Dynastic Potential Crossover Operator

An optimal recombination operator for two parent solutions provides the best solution among those that take the value for each variable from one of the parents (gene transmission property). If the solutions are bit strings, the offspring of an optimal recombination operator is optimal in the smallest hyperplane containing the two parent solutions. Exploring this hyperplane is computationally costly, in general, requiring exponential time in the worst case. However, when the variable interaction graph of the objective function is sparse, exploration can be done in polynomial time. In this paper, we present a recombination operator, called Dynastic Potential Crossover (DPX), that runs in polynomial time and behaves like an optimal recombination operator for low-epistasis combinatorial problems. We compare this operator, both theoretically and experimentally, with traditional crossover operators, like uniform crossover and network crossover, and with two recently defined efficient recombination operators: partition crossover and articulation points partition crossover. The empirical comparison uses NKQ Landscapes and MAX-SAT instances. DPX outperforms the other crossover operators in terms of quality of the offspring and provides better results included in a trajectory and a population-based metaheuristic, but it requires more time and memory to compute the offspring.This research is partially funded by the Universidad de M\'alaga, Consejería de Economía y Conocimiento de la Junta de Andalucía and FEDER under grant number UMA18-FEDERJA-003 (PRECOG); under grant PID 2020-116727RB-I00 (HUmove) funded by MCIN/AEI/10.13039/501100011033; and TAILOR ICT-48 Network (No 952215) funded by EU Horizon 2020 research and innovation programme. The work is also partially supported in Brazil by São Paulo Research Foundation (FAPESP), under grants 2021/09720-2 and 2019/07665-4, and National Council for Scientific and Technological Development (CNPq), under grant 305755/2018-8

Analysis of combinatorial search spaces for a class of NP-hard problems, An

2011 Spring.Includes bibliographical references.Given a finite but very large set of states X and a real-valued objective function ƒ defined on X, combinatorial optimization refers to the problem of finding elements of X that maximize (or minimize) ƒ. Many combinatorial search algorithms employ some perturbation operator to hill-climb in the search space. Such perturbative local search algorithms are state of the art for many classes of NP-hard combinatorial optimization problems such as maximum k-satisfiability, scheduling, and problems of graph theory. In this thesis we analyze combinatorial search spaces by expanding the objective function into a (sparse) series of basis functions. While most analyses of the distribution of function values in the search space must rely on empirical sampling, the basis function expansion allows us to directly study the distribution of function values across regions of states for combinatorial problems without the need for sampling. We concentrate on objective functions that can be expressed as bounded pseudo-Boolean functions which are NP-hard to solve in general. We use the basis expansion to construct a polynomial-time algorithm for exactly computing constant-degree moments of the objective function ƒ over arbitrarily large regions of the search space. On functions with restricted codomains, these moments are related to the true distribution by a system of linear equations. Given low moments supplied by our algorithm, we construct bounds of the true distribution of ƒ over regions of the space using a linear programming approach. A straightforward relaxation allows us to efficiently approximate the distribution and hence quickly estimate the count of states in a given region that have certain values under the objective function. The analysis is also useful for characterizing properties of specific combinatorial problems. For instance, by connecting search space analysis to the theory of inapproximability, we prove that the bound specified by Grover's maximum principle for the Max-Ek-Lin-2 problem is sharp. Moreover, we use the framework to prove certain configurations are forbidden in regions of the Max-3-Sat search space, supplying the first theoretical confirmation of empirical results by others. Finally, we show that theoretical results can be used to drive the design of algorithms in a principled manner by using the search space analysis developed in this thesis in algorithmic applications. First, information obtained from our moment retrieving algorithm can be used to direct a hill-climbing search across plateaus in the Max-k-Sat search space. Second, the analysis can be used to control the mutation rate on a (1+1) evolutionary algorithm on bounded pseudo-Boolean functions so that the offspring of each search point is maximized in expectation. For these applications, knowledge of the search space structure supplied by the analysis translates to significant gains in the performance of search

Using Constraint Satisfaction Techniques and Variational Methods for Probabilistic Reasoning

