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This work proposes a discretization of the acoustic wave equation with possibly oscillatory coefficients based on a superposition of discrete solutions to spatially localized subproblems computed with an implicit time discretization. Based…
Optimization problems involving mixed variables (i.e., variables of numerical and categorical nature) can be challenging to solve, especially in the presence of mixed-variable constraints. Moreover, when the objective function is the result…
The discretization of constrained nonlinear optimization problems arising in the field of topology optimization yields algebraic systems which are challenging to solve in practice, due to pathological ill-conditioning, strong nonlinearity…
We introduce a novel approach to reduce the computational effort of solving mixed-integer convex chance constrained programs through the scenario approach. Instead of reducing the number of required scenarios, we directly minimize the…
Issues of inequity in U.S. high schools' course scheduling did not previously exist. However, in recent years, with the increase in student population and course variety, students perceive that the course scheduling method is unfair.…
In this paper, we investigate a neural network-based learning approach towards solving an integer-constrained programming problem using very limited training. To be specific, we introduce a symmetric and decomposed neural network structure,…
Adaptive learning systems can produce substantial learning gains, yet many students engage for too brief or too superficial a period to benefit. A central obstacle is measuring effort. Effort during multi-step problem solving is rarely…
This paper proposes a thought experiment to search for efficient bounded algorithms of NPC problems by machine enumeration. The key contributions are: -- On Universal Turing Machines, a program's time complexity should be characterized as:…
The constraint satisfaction problem (CSP) is a central generic problem in computer science and artificial intelligence: it provides a common framework for many theoretical problems as well as for many real-life applications. Soft constraint…
Multi-objectivization is a term used to describe strategies developed for optimizing single-objective problems by multi-objective algorithms. This paper focuses on multi-objectivizing the sum-of-the-parts combinatorial optimization…
This paper presents a hybrid CPU-GPU framework for solving combinatorial scheduling problems formulated as Integer Linear Programming (ILP). While scheduling underpins many optimization tasks in computing systems, solving these problems…
We consider a version of geometric programming problem consisting in minimizing a function given by the maximum of finitely many log-Laplace transforms of discrete nonnegative measures on a Euclidean space. Under a coerciveness assumption,…
We formulate and study a fundamental search and detection problem, Schedule Optimization, motivated by a variety of real-world applications, ranging from monitoring content changes on the web, social networks, and user activities to…
In this thesis I explore challenging discrete energy minimization problems that arise mainly in the context of computer vision tasks. This work motivates the use of such "hard-to-optimize" non-submodular functionals, and proposes methods…
Dynamic multi-objective optimization with a changing number of objectives has recently attracted increasing attention due to its relevance to real-world problems whose evaluation criteria may evolve over time. However, existing benchmark…
We present an efficient task and motion replanning approach for sequential multi-object manipulation in dynamic environments. Conventional Task And Motion Planning (TAMP) solvers experience an exponential increase in planning time as the…
To solve hard problems, AI relies on a variety of disciplines such as logic, probabilistic reasoning, machine learning and mathematical programming. Although it is widely accepted that solving real-world problems requires an integration…
Numerical optimization (solving optimization problems using digital computers) currently dominates but has three major drawbacks: high energy consumption, poor scalability, and lack of an execution time certificate. To address these…
Research efforts of the past fifty years have led to a development of linear integer programming as a mature discipline of mathematical optimization. Such a level of maturity has not been reached when one considers nonlinear systems subject…
Sequential testing problems involve a complex system with several components, each of which is "working" with some independent probability. The outcome of each component can be determined by performing a test, which incurs some cost. The…