procedure try (iinteger)begin if then if inclusion is acceptable then include -th objecttry( + )eliminate -th object endif exclusion is acceptable then try( + end else check optimality end end try from this pattern it is evident that there are possible setsclearlyappropriate acceptability criteria must be employed to reduce the number of investigated candidates very drastically in order to elucidate this processlet us choose concrete example for selection problemlet each of the objects an- be characterized by its weight and its value let the optimal set be the one with the largest sum of the values of its componentsand let the constraint be limit on the sum of their weight this is problem well known to all travellers who pack suitcases by selecting from items in such way that their total value is optimal and that their total weight does not exceed specific allowance we are now in position to decide upon the representation of the given facts in terms of global variables the choices are easily derived from the foregoing developmentstype object record weightvalueinteger endvar aarray of objectlimwtotvmaxvintegersoptsset the variables limw and totv denote the weight limit and the total value of all objects these two values are actually constant during the entire selection process represents the current selection of objects in which each object is represented by its name (indexopts is the optimal selection so far encounteredand maxv is its value which are now the criteria for acceptability of an object for the current selectionif we consider inclusionthen an object is selectableif it fits into the weight allowance if it does not fitwe may stop trying to add further objects to the current selection ifhoweverwe consider exclusionthen the criterion for acceptabilityi for the continuation of building up the current selectionis that the total value which is still achievable after this exclusion is not less than the value of the optimum so far encountered forif it is lesscontinuation of the searchalthough it may produce some solutionwill not yield the optimal solution hence any further search on the current path is fruitless from these two conditions we determine the relevant quantities to be computed for each step in the selection process the total weight tw of the selection so far made the still achievable value av of the current selection these two entities are appropriately represented as parameters of the procedure try the condition inclusion is acceptable can now be formulated as tw [iweight limw and the subsequent check for optimality as