RÉSUMÉ Cette thèse présente un certain nombre de contributions à la recherche pour la création de systèmes efficaces de raisonnement probabiliste sur les modèles graphiques de problèmes issus d'une variété d'applications scientifiques et d'ingénierie. Ce thème touche plusieurs sous-disciplines de l'intelligence artificielle. Généralement, la plupart de ces problèmes ont des modèles graphiques expressifs qui se traduisent par de grands réseaux impliquant déterminisme et des cycles, ce qui représente souvent un goulot d'étranglement pour tout système d'inférence probabiliste et affaiblit son exactitude ainsi que son évolutivité. Conceptuellement, notre recherche confirme les hypothèses suivantes. D'abord, les techniques de satisfaction de contraintes et méthodes variationnelles peuvent être exploitées pour obtenir des algorithmes précis et évolutifs pour l'inférence probabiliste en présence de cycles et de déterminisme. Deuxièmement, certaines parties intrinsèques de la structure du modèle graphique peuvent se révéler bénéfiques pour l'inférence probabiliste sur les grands modèles graphiques, au lieu de poser un défi important pour elle. Troisièmement, le re-paramétrage du modèle graphique permet d'ajouter à sa structure des caractéristiques puissantes qu'on peut utiliser pour améliorer l'inférence probabiliste. La première contribution majeure de cette thèse est la formulation d'une nouvelle approche de passage de messages (message-passing) pour inférer dans un graphe de facteurs étendu qui combine des techniques de satisfaction de contraintes et des méthodes variationnelles. Contrairement au message-passing standard, il formule sa structure sous forme d'étapes de maximisation de l'espérance variationnelle. Ainsi, on a de nouvelles règles de mise à jour des marginaux qui augmentent une borne inférieure à chaque mise à jour de manière à éviter le dépassement d'un point fixe. De plus, lors de l'étape d'espérance, nous mettons à profit les structures locales dans le graphe de facteurs en utilisant la cohérence d'arc généralisée pour effectuer une approximation de champ moyen variationnel. La deuxième contribution majeure est la formulation d'une stratégie en deux étapes qui utilise le déterminisme présent dans la structure du modèle graphique pour améliorer l'évolutivité du problème d'inférence probabiliste. Dans cette stratégie, nous prenons en compte le fait que si le modèle sous-jacent implique des contraintes inviolables en plus des préférences, alors c'est potentiellement un gaspillage d'allouer de la mémoire pour toutes les contraintes à l'avance lors de l'exécution de l'inférence. Pour éviter cela, nous commençons par la relaxation des préférences et effectuons l'inférence uniquement avec les contraintes inviolables. Cela permet d'éviter les calculs inutiles impliquant les préférences et de réduire la taille effective du réseau graphique. Enfin, nous développons une nouvelle famille d'algorithmes d'inférence par le passage de messages dans un graphe de facteurs étendus, paramétrées par un facteur de lissage (smoothing parameter). Cette famille permet d'identifier les épines dorsales (backbones) d'une grappe qui contient des solutions potentiellement optimales. Ces épines dorsales ne sont pas seulement des parties des solutions optimales, mais elles peuvent également être exploitées pour intensifier l'inférence MAP en les fixant de manière itérative afin de réduire les parties complexes jusqu'à ce que le réseau se réduise à un seul qui peut être résolu avec précision en utilisant une méthode MAP d'inférence classique. Nous décrivons ensuite des variantes paresseuses de cette famille d'algorithmes. Expérimentalement, une évaluation empirique approfondie utilisant des applications du monde réel démontre la précision, la convergence et l'évolutivité de l'ensemble de nos algorithmes et stratégies par rapport aux algorithmes d'inférence existants de l'état de l'art.----------ABSTRACT This thesis presents a number of research contributions pertaining to the theme of creating efficient probabilistic reasoning systems based on graphical models of real-world problems from relational domains. These models arise in a variety of scientific and engineering applications. Thus, the theme impacts several sub-disciplines of Artificial Intelligence. Commonly, most of these problems have expressive graphical models that translate into large probabilistic networks involving determinism and cycles. Such graphical models frequently represent a bottleneck for any probabilistic inference system and weaken its accuracy and scalability. Conceptually, our research here hypothesizes and confirms that: First, constraint satisfaction techniques and variational methods can be exploited to yield accurate and scalable algorithms for probabilistic inference in the presence of cycles and determinism. Second, some intrinsic parts of the structure of the graphical model can turn out to be beneficial to probabilistic inference on large networks, instead of posing a significant challenge to it. Third, the proper re-parameterization of the graphical model can provide its structure with characteristics that we can use to improve probabilistic inference. The first major contribution of this thesis is the formulation of a novel message-passing approach to inference in an extended factor graph that combines constraint satisfaction techniques with variational methods. In contrast to standard message-passing, it formulates the Message-Passing structure as steps of variational expectation maximization. Thus it has new marginal update rules that increase a lower bound at each marginal update in a way that avoids overshooting a fixed point. Moreover, in its expectation step, we leverage the local structures in the factor graph by using generalized arc consistency to perform a variational mean-field approximation. The second major contribution is the formulation of a novel two-stage strategy that uses the determinism present in the graphical model's structure to improve the scalability of probabilistic inference. In this strategy, we take into account the fact that if the underlying model involves mandatory constraints as well as preferences then it is potentially wasteful to allocate memory for all constraints in advance when performing inference. To avoid this, we start by relaxing preferences and performing inference with hard constraints only. This helps avoid irrelevant computations involving preferences, and reduces the effective size of the graphical network. Finally, we develop a novel family of message-passing algorithms for inference in an extended factor graph, parameterized by a smoothing parameter. This family allows one to find the ”backbones” of a cluster that involves potentially optimal solutions. The cluster's backbones are not only portions of the optimal solutions, but they also can be exploited for scaling MAP inference by iteratively fixing them to reduce the complex parts until the network is simplified into one that can be solved accurately using any conventional MAP inference method. We then describe lazy variants of this family of algorithms. One limiting case of our approach corresponds to lazy survey propagation, which in itself is novel method which can yield state of the art performance. We provide a thorough empirical evaluation using real-world applications. Our experiments demonstrate improvements to the accuracy, convergence and scalability of all our proposed algorithms and strategies over existing state-of-the-art inference algorithms

