Set Of Optimal Points Research Articles

Improved multi-objective differential evolution algorithm and its application in the capacity configuration of urban rail photovoltaic hybrid energy storage systems

With the rapid expansion of urban rail transit, energy demand is continuously increasing. Integrating photovoltaic (PV) systems into hybrid energy storage systems (HESS) to form a rail transit PV hybrid energy storage system (RTPHESS) is an effective energy-saving and emission reduction measure. However, the integration changes the energy composition of the rail power supply system, making traditional HESS capacity configuration schemes inadequate to meet the stability requirement. In light of this, an RTPHESS model was established aiming at suppressing traction network voltage fluctuations and minimizing the total life-cycle cost of HESS. The model introduces traction network voltage fluctuation rate and HESS total life-cycle cost as evaluation objectives. Based on this, an improved multi-objective differential evolution algorithm (IMODE) was proposed to optimize HESS capacity. Optimal point set theory was used for population initialization to enhance the uniformity and diversity of the initial population, thereby improving global optimization capabilities. During the mutation phase, a hybrid Gaussian-Cauchy mutation strategy was introduced to improve both global and local search capabilities. The proposed algorithm's effectiveness was evaluated using IGD, SP, MS, and ER metrics on eight benchmark test functions with different characteristics, and compared with SaMODE_LS, MODE, MOPSO, MOALO, and MOMGA. Finally, IMODE was applied to the capacity configuration of RTPHESS. The results demonstrate that IMODE outperforms traditional algorithms in terms of accuracy and stability, reducing traction network voltage fluctuations by approximately 4.1 % and lowering the total life-cycle cost to 3,201,100 yuan.

Multi-objective optimization of daylight illuminance indicators and energy usage intensity for office space in Tehran by genetic algorithm

One of the important categories in office spaces is the control of daylight and energy consumption. By controlling natural light, it is possible to provide uniform light in the entire space, sufficient daylight, and visual comfort for office workers. In many cases, this important issue can be resolved by choosing the right shading. In this study, the aim is to investigate the significance of some important parameters such as DoS (Depth of Shading), FO (Facade Offset), FSoS (Flip Start of Shading), LoS (Location of Shading), WWR (Window to Wall Ratio), CoS (Count of Shading), AoS (Angle of Shading), and HoW (Height of Window) in the optimal design of shading for an office environment in Tehran. For this purpose, eight variables have been designed and the aim is to improve the indicators of Energy Usage Intensity (EUI), Spatial Daylight Autonomy(sDA), Daylight Glare Probability (DGP), and Tc (Thermal comfort) in the office space. For optimization in the grasshopper environment, Wallacei’s algorithm was used. Then, the algorithm provides a set of optimal points. Then a point was selected as optimal by the WSM (Weighted Sum Method) method. According to the input variables that are DoS, FO, FSoS, LoS, WWR, CoS, AoS, and HoW its optimal point values are 0.4, 0, Up, Horizontal, 80, 5, 30, 0.5, respectively. The results show that the values of sDA, DGP, EUI, and Tc were improved by 43.6%, 52.77%, 13.9, and 3.696%, respectively, before and after shading optimization. Also, the annual glare and the hottest and coldest day of the year were checked where there were around 500(cd/m2) and 200(cd/m2) reduction of glare value in winter and summer seasons, respectively. Finally, the value of Useful Daylight Illuminance (UDI)before and after the installation of the optimal shading was 25.8 and 68.4, respectively.

The Optimal Transportation Option in an Underground Hard Coal Mine: A Multi-Criteria Cost Analysis

