Multidisciplinary design optimization (MDO) for large-scale engineering problems poses many challenges (e.g., the design of an efficient concurrent paradigm for global optimization based on disciplinary analyses, expensive computations over vast data sets, etc.) This work focuses on the application of distributed schemes for massively parallel architectures to MDO problems, as a tool for reducing computation time and solving larger problems. The specific problem considered here is configuration optimization of a high speed civil transport (HSCT), and the efficient parallelization of the embedded paradigm for reasonable design space identification. Two distributed dynamic load balancing techniques (random polling and global round robin with message combining) and two necessary termination detection schemes (global task count and token passing) were implemented and evaluated in terms of effectiveness and scalability to large problem sizes and a thousand processors. The effect of certain parameters on execution time was also inspected. Empirical results demonstrated stable performance and effectiveness for all schemes, and the parametric study showed that the selected algorithmic parameters have a negligible effect on performance. / Master of Science

This study presents a new Python-based novel framework, in a distributed computing environment for multidisciplinary design optimization (MDO) called DELWARX. DELWARX also includes a transonic flutter analysis approach that is computationally very efficient, yet accurate enough for conceptual design and optimization studies. This transonic flutter analysis approach is designed for large aspect-ratio wings and attached flow. The framework employs particle swarm optimization with penalty functions for exploring optimal Transonic Truss Braced Wing (TTBW) aircraft design, similar to the Boeing 737-800 type of mission with a cruise Mach of 0.8, a range of 3115 n miles, and 162 passengers, with two different objective functions, the fuel weight and the maximum take-off gross weight, while satisfying all the required constraints. Proper memory management is applied to effectively address memory-related issues, which are often a limiting factor in distributed computing. The parallel implementation in MDO using 60 processors allowed a reduction in the wall-clock time by 96% which is around 24 times faster than the optimization using a single processor. The results include a comparison of the TTBW designs for the medium-range missions with and without the flutter constraint. Importantly, the framework achieves extremely low computation times due to its parallel optimization capability, retains all the previous functionalities of the previous Virginia Tech MDO framework, and replaces the previously employed linear flutter analysis with a more accurate nonlinear transonic flutter computation. These features of DELWARX are expected to facilitate a more accurate MDO study for innovative transport aircraft configurations operating in the transonic flight regime. High-fidelity CFD simulation is performed to verify the result obtained from extended Strip theory based aerodynamic analysis method. An approach is presented to develop a deep neural network (DNN)-based surrogate model for fast and accurate prediction of flutter constraints in multidisciplinary design optimization (MDO) of Transonic Truss Braced Wing (TTBW) aircraft in the transonic region. The integration of the surrogate model in the MDO framework shows lower computation times than the MDO with nonlinear flutter analysis. The developed surrogate models can predict the optimum design. The wall-clock time of the design analysis method was reduced by 1500 times as compared to the result implemented in the previous framework, DELWARX. / Doctor of Philosophy / The current study presents DELWARX, a novel Python-based framework specifically engineered for the optimization of aircraft designs, with a primary focus on enhancing the performance of aircraft wings under transonic conditions (speeds approaching the speed of sound). This advancement is particularly pertinent for aircraft with a mission analogous to the Boeing 737-800, which necessitates a harmonious balance between speed, range, passenger capacity, and fuel efficiency. A salient feature of DELWARX is its adeptness in analyzing and optimizing wing flutter, a critical issue where wings may experience hazardous vibrations at certain velocities. This is particularly vital for wings characterized by a high aspect ratio (wings that are long and narrow), presenting a substantial challenge in the domain of aircraft design. DELWARX surpasses preceding methodologies by implementing a sophisticated computational technique known as particle swarm optimization, analogous to the collective movement observed in bird flocks, integrated with penalty functions that serve to exclude design solutions that fail to meet predefined standards. This approach is akin to navigating through a maze with specific pathways rendered inaccessible due to certain constraints. The efficiency of DELWARX is markedly enhanced by its ability to distribute computational tasks across 60 processors, achieving a computation speed that is 24 times faster than that of a single-processor operation. This distribution results in a significant reduction of overall computation time by 96%, representing a substantial advancement in processing efficiency. Further, DELWARX introduces an enhanced level of precision in its operations. It supplants former methods of flutter analysis with a more sophisticated, nonlinear approach tailored for transonic speeds. Consequently, the framework's predictions and optimization strategies for aircraft wing designs are imbued with increased reliability and accuracy. Moreover, DELWARX also integrates a Deep Neural Network (DNN), an advanced form of artificial intelligence, to swiftly and precisely predict flutter constraints. This integration manifests as a highly intelligent system capable of instantaneously estimating the performance of various designs, thereby expediting the optimization process. DELWARX employs high-fidelity Computational Fluid Dynamics (CFD) simulations to verify its findings. These simulations utilize intricate models to simulate the aerodynamics of air flow over aircraft wings, thereby ensuring that the optimized designs are not only theoretically sound but also pragmatically effective. In conclusion, DELWARX represents a significant leap in the field of multidisciplinary design optimization. It offers a robust and efficient tool for the design of aircraft wings, especially in the context of transonic flight. This framework heralds a new era in the optimization of aircraft designs, enabling more innovative and efficient solutions in the aerospace industry.

