Current advancements in nuclear reactor core design are pushing reactor cores towards greater heterogeneity in an attempt to make nuclear power more sustainable in terms of fuel utilization and long-term disposal needs. These new designs are now being limited by the accuracy of the core simulators/methods. Increasing attention has been given to full core transport as the flux module in future core simulators. However, the current transport methods, due to their significant memory and computational time requirements, are not practical for whole core calculations. While most researchers are working on developing new acceleration and phase space parallelization techniques for the current fine mesh transport methods, this dissertation focuses on the development of a practical heterogeneous coarse mesh transport method. In this thesis, a heterogeneous coarse mesh transport method is extended from two to three dimensions in Cartesian geometry and new techniques are developed to reduce the strain on computational resources. The high efficiency of the method is achieved by decoupling the problem into a series of fixed source calculations in smaller sub-volume elements (e.g. coarse meshes). This decoupling lead to shifting the computation time to a priori calculations of response functions in unique sub-volumes in the system. Therefore, the method is well suited for large problems with repeated geometry such as those found in nuclear reactor cores. Even though the response functions can be generated with any available existing fine-mesh (deterministic or stochastic) code, a stochastic method was selected in this dissertation. Previous work in two dimensions used discrete polynomial expansions that are better suited for treating discrete variables found in pure deterministic transport methods. The amount of data needed to represent very heterogeneous problems accurately became quite large making the three dimensional extension impractical. The deterministic method was thus replaced by a stochastic response function generator making the transition to continuous variables fairly simple. This choice also improves the geometry handling capability of the coarse mesh method.

This thesis aims to review and analyze the scheduling problem in general and Job Shop Scheduling Problem (JSSP) in particular and the solution techniques applied to these problems. The JSSP is the most general and popular hard combinational optimization problem in manufacturing systems. For the past sixty years, an enormous amount of research has been carried out to solve these problems. The literature review showed the inherent shortcomings of solutions to scheduling problems. This has directed researchers to develop hybrid approaches, as no single technique for scheduling has yet been successful in providing optimal solutions to these difficult problems, with much potential for improvements in the existing techniques. The hybrid approach complements and compensates for the limitations of each individual solution technique for better performance and improves results in solving both static and dynamic production scheduling environments. Over the past years, hybrid approaches have generally outperformed simple Genetic Algorithms (GAs). Therefore, two novel priority heuristic rules are developed: Index Based Heuristic and Hybrid Heuristic. These rules are applied to benchmark JSSP and compared with popular traditional rules. The results show that these new heuristic rules have outperformed the traditional heuristic rules over a wide range of benchmark JSSPs. Furthermore, a hybrid GA is developed as an alternate scheduling approach. The hybrid GA uses the novel heuristic rules in its key steps. The hybrid GA is applied to benchmark JSSPs. The hybrid GA is also tested on benchmark flow shop scheduling problems and industrial case studies. The hybrid GA successfully found solutions to JSSPs and is not problem dependent. The hybrid GA performance across the case studies has proved that the developed scheduling model can be applied to any real-world scheduling problem for achieving optimal or near-optimal solutions. This shows the effectiveness of the hybrid GA in real-world scheduling problems. In conclusion, all the research objectives are achieved. Finaly, the future work for the developed heuristic rules and the hybrid GA are discussed and recommendations are made on the basis of the results.

This thesis aims to review and analyze the scheduling problem in general and Job Shop Scheduling Problem (JSSP) in particular and the solution techniques applied to these problems. The JSSP is the most general and popular hard combinational optimization problem in manufacturing systems. For the past sixty years, an enormous amount of research has been carried out to solve these problems. The literature review showed the inherent shortcomings of solutions to scheduling problems. This has directed researchers to develop hybrid approaches, as no single technique for scheduling has yet been successful in providing optimal solutions to these difficult problems, with much potential for improvements in the existing techniques. The hybrid approach complements and compensates for the limitations of each individual solution technique for better performance and improves results in solving both static and dynamic production scheduling environments. Over the past years, hybrid approaches have generally outperformed simple Genetic Algorithms (GAs). Therefore, two novel priority heuristic rules are developed: Index Based Heuristic and Hybrid Heuristic. These rules are applied to benchmark JSSP and compared with popular traditional rules. The results show that these new heuristic rules have outperformed the traditional heuristic rules over a wide range of benchmark JSSPs. Furthermore, a hybrid GA is developed as an alternate scheduling approach. The hybrid GA uses the novel heuristic rules in its key steps. The hybrid GA is applied to benchmark JSSPs. The hybrid GA is also tested on benchmark flow shop scheduling problems and industrial case studies. The hybrid GA successfully found solutions to JSSPs and is not problem dependent. The hybrid GA performance across the case studies has proved that the developed scheduling model can be applied to any real-world scheduling problem for achieving optimal or near-optimal solutions. This shows the effectiveness of the hybrid GA in real-world scheduling problems. In conclusion, all the research objectives are achieved. Finaly, the future work for the developed heuristic rules and the hybrid GA are discussed and recommendations are made on the basis of the results. / Board of Trustees, Endowment Fund Project, KPK University of Engineering and Technology (UET), Peshawar and Higher Education Commission (HEC), Pakistan

