This subpart is meant to provide a flexible framework for implementing spatial branch-and-bound based optimization routines in Julia. All components of the branch-and-bound routine can be customized by the individual user: lower bounding problem, upper bounding problem. The branch and bound routine consists of a main solve algorithm that executes as depicted in the flowchart below. Routines for setting the objects to implement standard B&B routines are also provided using a set_default!() function.

• The preprocessing routine has inputs (feas,X,UBD,k,d,opt) and outputs feas::Bool,X::Vector{Interval{Float64}}. The initial feasibility flag is feas, the bounds on the variables are X, the current upper bound is UBD, the iteration number is k, the node depth is d, and a solver option storage object is opt.

• The lower bounding routine has inputs (X,k,d,opt,UBDg) and provides outputs (val,soln,feas,Lsto). The value of the subproblem is val, the solution of the subproblem is soln, it's feasibility is feas, and Lsto is a problem information storage object.

• The upper bounding routine has inputs (X,k,d,opt,UBDg) and provides outputs (val,soln,feas,Usto). he value of the subproblem is val, the solution of the subproblem is soln, it's feasibility is feas, and Uto is a problem information storage object.

• The postprocessing routine has inputs (feas,X,k,d,opt,Lsto,Usto,LBDg,UBDg) and outputs feas::Bool,X::Vector{Interval{Float64}}.

• The repeat check has inputs (s,m,X0,X) where s::BnBSolver is a solver object, m::BnBModel is a model object, X0::Vector{Interval{Float64}} are node bounds after preprocessing, and X::Vector{Interval{Float64}} are the node bounds generated after postprocessing. Returns a boolean.

• The bisection function has inputs (s,m,X) where s::BnBSolver is a solver object, m::BnBModel is a model object, and X::Vector{Interval{Float64}} is the box to bisect. It returns two boxes.

• The termination check has inputs (s,m,k) where s::BnBSolver is a solver object, m::BnBModel is a model object, and k::Int64 is the iteration number. Returns a boolean.

• The convergence check has inputs (s,UBDg,LBD) where s::BnBSolver is a solver object, UBDg is the global upper bound, and LBD is the lower bound.