<p>Based on the compressed sensing theorem, we present the integrated software and hardware platform for developing a total-variation based image restoration algorithm by applying prior image information and free-form deformation fields for image guided therapy. The core algorithm we developed solves the image restoration problem for handling missing structures in one image set with prior information, and it enhances the quality of the image and the anatomical information of the volume of the on-board computed tomographic (CT) with limited-angle projections. Through the use of the algorithm, prior anatomical CT scans were used to provide additional information to help reduce radiation doses associated with the improved quality of the image volume produced by on-board Cone-Beam CT, thus reducing the total radiation doses that patients receive and removing distortion artifacts in 3D Digital Tomosynthesis (DTS) and 4D-DTS. The proposed restoration algorithm enables the enhanced resolution of temporal image and provides more anatomical information than conventional reconstructed images.</p><p>The performance of the algorithm was determined and evaluated by two built-in parameters in the algorithm, i.e., B-spline resolution and the regularization factor. These parameters can be adjusted to meet different requirements in different imaging applications. Adjustments also can determine the flexibility and accuracy during the restoration of images. Preliminary results have been generated to evaluate the image similarity and deformation effect for phantoms and real patient's case using shifting deformation window. We incorporated a graphics processing unit (GPU) and visualization interface into the calculation platform, as the acceleration tools for medical image processing and analysis. By combining the imaging algorithm with a GPU implementation, we can make the restoration calculation within a reasonable time to enable real-time on-board visualization, and the platform potentially can be applied to solve complicated, clinical-imaging algorithms.</p> / Dissertation

A less-than-truckload (LTL) carrier typically delivers shipments less than 10,000 pounds (classified as LTL shipment). The size of the shipment in LTL networks provides ample opportunities for consolidation. LTL carriers have focused on hub-and-spoke based consolidation to realize economies of scale. Generally, hub-and-spoke systems work as follows: the shipment is picked up from the shipper and brought to an origin terminal, which is the entry point into the hub-and-spoke system. From the terminal, the freight is sent to the first hub, where it is sorted and consolidated with other shipments, and then sent on to a second hub. It is finally sent from the second hub to the destination terminal, which is the exit point of the hub-and-spoke system. However, the flow of shipments is often more complicated in practice. In an attempt to reduce sorting costs, load planners sometimes take this hub-and-spoke infrastructure and modify it considerably to maximize their truck utilization while satisfying service constraints. Decisions made by a load planner may have a cascading effect on load building throughout the network. As a result, decentralized load planning may result in expensive global solutions. Academic as well as industrial researchers have adapted a hierarchical approach to design the hub-and-spoke networks: generate the hub-and-spoke network, route shipments within this hub-and-spoke network (generate a load plan) and finally, balance the empty trailers. We present mathematical models and heuristics for each of the steps involved in the design of the hub-and-spoke network. The heuristics are implemented in a user-friendly graphical tool that can help understand patterns of freight flow and provide insights into the design of the hub-and-spoke network. We also solved the load planning sub-problem in a parallel computation environment to achieve significant speed-ups. Because of the quick solution times, the tool lays the foundation to address pressing further research questions such as deciding location and number of hubs. We have used data provided by Roadway Parcel Services, Inc. (RPS), now FedEx Ground, as a case-study for the heuristics. Our solutions rival the existing industry solutions which have been a product of expensive commercial software and knowledge acquired by the network designers in the industry.

