In this work, a Column-and-Constraint Generation (CCG) algorithm is proposed to tackle this challenge. More precisely, the master problem finds a candidate for Nash equilibrium and the oracle identifies whether this candidate point is indeed an equilibrium. A set of numerical experiments was ...
A column-and-constraint generation algorithm In this section, we present another cutting plane procedure to solve two-stage RO problems. Because the generated cutting planes are defined by a set of created recourse decision variables in the forms of constraints of the recourse problem, the whole ...
5. Inexact column-and-constraint generation (i-C&CG) method i-C&CG Algorithm 2 summarizes our proposed i-C&CG method, which shares a similar structure with the previously stated C&CG method except for a few additional simple updates in step 1 and the additional backtracking routine in ...
Inthispaper,wepresentacolumn-and-constraintgenerationalgorithmtosolvetwo-stagerobust optimizationproblems.ComparedwithexistingBenders-stylecuttingplanemethods,thecolumn-and- constraintgenerationalgorithmisageneralprocedurewithaunifiedapproachtodealwithoptimality
3. A column-and-constraint generation algorithm In this section, we present another cutting plane procedure to solve two-stage RO problems. Because the generated cutting ? which can compute an optimal solution (y? k+1 , ηk+1 ). Note that ? ? T ? T ? c yk + Q(yk ) provides an...
This paper presents a column-and-constraint generation algorithm for two-stage stochastic programming problems. A distinctive feature of the algorithm is that it does not assume fixed recourse and as a consequence the values and dimensions of the recourse matrix can be uncertain. The proposed ...
We also provide theoretical properties of the general algorithm and an extensive computational study. Our main empirical conclusion is that the algorithm is able to significantly reduce the gap when initial bounds and/or heuristic policies perform poorly....
Based on adjustable RO theories and corresponding validations, the constraint-wise property of some uncertainties is recast and simplified before Column-and-Constraint Generation (CCG) is applied, thus we proposed a Modified CCG (MCCG) algorithm, which is even more efficient in large-scale problems...
An algorithm of the subject invention can include column-and-constraint generation and can be used to solve a set of system interdiction, vulnerability analysis, and reliability based design problems, including a power grid vulnerability analysis problem and an edge-interdiction minimum dominating set ...
An algorithm of the subject invention can include column-and-constraint generation and can be used to solve a set of system interdiction, vulnerability analysis, and reliability based design problems, including a power grid vulnerability analysis problem and an edge-interdiction minimum dominating set ...