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problems is discussed. Various propcrties of this algorithm will be discussed in the next
section.
The first step determines that the whole problem is feasible or not by detecting the
infeasibility of subproblems, as proven in the next section. If any subproblem is infeasible,
then the algorithm stops because the original problem is determined to be infeasible. and if
each subproblem has its own feasible solutions, then the algorithm proceeds to the next steps
because the original pmblem is feasible.
in Steps 1 and 2. the scalar E>O is defined by the user. and the aigorithm solves each
subproblem. exchanges the information between each pair of subproblems in the hierarchical
manner and tries to reach the prescribed tolerance between the upper bound and the lower
bound. :," and c"' represent the objective values of SP~" and SP"' respectively, at first level
iteration k and second level iteration i. :14 and represent the objective values of S P and ~ ~
spJ4, respectively, at fint level iteration k and second level iteration j. Up-Opt and Low-Opt
are set to 1 if Pu and Pr reach optimaiity; othenvise 0. respectively.
DO IN PARALLEC
frocessor 1
Step O. Set level I counter k= 1. level II counter i=l, DO. and determine whether P is
infeasible.
- solve spi.' : if it is infeasible. send a stop signai to al1 other subproblems and stop, P
is infeasible;
- if a stop signai frorn any other subproblem is received stop, P is infeasible;