The issue of transport in underground hard coal mines is very rarely described in the literature. The financial aspects of this issue are even less often analyzed. Publications in this area focus on technical issues and the safety of mining crews. More attention is paid to transport in open-pit mines. The above premises and practical needs imply the need to conduct economic analyses of transport systems in underground hard coal mines. This paper is a scientific communication, which presents the concept of a multi-criteria cost analysis as a tool to support the selection of the optimal transportation option in an underground hard coal mine. Considerations in this area have not been carried out in the relevant literature, and the problem of selecting a transportation option is a complex and necessary issue in the practice of underground mines with extensive mine workings. The methodology presented includes five cost criteria (costs of carrying out the transportation task; route expansion costs; rolling stock maintenance costs; depreciation costs; and additional personnel costs). The simultaneous application of criteria relating to utility properties in addition to cost criteria makes it possible to adopt a specific technical and organizational model of the transportation system based on the indication of the optimal solution, resulting from the mathematical construction of functions of objectives relating to utility and cost. The optimal variant of the designed system and configuration of the material transportation system in underground workings takes into consideration the following: (1) seven utility criteria (KU1—transportation task completion time; KU2—compatibility of transportation systems; KU3—continuous connectivity; KU4—co-use with other transportation tasks; KU5—safety; KU6—inconvenience; KU7—operation under overplanning conditions) and (2) five cost criteria (KK1—costs of implementing the transportation task; KK2—costs of route expansion; KK3—rolling stock maintenance costs; KK4—depreciation costs; KK5—additional personnel costs). Based on the aforementioned criteria, two objective functions are built for each option: utility and cost. They present divergent goals; therefore, they are non-cooperative functions. Both utility and costs strive for the maximum. In the developed methodology, an ideal point is usually a fictitious solution representing a set of maximum values among all the achievable values in a set of solutions, but it is impossible to achieve this simultaneously based on all the criteria. This point illustrates the maximum utility and lowest cost among the alternatives considered, which is obviously impossible for any of the variants to meet at the same time, although it indicates the possibilities of the technique and the range of costs. For the developed method, a so-called “PND” nadir point is also determined, representing the least-preferred level of achievement of all goals simultaneously, determined from the set of optimal points in the Pareto sense. The originality of the conceptual considerations undertaken stems from: filling the gap in the economic methodology of complex transportation systems evaluation; embedding considerations in the trend concerning complex transportation systems of underground mines; and focusing considerations on the pre-investment phase, making it possible to optimize costs before expenditures are incurred.

Selective Imputation for Multivariate Time Series Datasets With Missing Values

Multivariate time series often contain missing values for reasons such as failures in data collection mechanisms. Since these missing values can complicate the analysis of time series data, imputation techniques are typically used to deal with this issue. However, the quality of the imputation directly affects the performance of downstream tasks. In this paper, we propose a selective imputation method that identifies a subset of timesteps with missing values to impute in a multivariate time series dataset. This selection, which will result in shorter and simpler time series, is based on both reducing the uncertainty of the imputations and representing the original time series as good as possible. In particular, the method uses multi-objective optimization techniques to select the optimal set of points, and in this selection process, we leverage the beneficial properties of the Multi-task Gaussian Process (MGP). The method is applied to different datasets to analyze the quality of the imputations and the performance obtained in downstream tasks, such as classification or anomaly detection. The results show that much shorter and simpler time series are able to maintain or even improve both the quality of the imputations and the performance of the downstream tasks.

Distinct Angle Problems and Variants

The Erdős distinct distance problem is a ubiquitous problem in discrete geometry. Less well known is Erdős’s distinct angle problem, the problem of finding the minimum number of distinct angles between n non-collinear points in the plane. The standard problem is already well understood. However, it admits many of the same variants as the distinct distance problem, many of which are unstudied. We provide upper and lower bounds on a broad class of distinct angle problems. We show that the number of distinct angles formed by n points in general position is $$O(n^{\log _{2}7})$$ providing the first non-trivial bound for this quantity. We introduce a new class of asymptotically optimal point configurations with no four cocircular points. Then, we analyze the sensitivity of asymptotically optimal point sets to perturbation, yielding a much broader class of asymptotically optimal configurations. In higher dimensions we show that a variant of Lenz’s construction admits fewer distinct angles than the optimal configurations in two dimensions. We also show that the minimum size of a maximal subset of n points in general position admitting only unique angles is $$\Omega (n^{1/5})$$ and $$O(n^{(\log _2{7)/3}})$$ . We also provide bounds on the partite variants of the standard distinct angle problem.

Data-driven optimal sensor placement for high-dimensional system using annealing machine

We propose a novel method for solving optimal sensor placement problem for high-dimensional system using an annealing machine. The sensor points are calculated as a maximum clique problem of the graph, the edge weight of which is determined by the proper orthogonal decomposition mode obtained from data based on the fact that a high-dimensional system usually has a low-dimensional representation. Since the maximum clique problem is equivalent to the independent set problem of the complement graph, the independent set problem is solved using Fujitsu Digital Annealer. In contrast to existing greedy methods, which select the optimal point at each step and never reconsider the point selected previously, the proposed method is superior because it is able to find the optimal set of points. As a demonstration of high dimensional system, the pressure distribution measured by the pressure-sensitive paint method, which is an optical flow diagnose method, is reconstructed from the pressure data at the calculated sensor points. The root mean square errors (RMSEs) between the pressures measured by pressure transducers and the pressures reconstructed from the proposed method, an existing greedy method, and random selection method are compared. The similar RMSE is achieved by the proposed method using approximately 1/5 number of sensor points calculated by the existing method. This method is of great importance as a novel approach for optimal sensor placement problem and a new engineering application of an annealing machine.