This thesis is concerned with problems of using computers to interpret scenes from television camera pictures. In particular, it tackles the problem of interpreting the picture in terms of lines and curves, rather like an artist's line drawing. This is very time consuming if done by a single, serial processor. However, if many processors were used simultaneously it could be done much more rapidly. In this thesis the task of line and curve extraction is expressed in terms of constraints, in a form that is susceptible to parallel computation. Iterative algorithms to perform this task have been designed and tested. They are proved to be convergent and to achieve the computation specified. Some previous work on the design of properly convergent, parallel algorithms has drawn on the mathematics of optimisation by relaxation. This thesis develops the use of these techniques for applying "continuity constraints" in line and curve description. First, the constraints are imposed "almost everywhere" on the grey-tone picture data, in two dimensions. Some "discontinuities" - places where the constraints are not satisfied - remain, and they form the lines and curves required for picture interpretation Secondly, a similar process is applied along each line or curve to segment it. Discontinuities in the angle of the tangent along the line or curve mark the positions of vertices. In each case the process is executed in parallel throughout the picture. It is shown that the specification of such a process as an optimisation problem is non-convex and this means that an optimal solution cannot necessarily be found in a reasonable time A method is developed for efficiently achieving a good sub-optimal solution. A parallel array processor is a large array of processor cells which can act simultaneously, throughout a picture. A software emulator of such a processor array was coded in C and a POP-2 based high level language, PARAPIC, to drive it was written and used to validate the parallel algorithms developed in the thesis It is argued that the scope, in a vision system, of parallel methods such as those exploited in this work is extensive. The implications for the design of hardware to perform low-level vision are discussed and it is suggested that a machine consisting of fewer, more powerful cells than in a parallel array processor would execute the parallel algorithms more efficiently.

O presente trabalho tem como objetivo o desenvolvimento de um sistema voltado à solução de problemas relacionados à Engenharia do Vento Computacional. Para o tratamento das estruturas turbulentas, a Simulação das Grandes Escalas é empregada. Esta metodologia resolve diretamente as estruturas que governam a dinâmica local do escoamento (grandes escalas) e utiliza modelos para resolver as escalas com características mais universais (pequenas escalas). Neste estudo, os efeitos sub-malha são obtidos a partir do modelo clássico de Smagorinsky. Na análise numérica, o método dos elementos finitos é avaliado a partir da utilização de elementos hexaédricos e uma formulação baseada nas equações governantes de escoamentos quase-incompressíveis. Para reduzir o requerimento de memória computacional, esquemas explícitos para solução de sistemas de equações são empregados. O primeiro aspecto a ser abordado para o desenvolvimento do sistema proposto é a redução do tempo de processamento. Partindo do algoritmo desenvolvido por [Petry, 2002], desenvolvese um estudo a cerca de técnicas computacionais de alto desempenho visando acelerar o processamento dos problemas. Assim, apresenta-se um comparativo entre alocações estática e dinâmica de vetores e matrizes, juntamente a implementação do paralelismo de memória compartilhada utilizando diretivas OpenMP. A verificação do aumento da velocidade de processamento é desenvolvida simulando o escoamento em um domínio contendo um corpo imerso aerodinamicamente rombudo. As técnicas utilizadas permitiram a obtenção de um aumento de aproximadamente cinco vezes em relação ao código originalmente avaliado. Uma importante dificuldade na avaliação de escoamentos externos está na solução numérica de problemas advectivo-dominantes. O esquema de Taylor-Galerkin explícito-iterativo, originalmente presente no código e validado para escoamentos internos, mostrou-se inadequado para avaliação do escoamento externo proposto, apresentando perturbações no campo de pressões e não convergindo para a solução correta do problema. Estas instabilidades persistiram em uma versão alternativa desenvolvida, a qual utilizava funções de interpolação de igual ordem para solução da pressão e velocidade. Para uma análise de escoamentos não confinados, é implementado o esquema temporal de dois passos utilizando funções de interpolação para velocidade e pressão de mesma ordem. Esta configuração apresentou resultados físicos de boa qualidade e importante redução no tempo de processamento. Após a identificação da alternativa que permitiu a avaliação dos resultados sem a presença de perturbações, apresenta-se a análise do escoamento sobre um prisma quadrado bidimensional, privilegiando o monitoramento da velocidade, pressão e energia cinética total da turbulência na linha central do domínio e nas proximidades do obstáculo. Esta avaliação é efetuada em malhas com configurações