) presented by Lim and Sherali [46], on the Lagrangian dual formulation of ATSP6. The preliminary results show that the near-optimal values obtained by the VTVM on solving the problem in the canonical format are the closest to the target optimal values. Another approach that we use is to derive a set of strong valid inequalities based on our tighter formulations through a suitable surrogation process for inclusion within the more compact manageable formulations. Our computational results show that, when the dual optimal solution is available, the associated strong valid inequalities generated from our procedure can successfully lift the LP relaxation of a less tight formulation, such as ATSP2R¯, to be as tight as the tightest formulation, such as ATSP6. We extend our new formulations to include precedence constraints in order to enforce a partial order on the sequence of cities to be visited in a tour. The presence of precedence constraints within the ATSP framework is encountered quite often in practice. Examples include: disassembly optimization (see Sarin et al. [62]), and scheduling of wafers/ ICs on automated testing equipments in a semiconductor manufacturing facility (see Chen and Hsia [17]); among others. Our flow-based ATSP formulation can very conveniently capture these precedence constraints. We also present computational results to depict the tightness of our precedence-constrained asymmetric traveling salesman problem (PCATSP) formulations. We, then, apply our formulations to the hot strip rolling scheduling problem, which involves the processing of hot steel slabs, in a pre-specified precedence order, on one or more rollers. The single-roller hot strip rolling scheduling problem can be directly formulated as a PCATSP. We also consider the multiple-roller hot strip rolling scheduling problem. This gives rise to the multiple-asymmetric traveling salesman problem (mATSP). Not many formulations have been presented in the literature for the mATSP, and there are none for the mATSP formulations involving a precedence order among the cities to be visited by the salesmen, which is the case for the multiple-roller hot strip rolling scheduling problem. To begin with, we develop new formulations for the mATSP and show the validity of our formulations, and present computational results to depict their tightness. Then, we extend these mATSP formulations to include a pre-specified, special type of precedence order in which to process the slabs, and designate the resulting formulations as the restricted precedence-constrained multiple-asymmetric traveling salesman problem (rPCmATSP) formulations. We directly formulate the multiple-roller hot strip rolling scheduling problem as a rPCmATSP. Furthermore, we consider the hot strip rolling scheduling problem with slab selection in which not all slabs need to be processed. We model the single-roller hot strip rolling scheduling problem with slab selection as a multiple-asymmetric traveling salesman problem with exactly two traveling salesmen. Similarly, the multiple-roller hot strip rolling scheduling problem with slab selection is modeled as a multiple-asymmetric traveling salesman problem with (m+1) traveling salesmen. A series of computational experiments are conducted to exhibit the effectiveness of our formulations for the solution of hot strip rolling scheduling problems. Furthermore, we develop two mixed-integer programming algorithms to solve our formulations. These are based on Benders΄ decomposition [13] and are designated Benders΄ decomposition and Modified Benders΄ methods. In concert with a special type of precedence order presented in the hot strip rolling scheduling problems, we further introduce an adjustable density ratio of the associated precedence network and we use randomly generated test problems to study the effect of various density ratios in solving these scheduling problems. Our experimentation shows the efficacy of our methods over CPLEX. Finally, we present a compact formulation for the job shop scheduling problem, designated as JSCD (job shop conjunctive-disjunctive) formulation, which is an extension of our ATSP formulations. We use two test problems given in Muth and Thompson [53] to demonstrate the optimal schedule and the lower bound values obtained by solving the LP relaxations of our formulations. However, we observe that the lower bound values obtained by solving the LP relaxations of all variations of our JSCD formulation equal to the maximum total processing time among the jobs in the problem. / Ph. D.