Generalized Benders Decomposition for one Class of MINLPs with Vector Conic Constraint

一种基于序列的Benders混合整数二次规划算法及其在CAMINO工具箱中的实现

A Sequential Benders-based Mixed-Integer Quadratic Programming Algorithm and Its Implementation in the CAMINO Toolbox

本文提出一种序列混合整数二次规划算法，用于求解混合整数非线性规划问题，结合Benders分解方法，通过迭代过程优化解，并在CAMINO工具箱中实现，适用于非凸问题的启发式求解。

Stochastic and Chance-Constrained Conic Distribution System Expansion Planning Using Bilinear Benders Decomposition

Second order conic programming (SOCP) has been used to model various applications in power systems, such as operation and expansion planning. In this paper, we present a two-stage stochastic mixed integer SOCP (MISOCP) model for the distribution system expansion planning problem that considers uncertainty and also captures the nonlinear AC power flow. To avoid costly investment plans due to some extreme scenarios, we further present a chance-constrained variant that could lead to cost-effective solutions. To address the computational challenge, we extend the basic Benders decomposition method …

Extended Formulations in Mixed-integer Convex Programming

We present a unifying framework for generating extended formulations for the polyhedral outer approximations used in algorithms for mixed-integer convex programming (MICP). Extended formulations lead to fewer iterations of outer approximation algorithms and generally faster solution times. First, we observe that all MICP instances from the MINLPLIB2 benchmark library are conic representable with standard symmetric and nonsymmetric cones. Conic reformulations are shown to be effective extended formulations themselves because they encode separability structure. For mixed-integer conic-representa…

通过角Benders割逼近值函数

Approximating value functions via corner Benders' cuts

本研究提出一种从高维多面体基导出的锥松弛生成Benders割的高效算法，可恢复Dantzig-Wolfe规划的线性规划界，并提升了随机需求车辆路径问题现有最优算法的性能。

A joint decomposition method for global optimization of multiscenario nonconvex mixed-integer nonlinear programs

This paper proposes a joint decomposition method that combines La- grangian decomposition and generalized Benders decomposition, to efficiently solve multiscenario nonconvex mixed-integer nonlinear programming (MINLP) problems to global optimality, without the need for explicit branch and bound search. In this approach, we view the variables coupling the scenario dependent variables and those causing nonconvexity as complicating variables. We systemat- ically solve the Lagrangian decomposition subproblems and the generalized Ben- ders decomposition subproblems in a unified framework. The metho…

现成MINLP求解器在拥塞容量设施选址问题基准集上的计算研究

A computational study of off-the-shelf MINLP solvers on a benchmark set of congested capacitated facility location problems

本文比较了Gurobi、Cplex、Mosek、Xpress和Scip五种现成优化求解器在混合整数锥规划形式的拥塞容量设施选址问题上的计算效率与策略，发现Mosek和Gurobi最具竞争力，Mosek在大规模问题上表现更优。