Mathematical models of linear and booleanlinearprogramming for the balanced two-stage transportation problem and its two modifications are analyzed. The first modification takes into account the upper limits on the ...
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Mathematical models of linear and booleanlinearprogramming for the balanced two-stage transportation problem and its two modifications are analyzed. The first modification takes into account the upper limits on the capacity of intermediate points, and the second modification allows choosing a fixed number of intermediate points, less than their total number. For all the cases, the necessary and sufficient conditions for the consistency of the systems of linear constraints of the corresponding mathematical programmingproblems are justified. Examples of applying the modifications for the optimal set partitioning, the p-median graph problem, and the problem of optimal arrangement of a given number of storages are considered. The results of the computing experiments using the Gurobi and CPLEX solvers and the AMPL modeling language are presented.
The quadratic optimization problem for finding the maximum k-plex in an undirected graph is constructed. Two families of superfluous quadratic constraints obtained by means of constraints of the booleanlinear program...
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The quadratic optimization problem for finding the maximum k-plex in an undirected graph is constructed. Two families of superfluous quadratic constraints obtained by means of constraints of the boolean linear programming problem for the maximum k-plex are presented. The influence of superfluous constraints on the improvement of the accuracy of Lagrangian dual bounds for the objective function of the quadratic problem is investigated. The algorithm for searching all the maximum k-plexes is developed and the results of test experiments for its implementation using the GLPK (GNU linearprogramming Kit) software package are presented.
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