Engineering Optimization: Theory and Practice, Fourth Edition

614 Integer Programming

Figure 10.6 Graphical solution of problem (E 5 ).

Next, the branching problems, with integer bounds onx 3 , are solved and the pro-

cedure is continued until the desired optimum solution is found. The results are shown

in Fig. 10.8.

10.7 Sequential Linear Discrete Programming

Let the nonlinear programming problem with discrete variables be stated as follows:

Minimizef (X) (10.52)

subject to

gj( X)≤ 0 , j= 1 , 2 ,... , m (10.53)

hk( X)= 0 , k= 1 , 2 ,... , p (10.54)

xi∈ {di 1 , di 2 ,... , diq} , i= 1 , 2 ,... , n 0 (10.55)

xi(l)≤xi≤xi(u), i=n 0 + 1 , n 0 + 2 ,... , n (10.56)