What Is Optimization Toolbox?

intprog• If the algorithm finds a new feasible integer point with lowerobjective value than that of the best integer point, it updates thecurrent best integer point and moves to the next node.• If the LP-relaxation problem is optimal but not integer and theoptimal objective value of the LP relaxation problem is less than thebest integer point, the algorithm branches according to the methodyou specify in the BranchStrategy option.See “Options” on page 8-4 for a description of the NodeSearchStrategyand BranchStrategy options.BoundsThe solution to the LP-relaxation problem provides a lower boundfor the binary integer programming problem. If the solution to theLP-relaxation problem is already a binary integer vector, it provides anupper bound for the binary integer programming problem.As the search tree grows more nodes, the algorithm updates the lowerand upper bounds on the objective function, using the bounds obtainedin the bounding step. The bound on the objective value serves as thethreshold to cut off unnecessary branches.Limits for the AlgorithmThe algorithm for bintprog could potentially search all 2 n binaryinteger vectors, where n is the number of variables. As a completesearch might take a very long time, you can limit the search using thefollowing options• MaxNodes — Maximum number of nodes the algorithm searches• MaxRLPIter — Maximum number of iterations the LP-solverperforms at any node• MaxTime — Maximum amount of time in seconds the algorithm runsSee “Options” on page 8-4 for more information.8-8