uniformes e irregulares para um número de Reynolds igual a 22000. / Development of a system to solve problems related to Computational Wind Engineering is the main aim of this work. In order to treat turbulent structures, Large Eddy Simulation is employed. This methodology compute directly scales governing local flow dynamics (large eddies) and it use models to solve those with universal character (small eddies). In this study, the sub-grid effects are considered using the standard Smagorinsky model. In the numerical analysis, hexahedral finite elements are used and a formulation based on the governing equations of quasi-compressible flows. To reduce the computational memory request, explicit schemes to solve the equations system are used. In order to reduce CPU time, an algorithm developed by [Petry, 2002] is evaluated and high-performance techniques aiming to accelerate the problem solution are studied. Thus, it is showed a comparison between dynamic and static allocations of vectors and matrices associated to the implementation of shared-memory parallelization using OpenMP directives. The speed up verification is developed simulating the flow around an immersed bluff body. As a consequence of the techniques employed here, an acceleration of approximately five times with respect of the original computational code is obtained. An important difficulty in the external flow evaluation is the numerical solution of convection dominated flows. The Taylor-Galerkin explicit-iterative scheme, (originally used by the program), which was validated for confined flows, did not present good results for external flows simulations and pressure field perturbations were observed. These instabilities were persevered even in an alternative version, where interpolations functions with the same order were used to compute velocity and pressure (in the original version, constant pressure field at element level were employed). To analyze unbounded flows accurately, a two-step explicit scheme using velocity and pressure interpolation functions with the same order was implemented. This configuration presented physical results with good quality and achieve an important reduction in the processing time. After identification of the best alternative without perturbations of the pressure field, the numerical simulation of the flow around a two-dimensional square cylinder was investigated favoring velocity, pressure and total kinetic energy evaluations along the mid line of the domain and in the obstacle vicinity. These evaluations were effectuated with uniform and stretched meshes for a Reynolds number equal to 22000.

O presente trabalho tem como objetivo o desenvolvimento de um sistema voltado à solução de problemas relacionados à Engenharia do Vento Computacional. Para o tratamento das estruturas turbulentas, a Simulação das Grandes Escalas é empregada. Esta metodologia resolve diretamente as estruturas que governam a dinâmica local do escoamento (grandes escalas) e utiliza modelos para resolver as escalas com características mais universais (pequenas escalas). Neste estudo, os efeitos sub-malha são obtidos a partir do modelo clássico de Smagorinsky. Na análise numérica, o método dos elementos finitos é avaliado a partir da utilização de elementos hexaédricos e uma formulação baseada nas equações governantes de escoamentos quase-incompressíveis. Para reduzir o requerimento de memória computacional, esquemas explícitos para solução de sistemas de equações são empregados. O primeiro aspecto a ser abordado para o desenvolvimento do sistema proposto é a redução do tempo de processamento. Partindo do algoritmo desenvolvido por [Petry, 2002], desenvolvese um estudo a cerca de técnicas computacionais de alto desempenho visando acelerar o processamento dos problemas. Assim, apresenta-se um comparativo entre alocações estática e dinâmica de vetores e matrizes, juntamente a implementação do paralelismo de memória compartilhada utilizando diretivas OpenMP. A verificação do aumento da velocidade de processamento é desenvolvida simulando o escoamento em um domínio contendo um corpo imerso aerodinamicamente rombudo. As técnicas utilizadas permitiram a obtenção de um aumento de aproximadamente cinco vezes em relação ao código originalmente avaliado. Uma importante dificuldade na avaliação de escoamentos externos está na solução numérica de problemas advectivo-dominantes. O esquema de Taylor-Galerkin explícito-iterativo, originalmente presente no código e validado para escoamentos internos, mostrou-se inadequado para avaliação do escoamento externo proposto, apresentando perturbações no campo de pressões e não convergindo para a solução correta do problema. Estas instabilidades persistiram em uma versão alternativa desenvolvida, a qual utilizava funções de interpolação de igual ordem para solução da pressão e velocidade. Para uma análise de escoamentos não confinados, é implementado o esquema temporal de dois passos utilizando funções de interpolação para velocidade e pressão de mesma ordem. Esta configuração apresentou resultados físicos de boa qualidade e importante redução no tempo de processamento. Após a identificação da alternativa que permitiu a avaliação dos resultados sem a presença de perturbações, apresenta-se a análise do escoamento sobre um prisma quadrado