X-Architecture Steiner Minimal Tree Construction Based on Discrete Differential Evolution

Abstract

As the best connection model for the multi-pin net of the non-Manhattan architecture global routing problem, the X-architecture Steiner Minimum Tree (XSMT) construction is a Non-deterministic Polynomial hard (NP-hard) problem. The Differential Evolution (DE) algorithm has shown good application effect in solving various NP-hard problems. For this reason, based on the idea of DE algorithm, this paper proposes an XSMT construction algorithm for solving this problem. First of all, because the traditional DE algorithm is designed for continuous problems, the optimization ability is limited in solving discrete problems. This paper proposes a novel crossover operator and mutation operator. At the same time, in order to maintain the effectiveness of the evolutionary algorithm, an Edge-to-Point coding strategy suitable for evolutionary algorithms is proposed to better preserve the optimal substructure of the population. Finally, in order to speed up the convergence speed and quality of the algorithm, this paper proposes an initial solution based on the minimum tree generation algorithm. Experiments show that the effectiveness of the proposed algorithm and related strategies can construct a high-quality XSMT solution.