Karyotype diversification in colorectal cancer

From the moment of conception, every human being is in the process of developing cancer. Whether or not you will ultimately be diagnosed with this disease is simply a matter of whether something else kills you first. Cancer is not one disease. Rather, the radical growth of malignant cells represents a phenotypical extreme of cells that escape homeostasis. There are astronomically many potential combinations of genetic, epigenetic and environmental influences that can push cells into malignancy. Therefore, not only is every type of cancer different, but every instance of cancer is its own unique disease. The standardized treatments given to patients with similar types of malignancy are simplified abstractions, born from our lack of understanding of optimal treatment. The development of personalized cancer treatment options is one of the defining goals of modern medicine. Fundamental research plays an important role in progressing toward this goal, since without a true understanding of cancer biology we cannot hope to develop truly personalized treatment protocols. This thesis describes technological advances aimed at investigating fundamental cancer biology using patient derived organoids as a model system. Patient derived organoid culture protocols allow in vitro culture of three-dimensional (3D) wild-type and malignant tissue structures. By allowing differentiated outgrowth in 3D space, organoid culture protocols more accurately recapitulate tissue composition, density and cell division dynamics of human tumors in vivo. When combined with fluorescent live cell imaging, patient derived tumor organoids provide spectacular tools to support fundamental cancer research.One of the protocols we developed is called 3D Live-Seq, which combines imaging of tumor organoid outgrowth and single-cell sequencing of each imaged cell to reconstruct evolving tumor karyotypes (the number of chromosomes or sub chromosomal fragments per cell) across consecutive cell generations. By using 3D Live-Seq, we showed that advanced colorectal cancer cells continuously generate both singular and very complex chromosome errors during outgrowth of a tumor. Collectively, these cells represent a body of genetic diversity from which treatment resistant or more aggressive subclones may emerge during disease progression. <br/

Metareasoning about propagators for constraint satisfaction

Given the breadth of constraint satisfaction problems (CSPs) and the wide variety of CSP solvers, it is often very difficult to determine a priori which solving method is best suited to a problem. This work explores the use of machine learning to predict which solving method will be most effective for a given problem. We use four different problem sets to determine the CSP attributes that can be used to determine which solving method should be applied. After choosing an appropriate set of attributes, we determine how well j48 decision trees can predict which solving method to apply. Furthermore, we take a cost sensitive approach such that problem instances where there is a great difference in runtime between algorithms are emphasized. We also attempt to use information gained on one class of problems to inform decisions about a second class of problems. Finally, we show that the additional costs of deciding which method to apply are outweighed by the time savings compared to applying the same solving method to all problem instances

Proceedings of the 22nd Conference on Formal Methods in Computer-Aided Design – FMCAD 2022

The Conference on Formal Methods in Computer-Aided Design (FMCAD) is an annual conference on the theory and applications of formal methods in hardware and system verification. FMCAD provides a leading forum to researchers in academia and industry for presenting and discussing groundbreaking methods, technologies, theoretical results, and tools for reasoning formally about computing systems. FMCAD covers formal aspects of computer-aided system design including verification, specification, synthesis, and testing

Self-Evaluation Applied Mathematics 2003-2008 University of Twente

This report contains the self-study for the research assessment of the Department of Applied Mathematics (AM) of the Faculty of Electrical Engineering, Mathematics and Computer Science (EEMCS) at the University of Twente (UT). The report provides the information for the Research Assessment Committee for Applied Mathematics, dealing with mathematical sciences at the three universities of technology in the Netherlands. It describes the state of affairs pertaining to the period 1 January 2003 to 31 December 2008

Neural Radiance Fields: Past, Present, and Future

The various aspects like modeling and interpreting 3D environments and surroundings have enticed humans to progress their research in 3D Computer Vision, Computer Graphics, and Machine Learning. An attempt made by Mildenhall et al in their paper about NeRFs (Neural Radiance Fields) led to a boom in Computer Graphics, Robotics, Computer Vision, and the possible scope of High-Resolution Low Storage Augmented Reality and Virtual Reality-based 3D models have gained traction from res with more than 1000 preprints related to NeRFs published. This paper serves as a bridge for people starting to study these fields by building on the basics of Mathematics, Geometry, Computer Vision, and Computer Graphics to the difficulties encountered in Implicit Representations at the intersection of all these disciplines. This survey provides the history of rendering, Implicit Learning, and NeRFs, the progression of research on NeRFs, and the potential applications and implications of NeRFs in today's world. In doing so, this survey categorizes all the NeRF-related research in terms of the datasets used, objective functions, applications solved, and evaluation criteria for these applications.Comment: 413 pages, 9 figures, 277 citation