bidimensional, privilegiando o monitoramento da velocidade, pressão e energia cinética total da turbulência na linha central do domínio e nas proximidades do obstáculo. Esta avaliação é efetuada em malhas com configurações uniformes e irregulares para um número de Reynolds igual a 22000. / Development of a system to solve problems related to Computational Wind Engineering is the main aim of this work. In order to treat turbulent structures, Large Eddy Simulation is employed. This methodology compute directly scales governing local flow dynamics (large eddies) and it use models to solve those with universal character (small eddies). In this study, the sub-grid effects are considered using the standard Smagorinsky model. In the numerical analysis, hexahedral finite elements are used and a formulation based on the governing equations of quasi-compressible flows. To reduce the computational memory request, explicit schemes to solve the equations system are used. In order to reduce CPU time, an algorithm developed by [Petry, 2002] is evaluated and high-performance techniques aiming to accelerate the problem solution are studied. Thus, it is showed a comparison between dynamic and static allocations of vectors and matrices associated to the implementation of shared-memory parallelization using OpenMP directives. The speed up verification is developed simulating the flow around an immersed bluff body. As a consequence of the techniques employed here, an acceleration of approximately five times with respect of the original computational code is obtained. An important difficulty in the external flow evaluation is the numerical solution of convection dominated flows. The Taylor-Galerkin explicit-iterative scheme, (originally used by the program), which was validated for confined flows, did not present good results for external flows simulations and pressure field perturbations were observed. These instabilities were persevered even in an alternative version, where interpolations functions with the same order were used to compute velocity and pressure (in the original version, constant pressure field at element level were employed). To analyze unbounded flows accurately, a two-step explicit scheme using velocity and pressure interpolation functions with the same order was implemented. This configuration presented physical results with good quality and achieve an important reduction in the processing time. After identification of the best alternative without perturbations of the pressure field, the numerical simulation of the flow around a two-dimensional square cylinder was investigated favoring velocity, pressure and total kinetic energy evaluations along the mid line of the domain and in the obstacle vicinity. These evaluations were effectuated with uniform and stretched meshes for a Reynolds number equal to 22000.

O presente trabalho tem como objetivo o desenvolvimento de um sistema voltado à solução de problemas relacionados à Engenharia do Vento Computacional. Para o tratamento das estruturas turbulentas, a Simulação das Grandes Escalas é empregada. Esta metodologia resolve diretamente as estruturas que governam a dinâmica local do escoamento (grandes escalas) e utiliza modelos para resolver as escalas com características mais universais (pequenas escalas). Neste estudo, os efeitos sub-malha são obtidos a partir do modelo clássico de Smagorinsky. Na análise numérica, o método dos elementos finitos é avaliado a partir da utilização de elementos hexaédricos e uma formulação baseada nas equações governantes de escoamentos quase-incompressíveis. Para reduzir o requerimento de memória computacional, esquemas explícitos para solução de sistemas de equações são empregados. O primeiro aspecto a ser abordado para o desenvolvimento do sistema proposto é a redução do tempo de processamento. Partindo do algoritmo desenvolvido por [Petry, 2002], desenvolvese um estudo a cerca de técnicas computacionais de alto desempenho visando acelerar o processamento dos problemas. Assim, apresenta-se um comparativo entre alocações estática e dinâmica de vetores e matrizes, juntamente a implementação do paralelismo de memória compartilhada utilizando diretivas OpenMP. A verificação do aumento da velocidade de processamento é desenvolvida simulando o escoamento em um domínio contendo um corpo imerso aerodinamicamente rombudo. As técnicas utilizadas permitiram a obtenção de um aumento de aproximadamente cinco vezes em relação ao código originalmente avaliado. Uma importante dificuldade na avaliação de escoamentos externos está na solução numérica de problemas advectivo-dominantes. O esquema de Taylor-Galerkin explícito-iterativo, originalmente presente no código e validado para escoamentos internos, mostrou-se inadequado para avaliação do escoamento externo proposto, apresentando perturbações no campo de pressões e não convergindo para a solução correta do problema. Estas instabilidades persistiram em uma versão alternativa desenvolvida, a qual utilizava funções de interpolação de igual ordem para solução da pressão e velocidade. Para uma análise de escoamentos não confinados, é implementado o esquema temporal de dois passos utilizando funções de interpolação para velocidade e pressão de mesma ordem. Esta configuração apresentou resultados físicos de boa