Affiliations: Information Technology Center, Tsinghua University, Beijing, China | E-mail: liangss@tsinghua.edu.cn
Correspondence:
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Corresponding author: Information Technology Center, Tsinghua University, Beijing, China. E-mail: liangss@tsinghua.edu.cn.
Abstract: Intelligent systems generally face optimization problems when solving specific problems, and complex optimization problems are usually non-deterministic polynomial complete (NPC) problems. To solve such problems, approximation methods are generally adopted. This paper presents an accurate method for finding an optimal solution to probability 1 in polynomial time. It combines intelligent optimization algorithms such as ordinal optimization, simulated annealing, genetic algorithm (differential evolution algorithm), tabu search, ant colony algorithm, particle swarm optimization, space neighborhood sampling, time neighborhood sampling, number neighborhood sampling (knowledge neighborhood sampling). Then it draws on the matrix ideas of Riemann Hypothesis, prime distribution formula, random number generator, maximum entropy heuristics (proposed by this paper), and combines a new group ordinal optimization algorithm framework proposed by this paper to Traveling Salesman Problem (TSP, a NPC problem) as an example and constructs a polynomial algorithm. The theoretical time complexity is O(N^4) (considering parallel computing), and is verified based on some examples.
Keywords: Riemann hypothesis, fractal number theory, random number generator, maximum entropy heuristics, NPC polynomial algorithm
