Related papers: Solving Sudoku using oscillatory neural networks
This paper presents a systematic method to solve difficult 9 x 9 Sudoku puzzles by hand. While computer algorithms exist to solve these puzzles, these algorithms are not good for human's to use because they involve too many steps and…
In this paper we present a new Ant Colony Optimisation-based algorithm for Sudoku, which out-performs existing methods on large instances. Our method includes a novel anti-stagnation operator, which we call Best Value Evaporation.
Constrained optimization problems appear in a wide variety of challenging real-world problems, where constraints often capture the physics of the underlying system. Classic methods for solving these problems rely on iterative algorithms…
Existing automated urban traffic management systems, designed to mitigate traffic congestion and reduce emissions in real time, face significant challenges in effectively adapting to rapidly evolving conditions. Predominantly reactive,…
We propose new mathematical optimization models for generating sparse dynamical graphs, or networks, that can achieve synchronization. The synchronization phenomenon is studied using the Kuramoto model, defined in terms of the adjacency…
Recent advances in graph neural network architectures and increased computation power have revolutionized the field of combinatorial optimization (CO). Among the proposed models for CO problems, Neural Improvement (NI) models have been…
We investigate a link between Graph Neural Networks (GNNs) and Quadratic Unconstrained Binary Optimization (QUBO) problems, laying the groundwork for GNNs to approximate solutions for these computationally challenging tasks. By analyzing…
Neural models and symbolic algorithms have recently been combined for tasks requiring both perception and reasoning. Neural models ground perceptual input into a conceptual vocabulary, on which a classical reasoning algorithm is applied to…
An efficient direct solver for volume integral equations with O(N) complexity for a broad range of problems is presented. The solver relies on hierarchical compression of the discretized integral operator, and exploits that off-diagonal…
Optimization has been widely used to generate smooth trajectories for motion planning. However, existing trajectory optimization methods show weakness when dealing with large-scale long trajectories. Recent advances in parallel computing…
Su-Doku, a popular combinatorial puzzle, provides an excellent testbench for heuristic explorations. Several interesting questions arise from its deceptively simple set of rules. How many distinct Su-Doku grids are there? How to find a…
The Hopfield network has been applied to solve optimization problems over decades. However, it still has many limitations in accomplishing this task. Most of them are inherited from the optimization algorithms it implements. The computation…
OPF problems are formulated and solved for power system operations, especially for determining generation dispatch points in real-time. For large and complex power system networks with large numbers of variables and constraints, finding the…
Parametric optimal control problems governed by partial differential equations (PDEs) are widely found in scientific and engineering applications. Traditional grid-based numerical methods for such problems generally require repeated…
Associative memory systems enable content-addressable storage and retrieval of patterns, a capability central to biological neural computation and artificial intelligence. Classical implementations such as Hopfield networks face fundamental…
The NP-hard problem of optimizing a shallow ReLU network can be characterized as a combinatorial search over each training example's activation pattern followed by a constrained convex problem given a fixed set of activation patterns. We…
Pattern-Based Constraint Satisfaction and Logic Puzzles develops a pure logic, pattern-based perspective of solving the finite Constraint Satisfaction Problem (CSP), with emphasis on finding the "simplest" solution. Different ways of…
In recent years, graph neural networks (GNNs) have become increasingly popular for solving NP-hard combinatorial optimization (CO) problems, such as maximum cut and maximum independent set. The core idea behind these methods is to represent…
How can we predict the difficulty of a Sudoku puzzle? We give an overview of difficulty rating metrics and evaluate them on extensive dataset on human problem solving (more then 1700 Sudoku puzzles, hundreds of solvers). The best results…
Operational Neural Networks (ONNs) have recently been proposed to address the well-known limitations and drawbacks of conventional Convolutional Neural Networks (CNNs) such as network homogeneity with the sole linear neuron model. ONNs are…