 
Summary: Opgaven Wiskundig Modelleren 3 Studiejaar 2002/2003
Hoofdstuk 8: Local Search and MultiCriteria Optimization
Inleveren tot 1822002, 13.45 uur
Plaats: vak DWMP/Dini, postrek naast de receptie van het INF gebouw
1. Local Search
Consider the following machine scheduling problem: Given are n jobs 1, . . . , n with pro
cessing times p 1 , . . . , p n which have to be processed by a single machine. The machine
can process only one job at a time and the jobs will be processed by the machine one after
the other without interruption. Thus, the completion time C i of a job i in a schedule
will be equal to the sum of processing times of the job scheduled before job i plus the
processing time of job i. The goal is to find a processing sequence of the jobs (called
schedule) such that the sum of the completion times of all jobs is minimized.
Since a solution of this problem is a sequence, the set of all feasible solutions is given by
all sequences of n elements (see set S 1 in Example 1 (a)).
(a) Consider the neighborhood N 1 given in Example 1 (a). Calculate the di#erence
between the objective values of the solutions # and # # = api(i)(#) in dependence of
the solution #.
(b) Show that iterative improvement using neighborhood N 1 leads to a globally optimal
solution independently on the used initial solution.
(c) Assume that the set of feasible solutions is restricted to the set S 2 of all sequences
