Set Of Combinatorial Optimization Problems Research Articles

Solving optimization problems using a hybrid systolic search on GPU plus CPU

In recent years, graphics processing units (GPUs) have emerged as a powerful architecture for solving a broad spectrum of applications in very short periods of time. However, most existing GPU optimization approaches do not exploit the full power available in a CPU–GPU platform. They have a tendency to leave one of them partially unused (usually the CPU) and fail to establish an accurate exchange of information that could help solve the target problem efficiently. Thus, better performance is expected from devising a hybrid CPU–GPU parallel algorithm that combines the highly parallel stream processing power of GPUs with the higher power of multi-core architectures. We have developed a hybrid methodology to efficiently solve optimization problems. We use a hybrid CPU–GPU architecture, to benefit from running it, in parallel, on both the CPU and the GPU. Our experiments over a heterogeneous set of combinatorial optimization problems with increasing dimensionality show a time gain of up to \(365\times \) in our proposal, while demonstrating high numerical accuracy. This work is intended to open up a new line of research that matches both architectures with new algorithms and cooperation techniques.

Diversities and the Geometry of Hypergraphs

Special issu PRIMA 2013 The embedding of finite metrics in 1 has become a fundamental tool for both combinatorial optimization and large-scale data analysis. One important application is to network flow problems as there is close relation between max-flow min-cut theorems and the minimal distortion embeddings of metrics into 1. Here we show that this theory can be generalized to a larger set of combinatorial optimization problems on both graphs and hypergraphs. This theory is not built on metrics and metric embeddings, but on diversities, a type of multi-way metric introduced recently by the authors. We explore diversity embeddings, 1 diversities, and their application to Steiner Tree Packing and Hypergraph Cut problems.

A Discrete-Time Quantized-State Hopfield Neural Network

A discrete-time quantized-state Hopfield neural network is analyzed with special emphasis in its convergence, complexity and scalability properties. This network can be considered as a generalization of the Hopfield neural network by Shrivastava et al. [27] into the interior of the unit hypercube. This extension allows its use in a larger set of combinatorial optimization problems and its properties make of it a good candidate to build hybrid algorithms along with other heuristics such as the evolutive algorithms. Finally, the network is illustrated in some instances of the linear assignment problem and the frequency assignment problem.

A genetic algorithm-based solution methodology for modular design

Combinatorial optimization problems usually have a finite number of feasible solutions. However, the process of solving these types of problems can be a very long and tedious task. Moreover, the cost and time for getting accurate and acceptable results is usually quite large. As the complexity and size of these problems grow, the current methods for solving problems such as the scheduling problem or the classification problem have become obsolete, and the need for an efficient method that will ensure good solutions for these complicated problems has increased. This paper presents a genetic algorithm (GA)-based method used in the solution of a set of combinatorial optimization problems. A definition of a combinatorial optimization problem is first given. The definition is followed by an introduction to genetic algorithms and an explanation of their role in solving combinatorial optimization problems such as the traveling salesman problem. A heuristic GA is then developed and used as a tool for solving various combinatorial optimization problems such as the modular design problem. A modularity case study is used to test and measure the performance of the developed algorithm.