Winograd Convolution for Deep Neural Networks: Efficient Point Selection

Convolutional neural networks (CNNs) have dramatically improved the accuracy of image, video, and audio processing for tasks such as object recognition, image segmentation, and interactive speech systems. CNNs require large amounts of computing resources for both training and inference, primarily because the convolution layers are computationally intensive. Fast convolution algorithms such as Winograd convolution can greatly reduce the computational cost of these layers. However, Winograd convolution has poor numeric properties, such that greater savings in computation cause exponentially increasing floating point errors. A defining feature of each Winograd convolution algorithm is a set of real-value points where polynomials are sampled. The choice of points impacts the numeric accuracy of the algorithm, but the optimal set of points for small convolutions remains unknown. Existing work considers only small integers and simple fractions as candidate points. In this work, we propose a novel approach to point selection using points of the form \(\lbrace -\frac{1}{c},-c,c,\frac{1}{c}\rbrace\) using the full range of real-valued numbers for c . We show that groups of this form cause cancellations in the Winograd transform matrices that reduce numeric error. We find empirically that the error for different values of c forms a rough curve across the range of real-value numbers. It is therefore possible to localize the values of c that lead to lower error. We show that it is not necessary to choose integers or simple fractions as evaluation points, and that lower errors can be achieved with non-obvious real-valued points. We study a range of sizes for small convolutions and achieve reduction in error ranging from 2% to around 59% for both 1D and 2D convolution, when compared to state of the art. Furthermore, we identify patterns in cases when we select a subset of our proposed points that will always lead to a lower error. Finally, we implement a complete Winograd convolution layer and use it to run state-of-the-art deep convolution neural networks on real datasets and show that our proposed points achieve reduction in error, ranging from 22% to 63%, while also showing how an increased Winograd output size can result in execution speed-up for some cases.

Thermodynamic-economic optimization of a solar-powered combined energy system with desalination for electricity and freshwater production

This study starts by modeling and analyzing a smart combined energy system that includes a concentrated solar power plant, steam Rankine, Brayton, organic Rankine cycles, reverse osmosis unit, and a thermoelectric generator. The system is then subjected to bi-criteria optimization, using non-dominated sorting genetic algorithm II (NSGA-II) and minimizing annual costs and maximizing exergy efficiency. The system is located in Isfahan (central Iran) and intended to produce electricity and freshwater. The thermodynamic results indicated the most critical parameters affecting system performance: direct normal irradiance, number of heliostats, turbine efficiency and inlet temperature, compressor pressure ratio, and steam Rankine cycle pump inlet temperature. A Pareto frontier was charted, producing a set of optimal points, where a decrease in costs was achieved if the exergy efficiency was slightly compromised, leading to the identification of an optimal location within the Pareto frontier.

Globally Optimal Point Set Registration by Joint Symmetry Plane Fitting

The present work proposes a solution to the challenging problem of registering two partial point sets of the same object with very limited overlap. We leverage the fact that most objects found in man-made environments contain a plane of symmetry. By reflecting the points of each set with respect to the plane of symmetry, we can largely increase the overlap between the sets and therefore boost the registration process. However, prior knowledge about the plane of symmetry is generally unavailable or at least very hard to find, especially with limited partial views. Finding this plane could strongly benefit from a prior alignment of the partial point sets. We solve this chicken-and-egg problem by jointly optimizing the relative pose and symmetry plane parameters. We present a globally optimal solver by employing the branch-and-bound paradigm and thereby demonstrate that joint symmetry plane fitting leads to a great improvement over the current state of the art in globally optimal point set registration for common objects. We conclude with an interesting application of our method to dense 3D reconstruction of scenes with repetitive objects.

