
HEPGAME and the Simplification of Expressions
Advances in high energy physics have created the need to increase comput...
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Exploiting Reduction Rules and Data Structures: Local Search for Minimum Vertex Cover in Massive Graphs
The Minimum Vertex Cover (MinVC) problem is a wellknown NPhard problem...
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Instance Scale, Numerical Properties and Design of Metaheuristics: A Study for the Facility Location Problem
Metaheuristics are known to be strong in solving largescale instances o...
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Characterization of neighborhood behaviours in a multineighborhood local search algorithm
We consider a multineighborhood local search algorithm with a large num...
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A LocalSearch Based Heuristic for the Unrestricted Block Relocation Problem
The unrestricted block relocation problem is an important optimization p...
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Approximating MAP using Local Search
MAP is the problem of finding a most probable instantiation of a set of ...
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A Telescopic Binary Learning Machine for Training Neural Networks
This paper proposes a new algorithm based on multiscale stochastic loca...
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Why Local Search Excels in Expression Simplification
Simplifying expressions is important to make numerical integration of large expressions from High Energy Physics tractable. To this end, Horner's method can be used. Finding suitable Horner schemes is assumed to be hard, due to the lack of local heuristics. Recently, MCTS was reported to be able to find near optimal schemes. However, several parameters had to be finetuned manually. In this work, we investigate the state space properties of Horner schemes and find that the domain is relatively flat and contains only a few local minima. As a result, the Horner space is appropriate to be explored by Stochastic Local Search (SLS), which has only two parameters: the number of iterations (computation time) and the neighborhood structure. We found a suitable neighborhood structure, leaving only the allowed computation time as a parameter. We performed a range of experiments. The results obtained by SLS are similar or better than those obtained by MCTS. Furthermore, we show that SLS obtains the good results at least 10 times faster. Using SLS, we can speed up numerical integration of many realworld large expressions by at least a factor of 24. For High Energy Physics this means that numerical integrations that took weeks can now be done in hours.
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