The construction example of algebra system is to verify the existence of a complex algebra system, and it is a NP-hard problem. In\nthis paper, to solve this kind of problems, firstly, a mathematical optimization model for construction example of algebra system\nis established. Secondly, an improved harmony search algorithm based on NGHS algorithm (INGHS) is proposed to find as more\nsolutions as possible for the optimization model; in the proposed INGHS algorithm, to achieve the balance between exploration\npower and exploitation power in the search process, a global best strategy and parameters dynamic adjustment method are present.\nFinally, nine construction examples of algebra system are used to evaluate the optimization model and performance of INGHS. The\nexperimental results show that the proposed algorithm has strong performance for solving complex construction example problems\nof algebra system.
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