Sheng-Jie Chen | Searcharxiv

arXiv2025

A Dynamic Relaxation Framework for Global Solution of ACOPF

Solving the Alternating Current Optimal Power Flow (AC OPF) problem to global optimality remains challenging due to its nonconvex quadratic constraints. In this paper, we present a unified framework that combines static piecewise relaxations with dynamic cut-generation mechanism to systematically tighten the classic Second-Order Cone Programming (SOCP) relaxation to arbitrarily small conic violation, thus enabling the recovery of globally optimal solutions. Two static formulations, Pyramidal Relaxation (PR) and Quasi-Pyramidal Relaxation (QPR), are introduced to tighten each branch-flow second-order cone via a finite union of wedges, providing controllable accuracy. Their dynamic counterparts, Dynamic PR (DPR) and Dynamic QPR (DQPR), embed on-the-fly cut generation within a branch-and-cut solver to improve scalability. Convergence is further accelerated through warm starts and a lightweight local-search post-processing. Extensive experiments on benchmarks demonstrate effective elimination of conic violations and flexible trade-offs between solution accuracy and runtime. Practical guidelines are derived for selecting appropriate variants based on network size and accuracy requirements.

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arXiv2023

Efficient presolving methods for the influence maximization problem

We consider the influence maximization problem (IMP) which asks for identifying a limited number of key individuals to spread influence in a network such that the expected number of influenced individuals is maximized. The stochastic maximal covering location problem (SMCLP) formulation is a mixed integer programming formulation that effectively approximates the IMP by the Monte-Carlo sampling. For IMPs with a large-scale network or a large number of samplings, however, the SMCLP formulation cannot be efficiently solved by existing exact algorithms due to its large problem size. In this paper, we attempt to develop presolving methods to reduce the problem size and hence enhance the capability of employing exact algorithms in solving large-scale IMPs. In particular, we propose two effective presolving methods, called strongly connected nodes aggregation (SCNA) and isomorphic nodes aggregation (INA), respectively. The SCNA enables to build a new SMCLP formulation that is potentially much more compact than the existing one, and the INA further eliminates variables and constraints in the SMCLP formulation. A theoretical analysis on two special cases of the IMP is provided to demonstrate the strength of the SCNA and INA in reducing the problem size of the SMCLP formulation. We integrate the proposed presolving methods, SCNA and INA, into the Benders decomposition algorithm, which is recognized as one of the state-of-the-art exact algorithms for solving the IMP. We show that the proposed SCNA and INA provide the possibility to develop a much faster separation algorithm for the Benders cuts. Numerical results demonstrate that with the SCNA and INA, the Benders decomposition algorithm is much more effective in solving the IMP in terms of solution time.

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