Many-core Algorithms for Combinatorial Optimization

Combinatorial Optimization is becoming ever more crucial, in these days. From natural sciences to economics, passing through urban centers administration and personnel management, methodologies and algorithms with a strong theoretical background and a consolidated real-word effectiveness is more and more requested, in order to find, quickly, good solutions to complex strategical problems. Resource optimization is, nowadays, a fundamental ground for building the basements of successful projects. From the theoretical point of view, Combinatorial Optimization rests on stable and strong foundations, that allow researchers to face ever more challenging problems. However, from the application point of view, it seems that the rate of theoretical developments cannot cope with that enjoyed by modern hardware technologies, especially with reference to the one of processors industry. In this work we propose new parallel algorithms, designed for exploiting the new parallel architectures available on the market. We found that, exposing the inherent parallelism of some resolution techniques (like Dynamic Programming), the computational benefits are remarkable, lowering the execution times by more than an order of magnitude, and allowing to address instances with dimensions not possible before. We approached four Combinatorial Optimization’s notable problems: Packing Problem, Vehicle Routing Problem, Single Source Shortest Path Problem and a Network Design problem. For each of these problems we propose a collection of effective parallel solution algorithms, either for solving the full problem (Guillotine Cuts and SSSPP) or for enhancing a fundamental part of the solution method (VRP and ND). We endorse our claim by presenting computational results for all problems, either on standard benchmarks from the literature or, when possible, on data from real-world applications, where speed-ups of one order of magnitude are usually attained, not uncommonly scaling up to 40 X factors.