Lower bounds for the error of quadrature formulas for Hilbert spaces

We prove lower bounds for the worst case error of quadrature formulas that use given sample points Xn={x1,…,xn}. We are mainly interested in optimal point sets Xn, but also prove lower bounds that hold with high probability for sets of independently and uniformly distributed points. As a tool, we use a recent result (and extensions thereof) of Vybíral on the positive semi-definiteness of certain matrices related to the product theorem of Schur. The new technique also works for spaces of analytic functions where known methods based on decomposable kernels cannot be applied.

Energy, exergy, and exergoeconomics (3E) analysis and multi-objective optimization of a multi-generation energy system for day and night time power generation - Case study: Dezful city

The present study aimed to investigate a multi-generation energy system for the production of hydrogen, freshwater, electricity, cooling, heating, and hot water. Steam Rankine cycle (SRC), organic Rankine cycle (ORC), absorption chiller, Parabolic trough collectors (PTCs), geothermal well, proton exchange membrane (PEM) electrolyzer, and reverse osmosis (RO) desalination are the main subsystems of the cycle. The amount of exergy destruction is calculated for each component after modeling and thermodynamic analysis. The PTCs, absorption chiller, and PEM electrolyzer had the highest exergy destruction, respectively. According to meteorological data, the system was annually and hourly tested for Dezful City. For instance, it had a production capacity of 13.25 kg/day of hydrogen and 147.42 m3/day of freshwater on 17th September. Five design parameters are considered for multi-objective optimization after investigating objective functions, including cost rate and exergy efficiency. Using a Group method of data handling (GMDH), a mathematical relation is obtained between the input and output of the system. Next, a multi-objective optimization algorithm, a non-dominated sorting genetic algorithm (NSGA-II), was used to optimize the relations. A Pareto frontier with a set of optimal points is obtained after the optimization. In the Pareto frontier, the best point is selected by the decision criterion of TOPSIS. At the TOPSIS point, the exergy efficiency is 31.66%, and the total unit cost rate is 21.9 $/GJ.

Multi-objective particle swarm optimization of thermal conductivity and dynamic viscosity of magnetic nanodiamond-cobalt oxide dispersed in ethylene glycolusing RSM

Optimization of Ethylene glycol- Nano Diamond- Cobalt oxide (EG-ND/Co3O4) nanofluids (NF) was investigated using the multi-objective particle swarm optimization (MOPSO) technique based on the experimental data. Increased thermal conductivity (TC) and reduced dynamic viscosity were considered as the optimum conditions. Also, a mathematical model was presented based on the response surface methodology (RSM) to predict the thermophysical properties of mentioned NF in the term of volume fraction (VF) of nanoparticles (NPs) at different temperatures. The results showed a adjusted regression coefficient greater than 0.99, indicating high precision modeling by response surface methodology (RSM). Furthermore, the mathematical model was integrated with MOPSO and evaluated in different steps of optimizing evaluation. Finally, a set of optimal points, known as a Pareto front and their corresponding design variables were presented. According to the optimization results, the maximum temperature gives the highest TC and lowest viscosity.

Non-Smooth Projected Primal-Dual Dynamical Approach to Solve the Extended Fermat-Torricelli Problem

The problem of finding a point in R <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</sup> , from which the sum-of-distances to a finite number of nonempty, closed and convex sets is minimum is called generalized Fermat-Torricelli Problem (FTP). In applications, along with the point that minimizes sum-of-distances, it is important to know the points in the convex sets at which the minimum sum-of-distances is achieved. Various formulations existing in literature do not involve finding the optimal points in the convex sets. In this letter, we formulate a non-smooth convex optimization problem, with both the point/set of points which yields the minimum sum-of-distances as well as the corresponding points in the convex sets as primal variables. We term this problem as extended FTP (eFTP). We adopt non-smooth projected primal-dual dynamical approach to solve this problem. The proposed dynamical system can exhibit a continuum of equilibria. Hence we show semistability of the set of optimal points, which is the pertinent notion of stability for such systems. A distributed implementation of the primal-dual dynamical system is also presented in this letter. Four illustrative examples are considered for the simulation based validation of the solution proposed for eFTP.

