arXiv subjects

Yukai Zheng

Publications and source records attributed to Yukai Zheng.

2 recordsLinked to original sources

arXiv2025

A Spectral Projected Gradient Method for Computational Protein Design problem

In this paper, we consider the computational protein design (CPD) problem, which is usually modeled as 0/1 programming and is extremely challenging due to its combinatorial properties. As a quadratic semi-assignment problem (QSAP), the CPD problem has been proved to be equivalent to its continuous relaxation problem (RQSAP), in terms of sharing the same optimal objective value. However, since the current algorithm for solving this RQSAP uses the projected Newton method, which requires direct computation of the Hessian matrix, its computational cost remains quite high. Precisely for this reason, we choose to employ the spectral projected gradient (SPG) method to solve the CPD problem, whose effectiveness relies on choosing the step lengths according to novel ideas that are related to the spectrum of the underlying local Hessian. Specifically, we apply the SPG method in two distinct ways: direct solving the relaxation problem and applying a penalty method. Numerical results on benchmark instances verify the superior performance of our approach over the current algorithms in both quality and efficiency.

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arXiv2024

An Efficient Algorithm for Computational Protein Design Problem

In this paper, we consider the computational protein design (CPD) problem, which is usually modeled as a 0/1 programming and is extremely challenging due to its combinatorial properties. We propose an efficient algorithm for solving it. Specifically, we study the quadratic semi-assignment problem formulation (QSAP) of the CPD problem, and show that it is equivalent to its continuous relaxation problem (RQSAP), in terms of sharing the same optimal objective value. Then, we propose an efficient penalty method to solve the QSAP based on the proposed formulations, which is guaranteed to converge to a global solution of the QSAP under certain conditions. Compared with existing branch-and-bound approaches that suffer from high computational complexity, the proposed algorithm is based on a continuous problem and enjoys a low per-iteration complexity, which makes it particularly suitable for solving large-scale CPD problems. Numerical results on benchmark instances verify the superior performance of our approach over the state-of-the-art branch-and-cut solvers. In particular, the proposed algorithm outperforms the state-of-the-art solvers by three order of magnitude in CPU time in most cases, while it still returns high-quality solutions.

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