qualidade e importante redução no tempo de processamento. Após a identificação da alternativa que permitiu a avaliação dos resultados sem a presença de perturbações, apresenta-se a análise do escoamento sobre um prisma quadrado bidimensional, privilegiando o monitoramento da velocidade, pressão e energia cinética total da turbulência na linha central do domínio e nas proximidades do obstáculo. Esta avaliação é efetuada em malhas com configurações uniformes e irregulares para um número de Reynolds igual a 22000. / Development of a system to solve problems related to Computational Wind Engineering is the main aim of this work. In order to treat turbulent structures, Large Eddy Simulation is employed. This methodology compute directly scales governing local flow dynamics (large eddies) and it use models to solve those with universal character (small eddies). In this study, the sub-grid effects are considered using the standard Smagorinsky model. In the numerical analysis, hexahedral finite elements are used and a formulation based on the governing equations of quasi-compressible flows. To reduce the computational memory request, explicit schemes to solve the equations system are used. In order to reduce CPU time, an algorithm developed by [Petry, 2002] is evaluated and high-performance techniques aiming to accelerate the problem solution are studied. Thus, it is showed a comparison between dynamic and static allocations of vectors and matrices associated to the implementation of shared-memory parallelization using OpenMP directives. The speed up verification is developed simulating the flow around an immersed bluff body. As a consequence of the techniques employed here, an acceleration of approximately five times with respect of the original computational code is obtained. An important difficulty in the external flow evaluation is the numerical solution of convection dominated flows. The Taylor-Galerkin explicit-iterative scheme, (originally used by the program), which was validated for confined flows, did not present good results for external flows simulations and pressure field perturbations were observed. These instabilities were persevered even in an alternative version, where interpolations functions with the same order were used to compute velocity and pressure (in the original version, constant pressure field at element level were employed). To analyze unbounded flows accurately, a two-step explicit scheme using velocity and pressure interpolation functions with the same order was implemented. This configuration presented physical results with good quality and achieve an important reduction in the processing time. After identification of the best alternative without perturbations of the pressure field, the numerical simulation of the flow around a two-dimensional square cylinder was investigated favoring velocity, pressure and total kinetic energy evaluations along the mid line of the domain and in the obstacle vicinity. These evaluations were effectuated with uniform and stretched meshes for a Reynolds number equal to 22000.

This thesis aims to implement dynamic load balancing mechanism into the parallel simulation model of the heat distribution in a CPU cooler. The first part introduces theoretical foundations for dynamic load balancing, describing current solution approaches. The second part refers to the heat distribution model and related topics such as MPI communications library or HDF library for data storage. Then it proceeds to the implementation of simulation model with dynamic 2D decomposition of square model domain. Custom geometry based dynamic load balancing algorithm was introduced, which works with this decomposition. Important part of the implementation is Zoltan library, used especially for data migration. At the end, a set of experiments was presented, which demonstrates load balancing abilities of designed model together with conclusions and motivation for future research.

The 3-satisfiability Problem (3-SAT) is a demanding combinatorial problem that is of central importance among the nondeterministic polynomial (NP) complete problems, with applications in circuit design, artificial intelligence, and logistics. Even with optimized algorithms, the solution space that needs to be explored grows exponentially with the increasing size of 3-SAT instances. Thus, large 3-SAT instances require excessive amounts of energy to solve with serial electronic computers. Network-based biocomputation (NBC) is a parallel computation approach with drastically reduced energy consumption. NBC uses biomolecular motors to propel cytoskeletal filaments through nanofabricated networks that encode mathematical problems. By stochastically exploring possible paths through the networks, the cytoskeletal filaments find possible solutions. However, to date, no NBC algorithm for 3-SAT has been available. Herein, an algorithm that converts 3-SAT into an NBC-compatible network format is reported and four small 3-SAT instances (with up to three variables and five clauses) using the actin–myosin biomolecular motor system are experimentally solved. Because practical polynomial conversions to 3-SAT exist for many important NP complete problems, the result opens the door to enable NBC to solve small instances of a wide range of problems.