A completely positive formulation of the graph isomorphism problem and its positive semidefinite relaxation

Aurora and Mehta (J Comb Optim 36(3):965–1006, 2018) show that two graphs $$G_1,G_2$$ , on n vertices each, are isomorphic if and only if the feasible region of a certain linear program, LP-GI, intersects with the Quadratic Assignment Problem (QAP)-polytope in $${\mathbb {R}}^{(n^4+n^2)/2}$$ . The linear program LP-GI in Aurora and Mehta (J Comb Optim 36(3):965–1006, 2018) is obtained by relaxing an integer linear program whose feasible points correspond to the isomorphisms between $$G_1,G_2$$ . In this paper we take an analogous approach with the linear programs replaced with conic programs. A completely positive description of the QAP-polytope was obtained in Povh and Rendl (Discrete Optim 6(3):231–241, 2009). By adding the graph conditions to this description we get a completely positive formulation of the graph isomorphism problem. However, analogous to integer linear programs, it is NP-hard to optimize over the cone of completely positive matrices. So we relax this formulation by replacing the cone of completely positive matrices with the cone of positive semidefinite matrices. We observe that the resulting SDP is the Lovasz Theta function (Lovasz in IEEE Trans Inf Theory 25(1):1–7, 1979) of a graph product of $$G_1,G_2$$ and can be efficiently computed. We provide a natural heuristic that uses the SDP to solve the graph isomorphism problem. We run our heuristic on several pairs of non-isomorphic strongly regular graphs and find the results to be encouraging. Further, by adding the non-negativity constraints to the SDP, we obtain a doubly non-negative formulation, DNN-GI. We show that if the set of optimal points in DNN-GI contains a point of rank at most 3, then the given pair of graphs must be isomorphic.

Characterizing optimal point sets determining one distinct triangle

In this paper we determine the maximum number of points in $\mathbb{R}^d$ which form exactly $t$ distinct triangles, where we restrict ourselves to the case of $t = 1$. We denote this quantity by $F_d(t)$. It was known from the work of Epstein et al. 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. This is an extension of a variant of the distinct distance problem put forward by Erd\H{o}s and Fishburn.

Generation of energy-minimizing point sets on spheres and their application in mesh-free interpolation and differentiation

It is known that discrete sets of uniformly distributed points on the hypersphere $\mathbb {S}^{d}\subset \mathbb {R}^{d+1}$ can be obtained from minimizing the energy functional corresponding to Riesz s-kernels $k_s(\boldsymbol {x},\boldsymbol {y})=\lVert \boldsymbol {x}-\boldsymbol {y}\rVert ^{-s}$ (s > 0) or the logarithmic kernel $k_{\log }(\boldsymbol {x},\boldsymbol {y})=-\log \lVert \boldsymbol {x}-\boldsymbol {y}\rVert +\log 2$. We prove the same for the kernel $k_{\log }(\boldsymbol {x},\boldsymbol {y})=\lVert \boldsymbol {x}-\boldsymbol {y}\rVert (\log {\frac {\lVert \boldsymbol {x}-\boldsymbol {y}\rVert }{2}}-1)+2$ which is a front-extension of the sequence of derivatives $k_{\log }, k_{1}, k_{2}, k_{3}, \dots $, up to sign and constants. The boundedness of the kernel simplifies the classical potential-theoretical proof of the asymptotic uniformity of the point distributions. Still, the property of a singular derivative for x → y is preserved, with the physical interpretation of infinite repulsive forces for touching particles. The quality of the resulting point distributions is exemplary compared with that of Riesz- and classical logarithmic point sets, and found to be competitive. Originally motivated by problems of high-dimensional data, the applicability of $\log $-optimal point sets with a novel concentric interpolation and differentiation scheme is demonstrated. The method is significantly optimized by the introduction of symmetrized kernels for both the generation of the minimum energy points and the spherical basis functions. Both the point generation and the Concentric Interpolation software are available as Open Source software and selected point sets are provided.

Multi-Objective Genetic Algorithm Assisted by an Artificial Neural Network Metamodel for Shape Optimization of a Centrifugal Blood Pump.

