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The Alternating Direction Method of Multipliers (ADMM) has gained a lot of attention for solving large-scale and objective-separable constrained optimization. However, the two-block variable structure of the ADMM still limits the practical…
The automatic generation of computer programs is one of the main applications with practical relevance in the field of evolutionary computation. With program synthesis techniques not only software developers could be supported in their…
We present an approach to constructing a practical coarsening algorithm and interpolation operator for the algebraic multigrid (AMG) method, tailored towards systems of partial differential equations (PDEs) with large near-kernels, such as…
Mathematical programming is widely employed across various sectors - such as logistics, energy, and workforce planning - to model and solve industrial optimisation problems, but its use requires substantial domain expertise. Large language…
The GEneral Matrix Multiplication (GEMM) is one of the essential algorithms in scientific computing. Single-thread GEMM implementations are well-optimised with techniques like blocking and autotuning. However, due to the complexity of…
Algebraic multigrid (AMG) solvers and preconditioners are some of the fastest numerical methods to solve linear systems, particularly in a parallel environment, scaling to hundreds of thousands of cores. Most AMG methods and theory assume a…
In optimizing real-world structures, due to fabrication or budgetary restraints, the design variables may be restricted to a set of standard engineering choices. Such variables, commonly called categorical variables, are discrete and…
We have developed a symbolic algebra approach to automatically produce, verify, and optimize computer code for the Fast Multipole Method (FMM) operators. This approach allows for flexibility in choosing a basis set and kernel, and can…
Mixed-integer linear programming (MILP) is widely employed for modeling combinatorial optimization problems. In practice, similar MILP instances with only coefficient variations are routinely solved, and machine learning (ML) algorithms are…
Genetic algorithms are modeled after the biological evolutionary processes that use natural selection to select the best species to survive. They are heuristics based and low cost to compute. Genetic algorithms use selection, crossover, and…
Adaptive gradient methods are typically used for training over-parameterized models. To better understand their behaviour, we study a simplistic setting -- smooth, convex losses with models over-parameterized enough to interpolate the data.…
The potential benefit of migrating software design from Structured to Object Oriented Paradigm is manifolded including modularity, manageability and extendability. This design migration should be automated as it will reduce the time…
Mixed-integer programming (MIP) technology offers a generic way of formulating and solving combinatorial optimization problems. While generally reliable, state-of-the-art MIP solvers base many crucial decisions on hand-crafted heuristics,…
What kind of programming language would be most appropriate to serve the needs of integrative, multi-paradigm, multi-software-system approaches to AGI? This question is broached via exploring the more particular question of how to create a…
We study the solution of block-structured linear algebra systems arising in optimization by using iterative solution techniques. These systems are the core computational bottleneck of many problems of interest such as parameter estimation,…
In this manuscript, we present a collective multigrid algorithm to solve efficiently the large saddle-point systems of equations that typically arise in PDE-constrained optimization under uncertainty, and develop a novel convergence…
In recent years the field of genetic programming has made significant advances towards automatic programming. Research and development of contemporary program synthesis methods, such as PushGP and Grammar Guided Genetic Programming, can…
Due to the wide range of timescales that are present in macromolecular systems, hierarchical multiscale strategies are necessary for their computational study. Coarse-graining (CG) allows to establish a link between different system…
Adam-type optimizers, as a class of adaptive moment estimation methods with the exponential moving average scheme, have been successfully used in many applications of deep learning. Such methods are appealing due to the capability on…
As a common method in Machine Learning, Ensemble Method is used to train multiple models from a data set and obtain better results through certain combination strategies. Stacking method, as representatives of Ensemble Learning methods, is…