Benchmark calculations for the validation of the coupled neutron kinetics/thermohydraulic code complex DYN3D-ATHLET are described. Two benchmark problems concerning hypothetical accident scenarios with leaks in the steam system for a VVER-440 type reactor and the TMI-1 PWR have been solved. The first benchmark task has been defined by FZR in the frame of the international association "Atomic Energy Research" (AER), the second exercise has been organised under the auspices of the OECD. While in the first benchmark the break of the main steam collector in the sub-critical hot zero power state of the reactor was considered, the break of one of the two main steam lines at full reactor power was assumed in the OECD benchmark. Therefore, in this exercise the mixing of the coolant from the intact and the defect loops had to be considered, while in the AER benchmark the steam collector break causes a homogeneous overcooling of the primary circuit. In the AER benchmark, each participant had to use its own macroscopic cross section libraries. In the OECD benchmark, the cross sections were given in the benchmark definition. The main task of both benchmark problems was to analyse the re-criticality of the scrammed reactor due to the overcooling. For both benchmark problems, a good agreement of the DYN3D-ATHLET solution with the results of other codes was achieved. Differences in the time of re-criticality and the height of the power peak between various solutions of the AER benchmark can be explained by the use of different cross section data. Significant differences in the thermohydraulic parameters (coolant temperature, pressure) occurred only at the late stage of the transient during the emergency injection of highly borated water. In the OECD benchmark, a broader scattering of the thermohydraulic results can be observed, while a good agreement between the various 3D reactor core calculations with given thermohydraulic boundary conditions was achieved. Reasons for the differences in the thermohydraulics were assumed in the difficult modelling of the vertical once-through steam generator with steam superheating. Sensitivity analyses which considered the influence of the nodalisation and the impact of the coolant mixing model were performed for the DYN3D-ATHLET solution of the OECD benchmark. The solution of the benchmarks essentially contributed to the qualification of the code complex DYN3D-ATHLET as an advanced tool for the accident analysis for both VVER type reactors and Western PWRs.

Benchmark calculations for the validation of the coupled neutron kinetics/thermohydraulic code complex DYN3D-ATHLET are described. Two benchmark problems concerning hypothetical accident scenarios with leaks in the steam system for a VVER-440 type reactor and the TMI-1 PWR have been solved. The first benchmark task has been defined by FZR in the frame of the international association "Atomic Energy Research" (AER), the second exercise has been organised under the auspices of the OECD. While in the first benchmark the break of the main steam collector in the sub-critical hot zero power state of the reactor was considered, the break of one of the two main steam lines at full reactor power was assumed in the OECD benchmark. Therefore, in this exercise the mixing of the coolant from the intact and the defect loops had to be considered, while in the AER benchmark the steam collector break causes a homogeneous overcooling of the primary circuit. In the AER benchmark, each participant had to use its own macroscopic cross section libraries. In the OECD benchmark, the cross sections were given in the benchmark definition. The main task of both benchmark problems was to analyse the re-criticality of the scrammed reactor due to the overcooling. For both benchmark problems, a good agreement of the DYN3D-ATHLET solution with the results of other codes was achieved. Differences in the time of re-criticality and the height of the power peak between various solutions of the AER benchmark can be explained by the use of different cross section data. Significant differences in the thermohydraulic parameters (coolant temperature, pressure) occurred only at the late stage of the transient during the emergency injection of highly borated water. In the OECD benchmark, a broader scattering of the thermohydraulic results can be observed, while a good agreement between the various 3D reactor core calculations with given thermohydraulic boundary conditions was achieved. Reasons for the differences in the thermohydraulics were assumed in the difficult modelling of the vertical once-through steam generator with steam superheating. Sensitivity analyses which considered the influence of the nodalisation and the impact of the coolant mixing model were performed for the DYN3D-ATHLET solution of the OECD benchmark. The solution of the benchmarks essentially contributed to the qualification of the code complex DYN3D-ATHLET as an advanced tool for the accident analysis for both VVER type reactors and Western PWRs.

Chorin’s method, Incremental Pressure Correction Scheme (IPCS) and Crank-Nicolson’s method (CN) are three numerical methods that were investigated in this study. These methods were here used for solving the incompressible Navier-Stokes equations, which describe the motion of an incompressible fluid, in three different benchmark problems. The methods were stabilized using residual based artificial viscosity, which was introduced to avoid instability. The methods were compared in terms of accuracy and computational time. Furthermore, a theoretical study of adaptivity was made, based on an a posteriori error estimate and an adjoint problem. The implementation of the adaptivity is left for future studies. In this study we consider the following three well-known benchmark problems: laminar 2D flow around a cylinder, Taylor-Green vortex and lid-driven cavity problem. The difference of the computational time for the three methods were in general relatively small and differed depending on which problem that was investigated. Furthermore the accuracy of the methods also differed in the benchmark problems, but in general Crank-Nicolson’s method gave less accurate results. Moreover the stabilization technique worked well when the kinematic viscosity of the fluid was relatively low, since it managed to stabilize the numerical methods. In general the solution was affected in a negative way when the problem could be solved without stabilization for higher viscosities.

This paper deals with multi-objective optimization problems (MOOP). It is explained, what solutions in multi-objetive search space are optimal and how are optimal (non-dominated) solutions found in the set of feasible solutions. Afterwards, principles of NSGA-II, MOPSO and GDE3 algorithms are described. In the following chapters, benchmark metrics and problems are introduced. In the last part of this paper, all the three algorithms are compared based on several benchmark metrics.