A centrifugal blood pump is a common type of the pump used as a left ventricular assist device (LVAD) in the medical industries. The reduction of the LVADs hemolysis level to reduce the blood damage is one of the major concerns in designing of such devices. Also, the enhancement of the LVADs efficiency to decrease the battery size is another design requirement. The blood damage critically depends on the state of the blood being pumped. Besides the blood state, the blood damage also depends on the pump impeller and volute geometries. In this research, a multi-objective optimization of a centrifugal blood pump is performed. A complete 3D-optimization platform is established for both impeller and volute of a centrifugal blood pump consisting of parametric modeling, automatic mesh generation, computational fluid dynamics (CFD) simulation, and optimization strategy. A vast number of cases with various impeller and volute shapes are numerically simulated. Three different metamodels are created using artificial neural networks (ANNs) in order to approximate the pump hydraulic efficiency, hemolysis index (HI), and pressure head. The inverse of the relative pressure head is defined as the first objective and the summation of relative hemolysis index and the inverse of the relative efficiency is assumed as the second objective. Non-dominated Sorting Genetic Algorithm-II (NSGA-II) is used to find the Pareto Front. A set of optimal points is selected. Finally, for the physiological flow conditions, the optimum design that provides 11.9% HI reduction and 7.2% efficiency enhancement is selected.

Locomotion Efficiency Optimization of Biologically Inspired Snake Robots

Snake robots constitute bio-inspired solutions that have been studied due to their ability to move in challenging environments where other types of robots, such as wheeled or legged robots, usually fail. In this paper, we consider both land-based and swimming snake robots. One of the principal concerns of the bio-inspired snake robots is to increase the motion efficiency in terms of the forward speed by improving the locomotion methods. Furthermore, energy efficiency becomes a crucial challenge for this type of robots due to the importance of long-term autonomy of these systems. In this paper, we take into account both the minimization of the power consumption and the maximization of the achieved forward velocity in order to investigate the optimal gait parameters for bio-inspired snake robots using lateral undulation and eel-like motion patterns. We furthermore consider possible negative work effects in the calculation of average power consumption of underwater snake robots. To solve the multi-objective optimization problem, we propose transforming the two objective functions into a single one using a weighted-sum method. For different set of weight factors, Particle Swarm Optimization is applied and a set of optimal points is consequently obtained. Pareto fronts or trade-off curves are illustrated for both land-based and swimming snake robots with different numbers of links. Pareto fronts represent trade-offs between the objective functions. For example, how increasing the forward velocity results in increasing power consumption. Therefore, these curves are a very useful tool for the control and design of snake robots. The trade-off curve thus constitutes a very useful tool for both the control and design of bio-inspired snake robots. In particular, the operators or designers of bio-inspired snake robots can choose a Pareto optimal point based on the trade-off curve, given the preferred number of links on the robot. The optimal gait parameters for the robot control system design are then directly given both for land-based and underwater snake robots. Moreover, we are able to obtain some observations about the optimal values of the gait parameters, which provide very important insights for future control design of bio-inspired snake robots.

Random search algorithm for optimal mixture experimental design

ABSTRACTIt is well known that it is difficult to obtain an accurate optimal design for a mixture experimental design with complex constraints. In this article, we construct a random search algorithm which can be used to find the optimal design for mixture model with complex constraints. First, we generate an initial set by the Monte-Carlo method, and then run the random search algorithm to get the optimal set of points. After that, we explain the effectiveness of this method by using two examples.

3D/2D Registration with superabundant vessel reconstruction for cardiac resynchronization therapy.

A key component of image guided interventions is the registration of preoperative and intraoperative images. Classical registration approaches rely on cross-modality information; however, in modalities such as MRI and X-ray there may not be sufficient cross-modality information. This paper proposes a fundamentally different registration approach which uses adjacent anatomical structures with superabundant vessel reconstruction and dynamic outlier rejection. In the targeted clinical scenario of cardiac resynchronization therapy (CRT) delivery, preoperative, non contrast-enhanced, MRI is registered to intraoperative, contrasted X-ray fluoroscopy. The adjacent anatomical structures are the left ventricle (LV) from MRI and the coronary veins reconstructed from two contrast-enhanced X-ray images. The novel concept of superabundant vessel reconstruction is introduced to bypass the standard reconstruction problem of establishing one-to-one correspondences. Furthermore, a new dynamic outlier rejection method is proposed, to enable globally optimal point set registration. The proposed approach has been qualitatively and quantitatively evaluated on phantom, clinical CT angiography with ground truth and clinical CRT data. A novel evaluation method is proposed for clinical CRT data based on previously implanted artificial aortic and mitral valves. The registration accuracy in 3D was 2.94 mm for the aortic and 3.86 mm for the mitral valve. The results are below the required accuracy identified by clinical partners to be the half-segment size (16.35 mm) of a standard American Heart Association (AHA) 16 segment model of the LV.